The fundamental constants of nature from lattice gauge theory simulations
Mackenzie, Paul B.; /Fermilab
2005-01-01
The fundamental laws of nature as we now know them are governed the fundamental parameters of the Standard Model. Some of these, such as the masses of the quarks, have been hidden from direct observation by the confinement of quarks. They are now being revealed through large scale numerical simulation of lattice gauge theory.
Lattice gauge theory simulations in the quantum information era
NASA Astrophysics Data System (ADS)
Dalmonte, M.; Montangero, S.
2016-07-01
The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behaviour of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from analysing the symmetric properties of Hamiltonian and states: the most striking examples are gauge theories such as quantum electrodynamics, where a local symmetry strongly constrains the microscopic dynamics. The physics of such gauge theories is relevant for the understanding of a diverse set of systems, including frustrated quantum magnets and the collective dynamics of elementary particles within the standard model. In the last few years, several approaches have been put forward to tackle the complex dynamics of gauge theories using quantum information concepts. In particular, quantum simulation platforms have been put forward for the realisation of synthetic gauge theories, and novel classical simulation algorithms based on quantum information concepts have been formulated. In this review, we present an introduction to these approaches, illustrating the basics concepts and highlighting the connections between apparently very different fields, and report the recent developments in this new thriving field of research.
Digital Quantum Simulation of Z2 Lattice Gauge Theories with Dynamical Fermionic Matter
NASA Astrophysics Data System (ADS)
Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio
2017-02-01
We propose a scheme for digital quantum simulation of lattice gauge theories with dynamical fermions. Using a layered optical lattice with ancilla atoms that can move and interact with the other atoms (simulating the physical degrees of freedom), we obtain a stroboscopic dynamics which yields the four-body plaquette interactions, arising in models with (2 +1 ) and higher dimensions, without the use of perturbation theory. As an example we show how to simulate a Z2 model in (2 +1 ) dimensions.
String Theory and Gauge Theories
Maldacena, Juan
2009-02-20
We will see how gauge theories, in the limit that the number of colors is large, give string theories. We will discuss some examples of particular gauge theories where the corresponding string theory is known precisely, starting with the case of the maximally supersymmetric theory in four dimensions which corresponds to ten dimensional string theory. We will discuss recent developments in this area.
Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices.
Zohar, Erez; Cirac, J Ignacio; Reznik, Benni
2016-01-01
Can high-energy physics be simulated by low-energy, non-relativistic, many-body systems such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure an atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective low-energy symmetry, or as an exact symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to a new type of (table-top) experiments which will be used to study various QCD (quantum chromodynamics) phenomena, such as the confinement of dynamical quarks, phase transitions and other effects, which are inaccessible using the currently known computational methods. In this report, we review the Hamiltonian formulation of lattice gauge theories, and then describe our recent progress in constructing the quantum simulation of Abelian and non-Abelian lattice gauge theories in 1 + 1 and 2 + 1 dimensions using ultracold atoms in optical lattices.
NASA Astrophysics Data System (ADS)
Decker, K. M.; Jayewardena, C.; Rehmann, R.
We describe the library lgtlib, and lgttool, the corresponding development environment for Monte Carlo simulations of lattice gauge theory on multiprocessor vector computers with shared memory. We explain why distributed memory parallel processor (DMPP) architectures are particularly appealing for compute-intensive scientific applications, and introduce the design of a general application and program development environment system for scientific applications on DMPP architectures.
Digital lattice gauge theories
NASA Astrophysics Data System (ADS)
Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio
2017-02-01
We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with 2 +1 dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a Z3 lattice gauge theory with dynamical fermionic matter in 2 +1 dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.
Optical Abelian lattice gauge theories
Tagliacozzo, L.; Celi, A.; Zamora, A.; Lewenstein, M.
2013-03-15
We discuss a general framework for the realization of a family of Abelian lattice gauge theories, i.e., link models or gauge magnets, in optical lattices. We analyze the properties of these models that make them suitable for quantum simulations. Within this class, we study in detail the phases of a U(1)-invariant lattice gauge theory in 2+1 dimensions, originally proposed by P. Orland. By using exact diagonalization, we extract the low-energy states for small lattices, up to 4 Multiplication-Sign 4. We confirm that the model has two phases, with the confined entangled one characterized by strings wrapping around the whole lattice. We explain how to study larger lattices by using either tensor network techniques or digital quantum simulations with Rydberg atoms loaded in optical lattices, where we discuss in detail a protocol for the preparation of the ground-state. We propose two key experimental tests that can be used as smoking gun of the proper implementation of a gauge theory in optical lattices. These tests consist in verifying the absence of spontaneous (gauge) symmetry breaking of the ground-state and the presence of charge confinement. We also comment on the relation between standard compact U(1) lattice gauge theory and the model considered in this paper. - Highlights: Black-Right-Pointing-Pointer We study the quantum simulation of dynamical gauge theories in optical lattices. Black-Right-Pointing-Pointer We focus on digital simulation of abelian lattice gauge theory. Black-Right-Pointing-Pointer We rediscover and discuss the puzzling phase diagram of gauge magnets. Black-Right-Pointing-Pointer We detail the protocol for time evolution and ground-state preparation in any phase. Black-Right-Pointing-Pointer We provide two experimental tests to validate gauge theory quantum simulators.
Proposals for quantum simulating simple lattice gauge theory models using optical lattices
NASA Astrophysics Data System (ADS)
Zhang, Jin; Unmuth-Yockey, Judah; Bazavov, Alexei; Meurice, Yannick; Tsai, Shan-Wen
We derive an effective spin Hamiltonian for the (1 +1)-dimensional Abelian Higgs model in the strongly coupled region by integrating out the link variables. With finite spin truncations, the Hamiltonian can be matched with a 1-dimensional two-species Bose Hubbard model in the strong-coupling limit that can be implemented with cold atoms on an optical lattice. We study the phase diagram of the original Abelian Higgs model with Monte Carlo simulation and Tensor Renormalization Group methods. The results show a crossover line which terminates near the Kosterlitz-Thouless transition point. The effective quantum Hamiltonian is also studied with the DMRG method, and we find that they have a similar behavior. We discuss practical experimental implementations for our quantum simulator. Species-dependent optical lattices and ladder systems with double-well potentials are considered. We show how to obtain each of the interaction parameters required in the Bose-Hubbard model that we obtained, and confirm the possibility of tuning these interactions to the region in which our mapping is valid. We emphasize that this proposal for quantum simulating a gauge theory uses a manifestly gauge-invariant formulation and Gauss's Law is therefore automatically satisfied. Supported by DoD ARO under Grant No. W911NF-13-1-0119 and by the NSF under Grants No. DMR-1411345.
Cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory.
Zohar, Erez; Cirac, J Ignacio; Reznik, Benni
2013-03-22
Non-Abelian gauge theories play an important role in the standard model of particle physics, and unfold a partially unexplored world of exciting physical phenomena. In this Letter, we suggest a realization of a non-Abelian lattice gauge theory-SU(2) Yang-Mills in (1 + 1) dimensions, using ultracold atoms. Remarkably, and in contrast to previous proposals, in our model gauge invariance is a direct consequence of angular momentum conservation and thus is fundamental and robust. Our proposal may serve as well as a starting point for higher-dimensional realizations.
NASA Astrophysics Data System (ADS)
Weisz, Peter; Majumdar, Pushan
2012-03-01
Lattice gauge theory is a formulation of quantum field theory with gauge symmetries on a space-time lattice. This formulation is particularly suitable for describing hadronic phenomena. In this article we review the present status of lattice QCD. We outline some of the computational methods, discuss some phenomenological applications and a variety of non-perturbative topics. The list of references is severely incomplete, the ones we have included are text books or reviews and a few subjectively selected papers. Kronfeld and Quigg (2010) supply a reasonably comprehensive set of QCD references. We apologize for the fact that have not covered many important topics such as QCD at finite density and heavy quark effective theory adequately, and mention some of them only in the last section "In Brief". These topics should be considered in further Scholarpedia articles.
Numerical simulations of necklaces in SU(2) gauge-Higgs field theory
NASA Astrophysics Data System (ADS)
Hindmarsh, Mark; Rummukainen, Kari; Weir, David J.
2017-03-01
We perform the first numerical simulations of necklaces in a non-Abelian gauge theory. Necklaces are composite classical solutions which can be interpreted as monopoles trapped on strings, rather generic structures in a Grand Unified Theory. We generate necklaces from random initial conditions, modeling a phase transition in the early Universe, and study the evolution. For all cases, we find that the necklace system shows scaling behavior similar to that of a network of ordinary cosmic strings. Furthermore, our simulations indicate that comoving distance between the monopoles or semipoles along the string asymptotes to a constant value at late times. This means that, while the monopole-to-string energy density ratio decreases as the inverse of the scale factor, a horizon-size length of string has a large number of monopoles, significantly affecting the dynamics of string loops. We argue that gravitational wave bounds from millisecond pulsar timing on the string tension in the Nambu-Goto scenario are greatly relaxed.
Introduction to lattice gauge theory
NASA Astrophysics Data System (ADS)
Gupta, R.
The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by which one calculates the long distance properties of a strongly interacting theory from first principles. The observables are measured as a function of the bare coupling g and a gauge invariant cut-off approx. = 1/alpha, where alpha is the lattice spacing. The continuum (physical) behavior is recovered in the limit alpha yields 0, at which point the lattice artifacts go to zero. This is the more powerful use of lattice formulation, so in these lectures the author focuses on setting up the theory for the purpose of numerical simulations to get hard numbers. The numerical techniques used in Lattice Gauge Theories have their roots in statistical mechanics, so it is important to develop an intuition for the interconnection between quantum mechanics and statistical mechanics.
Semistrict higher gauge theory
NASA Astrophysics Data System (ADS)
Jurčo, Branislav; Sämann, Christian; Wolf, Martin
2015-04-01
We develop semistrict higher gauge theory from first principles. In particular, we describe the differential Deligne cohomology underlying semistrict principal 2-bundles with connective structures. Principal 2-bundles are obtained in terms of weak 2-functors from the Čech groupoid to weak Lie 2-groups. As is demonstrated, some of these Lie 2-groups can be differentiated to semistrict Lie 2-algebras by a method due to Ševera. We further derive the full description of connective structures on semistrict principal 2-bundles including the non-linear gauge transformations. As an application, we use a twistor construction to derive superconformal constraint equations in six dimensions for a non-Abelian tensor multiplet taking values in a semistrict Lie 2-algebra.
Cuzinatto, R.R. . E-mail: rodrigo@ift.unesp.br; Melo, C.A.M. de . E-mail: cassius.anderson@gmail.com; Pompeia, P.J. . E-mail: pompeia@ift.unesp.br
2007-05-15
A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama's program. A novel field strength G = {partial_derivative}F + fAF arises besides the one of the first order treatment, F = {partial_derivative}A - {partial_derivative}A + fAA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is L {sub P} {proportional_to} G {sup 2}. In this application the photon mass is estimated. The SU (N) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov's Lagrangian.
On lattice chiral gauge theories
NASA Technical Reports Server (NTRS)
Maiani, L.; Rossi, G. C.; Testa, M.
1991-01-01
The Smit-Swift-Aoki formulation of a lattice chiral gauge theory is presented. In this formulation the Wilson and other non invariant terms in the action are made gauge invariant by the coupling with a nonlinear auxilary scalar field, omega. It is shown that omega decouples from the physical states only if appropriate parameters are tuned so as to satisfy a set of BRST identities. In addition, explicit ghost fields are necessary to ensure decoupling. These theories can give rise to the correct continuum limit. Similar considerations apply to schemes with mirror fermions. Simpler cases with a global chiral symmetry are discussed and it is shown that the theory becomes free at decoupling. Recent numerical simulations agree with those considerations.
Program package for multicanonical simulations of U(1) lattice gauge theory-Second version
NASA Astrophysics Data System (ADS)
Bazavov, Alexei; Berg, Bernd A.
2013-03-01
A new version STMCMUCA_V1_1 of our program package is available. It eliminates compatibility problems of our Fortran 77 code, originally developed for the g77 compiler, with Fortran 90 and 95 compilers. New version program summaryProgram title: STMC_U1MUCA_v1_1 Catalogue identifier: AEET_v1_1 Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html Programming language: Fortran 77 compatible with Fortran 90 and 95 Computers: Any capable of compiling and executing Fortran code Operating systems: Any capable of compiling and executing Fortran code RAM: 10 MB and up depending on lattice size used No. of lines in distributed program, including test data, etc.: 15059 No. of bytes in distributed program, including test data, etc.: 215733 Keywords: Markov chain Monte Carlo, multicanonical, Wang-Landau recursion, Fortran, lattice gauge theory, U(1) gauge group, phase transitions of continuous systems Classification: 11.5 Catalogue identifier of previous version: AEET_v1_0 Journal Reference of previous version: Computer Physics Communications 180 (2009) 2339-2347 Does the new version supersede the previous version?: Yes Nature of problem: Efficient Markov chain Monte Carlo simulation of U(1) lattice gauge theory (or other continuous systems) close to its phase transition. Measurements and analysis of the action per plaquette, the specific heat, Polyakov loops and their structure factors. Solution method: Multicanonical simulations with an initial Wang-Landau recursion to determine suitable weight factors. Reweighting to physical values using logarithmic coding and calculating jackknife error bars. Reasons for the new version: The previous version was developed for the g77 compiler Fortran 77 version. Compiler errors were encountered with Fortran 90 and Fortran 95 compilers (specified below). Summary of revisions: epsilon=one/10**10 is replaced by epsilon/10.0D10 in the parameter statements of the subroutines u1_bmha.f, u1_mucabmha.f, u1wl
A highly optimized vectorized code for Monte Carlo simulations of SU(3) lattice gauge theories
NASA Technical Reports Server (NTRS)
Barkai, D.; Moriarty, K. J. M.; Rebbi, C.
1984-01-01
New methods are introduced for improving the performance of the vectorized Monte Carlo SU(3) lattice gauge theory algorithm using the CDC CYBER 205. Structure, algorithm and programming considerations are discussed. The performance achieved for a 16(4) lattice on a 2-pipe system may be phrased in terms of the link update time or overall MFLOPS rates. For 32-bit arithmetic, it is 36.3 microsecond/link for 8 hits per iteration (40.9 microsecond for 10 hits) or 101.5 MFLOPS.
Nonperturbative Regulator for Chiral Gauge Theories?
NASA Astrophysics Data System (ADS)
Grabowska, Dorota M.; Kaplan, David B.
2016-05-01
We propose a nonperturbative gauge-invariant regulator for d -dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in d +1 dimensions with quantum gauge fields that reside on one d -dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local d -dimensional interpretation only if the chiral fermion representation is anomaly free. A physical realization of this construction would imply the existence of mirror fermions in the standard model that are invisible except for interactions induced by vacuum topology, and which could gravitate differently than conventional matter.
Monte Carlo algorithms for lattice gauge theory
Creutz, M.
1987-05-01
Various techniques are reviewed which have been used in numerical simulations of lattice gauge theories. After formulating the problem, the Metropolis et al. algorithm and some interesting variations are discussed. The numerous proposed schemes for including fermionic fields in the simulations are summarized. Langevin, microcanonical, and hybrid approaches to simulating field theories via differential evolution in a fictitious time coordinate are treated. Some speculations are made on new approaches to fermionic simulations.
Lattice simulations with eight flavors of domain wall fermions in SU(3) gauge theory
NASA Astrophysics Data System (ADS)
Appelquist, T.; Brower, R. C.; Fleming, G. T.; Kiskis, J.; Lin, M. F.; Neil, E. T.; Osborn, J. C.; Rebbi, C.; Rinaldi, E.; Schaich, D.; Schroeder, C.; Syritsyn, S.; Voronov, G.; Vranas, P.; Weinberg, E.; Witzel, O.; Lattice Strong Dynamics LSD Collaboration
2014-12-01
We study an SU(3) gauge theory with Nf=8 degenerate flavors of light fermions in the fundamental representation. Using the domain wall fermion formulation, we investigate the light hadron spectrum, chiral condensate ⟨ψ ¯ ψ ⟩ and electroweak S parameter. We consider a range of light fermion masses on two lattice volumes at a single gauge coupling chosen so that IR scales approximately match those from our previous studies of the two- and six-flavor systems. Our results for the Nf=8 spectrum suggest spontaneous chiral symmetry breaking, though fits to the fermion mass dependence of spectral quantities do not strongly disfavor the hypothesis of mass-deformed infrared conformality. Compared to Nf=2 we observe a significant enhancement of ⟨ψ ¯ψ ⟩ relative to the symmetry breaking scale F , similar to the situation for Nf=6 . The reduction of the S parameter, related to parity doubling in the vector and axial-vector channels, is also comparable to our six-flavor results.
Gauge Theories of Vector Particles
DOE R&D Accomplishments Database
Glashow, S. L.; Gell-Mann, M.
1961-04-24
The possibility of generalizing the Yang-Mills trick is examined. Thus we seek theories of vector bosons invariant under continuous groups of coordinate-dependent linear transformations. All such theories may be expressed as superpositions of certain "simple" theories; we show that each "simple theory is associated with a simple Lie algebra. We may introduce mass terms for the vector bosons at the price of destroying the gauge-invariance for coordinate-dependent gauge functions. The theories corresponding to three particular simple Lie algebras - those which admit precisely two commuting quantum numbers - are examined in some detail as examples. One of them might play a role in the physics of the strong interactions if there is an underlying super-symmetry, transcending charge independence, that is badly broken. The intermediate vector boson theory of weak interactions is discussed also. The so-called "schizon" model cannot be made to conform to the requirements of partial gauge-invariance.
Confinement and lattice gauge theory
Creutz, M
1980-06-01
The motivation for formulating gauge theories on a lattice to study non-perturbative phenomena is reviewed, and recent progress supporting the compatibility of asymptotic freedom and quark confinement in the standard SU(3) Yang-Mills theory of the strong interaction is discussed.
Gauge theories, tessellations & Riemann surfaces
NASA Astrophysics Data System (ADS)
He, Yang-Hui; van Loon, Mark
2014-06-01
We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories. These tessellations are generalizations of brane tilings, or bipartite graphs on the torus as well as the Platonic and Archimedean solids on the sphere. On higher genus they give rise to intricate patterns. Special attention will be paid to the master space and the moduli space of vacua of the gauge theory and to how their geometry is determined by the tessellations.
Entwinement in discretely gauged theories
NASA Astrophysics Data System (ADS)
Balasubramanian, V.; Bernamonti, A.; Craps, B.; De Jonckheere, T.; Galli, F.
2016-12-01
We develop the notion of "entwinement" to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an S N gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to AdS3 at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the system which are gravitationally described as conical defects and the M = 0 BTZ black hole. The possible types of entwinement that can be computed define a very large new class of quantities characterizing the fine structure of quantum wavefunctions.
Asymptotically Free Gauge Theories. I
DOE R&D Accomplishments Database
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Towards a Neuronal Gauge Theory
Sengupta, Biswa; Tozzi, Arturo; Cooray, Gerald K.; Douglas, Pamela K.; Friston, Karl J.
2016-01-01
Given the amount of knowledge and data accruing in the neurosciences, is it time to formulate a general principle for neuronal dynamics that holds at evolutionary, developmental, and perceptual timescales? In this paper, we propose that the brain (and other self-organised biological systems) can be characterised via the mathematical apparatus of a gauge theory. The picture that emerges from this approach suggests that any biological system (from a neuron to an organism) can be cast as resolving uncertainty about its external milieu, either by changing its internal states or its relationship to the environment. Using formal arguments, we show that a gauge theory for neuronal dynamics—based on approximate Bayesian inference—has the potential to shed new light on phenomena that have thus far eluded a formal description, such as attention and the link between action and perception. PMID:26953636
Gravity: A gauge theory perspective
NASA Astrophysics Data System (ADS)
Nester, James M.; Chen, Chiang-Mei
2016-07-01
The evolution of a generally covariant theory is under-determined. One hundred years ago such dynamics had never before been considered; its ramifications were perplexing, its future important role for all the fundamental interactions under the name gauge principle could not be foreseen. We recount some history regarding Einstein, Hilbert, Klein and Noether and the novel features of gravitational energy that led to Noether’s two theorems. Under-determined evolution is best revealed in the Hamiltonian formulation. We developed a covariant Hamiltonian formulation. The Hamiltonian boundary term gives covariant expressions for the quasi-local energy, momentum and angular momentum. Gravity can be considered as a gauge theory of the local Poincaré group. The dynamical potentials of the Poincaré gauge theory of gravity are the frame and the connection. The spacetime geometry has in general both curvature and torsion. Torsion naturally couples to spin; it could have a significant magnitude and yet not be noticed, except on a cosmological scale where it could have significant effects.
Invariance, symmetry and periodicity in gauge theories
Jackiw, R
1980-02-01
The interplay between gauge transformations and coordinate transformations is discussed; the theory will aid in understanding the mixing of space-time and internal degrees of freedom. The subject is presented under the following headings: coordinate transformation laws for arbitrary fields, coordinate transformation laws for gauge fields, properties of symmetric gauge fields, construction of symmetric gauge fields, physical significance of gauge transformations, and magnetic monopole topology without Higgs fields. The paper ends with conclusions and suggestions for further research. (RWR)
A nilpotent symmetry of quantum gauge theories
NASA Astrophysics Data System (ADS)
Lahiri, Amitabha
2001-09-01
For the Becchi-Rouet-Stora-Tyutin invariant extended action for any gauge theory, there exists another off-shell nilpotent symmetry. For linear gauges, it can be elevated to a symmetry of the quantum theory and used in the construction of the quantum effective action. Generalizations for nonlinear gauges and actions with higher-order ghost terms are also possible.
BRST symmetry in the general gauge theories
NASA Astrophysics Data System (ADS)
Hyuk-Jae, Lee; Jae, Hyung, Yee
1994-01-01
By using the residual gauge symmetry interpretation of BRST invariance we have constructed a new BRST formulation for general gauge theories including those with open algebras. For theories with open gauge algebra the formulation leads to a BRST invariant effective action which does not contain any higher order terms in the ghost fields.
Superpotentials for Quiver Gauge Theories
Aspinwall, Paul S.; Fidkowski, Lukasz M.; /Stanford U., Phys. Dept.
2005-06-10
We compute superpotentials for quiver gauge theories arising from marginal D-Brane decay on collapsed del Pezzo cycles S in a Calabi-Yau X. This is done using the machinery of A{sub {infinity}} products in the derived category of coherent sheaves of X, which in turn is related to the derived category of S and quiver path algebras. We confirm that the superpotential is what one might have guessed from analyzing the moduli space, i.e., it is linear in the fields corresponding to the Exts of the quiver and that each such Ext multiplies a polynomial in Exts equal to precisely the relation represented by the Ext.
Gauge invariants and correlators in flavoured quiver gauge theories
NASA Astrophysics Data System (ADS)
Mattioli, Paolo; Ramgoolam, Sanjaye
2016-10-01
In this paper we study the construction of holomorphic gauge invariant operators for general quiver gauge theories with flavour symmetries. Using a characterisation of the gauge invariants in terms of equivalence classes generated by permutation actions, along with representation theory results in symmetric groups and unitary groups, we give a diagonal basis for the 2-point functions of holomorphic and anti-holomorphic operators. This involves a generalisation of the previously constructed Quiver Restricted Schur operators to the flavoured case. The 3-point functions are derived and shown to be given in terms of networks of symmetric group branching coefficients. The networks are constructed through cutting and gluing operations on the quivers.
Matrix product states for gauge field theories.
Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
2014-08-29
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.
Toward a gauge field theory of gravity.
NASA Astrophysics Data System (ADS)
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Entanglement of Distillation for Lattice Gauge Theories
NASA Astrophysics Data System (ADS)
Van Acoleyen, Karel; Bultinck, Nick; Haegeman, Jutho; Marien, Michael; Scholz, Volkher B.; Verstraete, Frank
2016-09-01
We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi [J. High Energy Phys. 1 (2016) 1], we show that the usual entanglement entropy for a spatial bipartition can be written as the sum of an undistillable gauge part and of another part corresponding to the local operations and classical communication distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure Abelian gauge theories at zero gauge coupling, while it is in general nonzero for the non-Abelian case. We also consider gauge theories with matter, and show in a perturbative approach how area laws—including a topological correction—emerge for the distillable entanglement. Finally, we also discuss the entanglement entropy of gauge fixed states and show that it has no relation to the physical distillable entropy.
NASA Astrophysics Data System (ADS)
Shih, Sheng-Yu Darren
This thesis covers two distinct parts: Holomorphic Anomaly in Gauge Theory on ALE Space and Freudenthal Gauge Theory. In part I, I presented a concise review of the Seiberg-Witten curve, Nekrasov's background, geometric engineering and the holomorphic anomaly equation followed by my published work: Holomorphic Anomaly in Gauge Theory on ALE Space, where an deformed N = 2 SU(2) gauge theory on A1 space and its five dimension lift is studied. We find that the partition functions can be reproduced via special geometry and the holomorphic anomaly equation. Schwinger type integral expressions for the boundary conditions at the monopole/dyon point in moduli space are inferred. The interpretation of the five dimensional partition function as the partition function of a refined topological string on A1x(local P1 x P1) is suggested. In part II, I give a comprehensive review of the Freudenthal Triple System, including Freudenthal's orginal construction from Jordan Triple Systems and its relation to Lie algebra, Yang-Baxter equation, and 4d N = 2 BPS black holes, where the novel Freudenthal-dual was discovered. I also present my published work on the Freudenthal Gauge Theory, where we construct the most generic gauge theory admitting F-dual, and prove a no-go theorem that forbids coupling of a F-dual invariant gauge theory to supersymmetry.
A supersymmetric extension of quantum gauge theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Scharf, G.
2003-01-01
We consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. The constructions of the model follows closely the usual construction of gauge models in the Epstein-Glaser framework for perturbative field theory. Accordingly, all the arguments are completely of quantum nature without reference to a classical supersymmetric theory. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.
Strong Coupling Gauge Theories in LHC ERA
NASA Astrophysics Data System (ADS)
Fukaya, H.; Harada, M.; Tanabashi, M.; Yamawaki, K.
2011-01-01
Higgs, or techni-dilaton - composite Higgs near conformality / Koichi Yamawaki -- Phase diagram of strongly interacting theories / Francesco Sannino -- Resizing conformal windows / O. Antipin and K. Tuominen -- Nearly conformal gauge theories on the lattice / Zoltan Fodor ... [et al.] -- Going beyond QCD in lattice gauge theory / G. T. Fleming -- Phases of QCD from small to large N[symbol]: (some) lattice results / A. Deuzeman, E. Pallante and M. P. Lombardo -- Lattice gauge theory and (quasi)-conformal technicolor / D. K. Sinclair and J. B. Kogut -- Study of the running coupling constant in 10-flavor QCD with the Schrodinger functional method / N. Yamada ... [et al.] -- Study of the running coupling in twisted Polyakov scheme / T. Aoyama ... [et al.].Running coupling in strong gauge theories via the lattice / Zoltan Fodor ... [et al.] -- Higgsinoless supersymmetry and hidden gravity / Michael L. Graesser, Ryuichiro Kitano and Masafumi Kurachi -- The latest status of LHC and the EWSB physics / S. Asai -- Continuum superpartners from supersymmetric unparticles / Hsin-Chia Cheng -- Review of minimal flavor constraints for technicolor / Hidenori S. Fukano and Francesco Sannino -- Standard model and high energy Lorentz violation / Damiano Anselmi -- Dynamical electroweak symmetry breaking and fourth family / Michio Hashimoto -- Holmorphic supersymmetric Nambu-Jona-Lasino model and dynamical electroweak symmetry breaking / Dong-Won Jung, Otto C. W. Kong and Jae Sik Lee -- Ratchet model of Baryogenesis / Tatsu Takeuchi, Azusa Minamizaki and Akio Sugamoto -- Classical solutions of field equations in Einstein Gauss-Bonnet gravity / P. Suranyi, C. Vaz and L. C. R. Wijewardhana -- Black holes constitute all dark matter / Paul H. Frampton -- Electroweak precision test and Z [symbol] in the three site Higgsless model / Tomohiro Abe -- Chiral symmetry and BRST symmetry breaking, quaternion reality and the lattice simulation / Sadataka Furui -- Holographic techni-dilaton, or
Two-Color Gauge Theory with Novel Infrared Behavior
NASA Astrophysics Data System (ADS)
Appelquist, T.; Brower, R. C.; Buchoff, M. I.; Cheng, M.; Fleming, G. T.; Kiskis, J.; Lin, M. F.; Neil, E. T.; Osborn, J. C.; Rebbi, C.; Schaich, D.; Schroeder, C.; Syritsyn, S.; Voronov, G.; Vranas, P.; Witzel, O.; Lattice Strong Dynamics (LSD) Collaboration
2014-03-01
Using lattice simulations, we study the infrared behavior of a particularly interesting SU(2) gauge theory, with six massless Dirac fermions in the fundamental representation. We compute the running gauge coupling derived nonperturbatively from the Schrödinger functional of the theory, finding no evidence for an infrared fixed point up through gauge couplings g¯2 of order 20. This implies that the theory either is governed in the infrared by a fixed point of considerable strength, unseen so far in nonsupersymmetric gauge theories, or breaks its global chiral symmetries producing a large number of composite Nambu-Goldstone bosons relative to the number of underlying degrees of freedom. Thus either of these phases exhibits novel behavior.
Weyl gravity as a gauge theory
NASA Astrophysics Data System (ADS)
Trujillo, Juan Teancum
In 1920, Rudolf Bach proposed an action based on the square of the Weyl tensor or CabcdCabcd where the Weyl tensor is an invariant under a scaling of the metric. A variation of the metric leads to the field equation known as the Bach equation. In this dissertation, the same action is analyzed, but as a conformal gauge theory. It is shown that this action is a result of a particular gauging of this group. By treating it as a gauge theory, it is natural to vary all of the gauge fields independently, rather than performing the usual fourth-order metric variation only. We show that solutions of the resulting vacuum field equations are all solutions to the vacuum Einstein equation, up to a conformal factor---a result consistent with local scale freedom. We also show how solutions for the gauge fields imply there is no gravitational self energy.
Scaling study of the step scaling function in SU(3) gauge theory with improved gauge actions
Takeda, S.; Aoki, S.; Iwasaki, Y.; Kanaya, K.; Fukugita, M.; Ishikawa, K-I.; Okawa, M.; Ishizuka, N.; Kuramashi, Y.; Taniguchi, Y.; Ukawa, A.; Yoshie, T.; Kaneko, T.
2004-10-01
We study the scaling behavior of the step scaling function for SU(3) gauge theory, employing the renormalization-group improved Iwasaki gauge action and the perturbatively improved Luescher-Weisz gauge action. We confirm that the step scaling functions from the improved gauge actions agree with that previously obtained from the plaquette action within errors in the continuum limit at both weak and strong coupling regions. We also investigate how different choices of boundary counterterms for the improved gauge actions affect the scaling behavior. In the extrapolation to the continuum limit, we observe that the cutoff dependence becomes moderate for the Iwasaki action, if a perturbative reduction of scaling violations is applied to the simulation results. We also measure the low energy scale ratio with the Iwasaki action and confirm its universality.
Noncommutative Gauge Theory with Covariant Star Product
Zet, G.
2010-08-04
We present a noncommutative gauge theory with covariant star product on a space-time with torsion. In order to obtain the covariant star product one imposes some restrictions on the connection of the space-time. Then, a noncommutative gauge theory is developed applying this product to the case of differential forms. Some comments on the advantages of using a space-time with torsion to describe the gravitational field are also given.
Lattice gauge theories and spin models
NASA Astrophysics Data System (ADS)
Mathur, Manu; Sreeraj, T. P.
2016-10-01
The Wegner Z2 gauge theory-Z2 Ising spin model duality in (2 +1 ) dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner Z2 gauge-spin duality is directly generalized to SU(N) lattice gauge theory in (2 +1 ) dimensions to obtain the SU(N) spin model in terms of the SU(N) magnetic fields and their conjugate SU(N) electric scalar potentials. The exact and complete solutions of the Z2, U(1), SU(N) Gauss law constraints in terms of the corresponding spin or dual potential operators are given. The gauge-spin duality naturally leads to a new gauge invariant magnetic disorder operator for SU(N) lattice gauge theory which produces a magnetic vortex on the plaquette. A variational ground state of the SU(2) spin model with nearest neighbor interactions is constructed to analyze SU(2) gauge theory.
Quantum Gauge Theories : A True Ghost Story
NASA Astrophysics Data System (ADS)
Scharf, Gunter
2001-03-01
An innovative new treatment of particle physics using quantum gauge theory as its basis If regarded as operator theories, ghost fields play a very important role in quantum gauge theory, which forms the basis of modern particle physics. The author argues that all known forces in nature-electromagnetism, weak and strong forces, and gravity-follow in a unique way from the basic principle of quantum gauge invariance. Using that as a starting point, this volume discusses gauge theories as quantum theories, as part of a streamlined modern approach. The simplicity of using only this one method throughout the book allows the reader a clear understanding of the mathematical structure of nature, while this modern and mathematically well-defined approach elucidates the standard theory of particle physics without overburdening the reader with the full range of various ideas and methods. Though the subject matter requires a basic knowledge of quantum mechanics, the book's unprecedented and uncomplicated coverage will offer readers little difficulty. This revolutionary volume is suitable for graduate students and researchers alike and includes a completely new treatment of gravity as well as important new ideas on massive gauge fields.
Topological resolution of gauge theory singularities
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-21
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
Discrete gauge symmetry in continuum theories
Krauss, L.M.; Wilczek, F.
1989-03-13
We point out that local symmetries can masquerade as discrete global symmetries to an observer equipped with only low-energy probes. The existence of the underlying local gauge invariance can, however, result in observable Aharonov-Bohm-type effects. Black holes can therefore carry discrete gauge charges: a form of nonclassical ''hair.'' Neither black-hole evaporation, wormholes, nor anything else can violate discrete gauge symmetries. In supersymmetric unified theories such discrete symmetries can forbid proton-decay amplitudes that might otherwise be catastrophic.
Origin of gauge invariance in string theory
NASA Technical Reports Server (NTRS)
Horowitz, G. T.; Strominger, A.
1986-01-01
A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.
Entanglement in weakly coupled lattice gauge theories
NASA Astrophysics Data System (ADS)
Radičević, Ðorđe
2016-04-01
We present a direct lattice gauge theory computation that, without using dualities, demonstrates that the entanglement entropy of Yang-Mills theories with arbitrary gauge group G contains a generic logarithmic term at sufficiently weak coupling e. In two spatial dimensions, for a region of linear size r, this term equals 1/2 dim( G) log( e 2 r) and it dominates the universal part of the entanglement entropy. Such logarithmic terms arise from the entanglement of the softest mode in the entangling region with the environment. For Maxwell theory in two spatial dimensions, our results agree with those obtained by dualizing to a compact scalar with spontaneous symmetry breaking.
Pion masses in quasiconformal gauge field theories
Dietrich, Dennis D.; Jaervinen, Matti
2009-03-01
We study modifications to Weinberg-like sum rules in quasiconformal gauge field theories. Beyond the two Weinberg sum rules and the oblique S parameter, we study the pion mass and the X parameter. Especially, we evaluate the pion mass for walking technicolor theories, in particular, minimal walking technicolor, and find contributions of the order of up to several hundred GeV.
Gauge theories in anti-selfdual variables
NASA Astrophysics Data System (ADS)
Bochicchio, Marco; Pilloni, Alessandro
2013-09-01
Some years ago the Nicolai map, viewed as a change of variables from the gauge connection in a fixed gauge to the anti-selfdual part of the curvature, has been extended by the first named author to pure Yang-Mills from its original definition in = 1 supersymmetric Yang-Mills. We study here the perturbative one-particle irreducible effective action in the anti-selfdual variables of any gauge theory, in particular pure Yang-Mills, QCD and = 1 supersymmetric Yang-Mills. We prove that the one-loop one-particle irreducible effective action of a gauge theory mapped to the anti-selfdual variables in any gauge is identical to the one of the original theory. This is due to the conspiracy between the Jacobian of the change to the anti-selfdual variables and an extra functional determinant that arises from the non-linearity of the coupling of the anti-selfdual curvature to an external source in the Legendre transform that defines the one-particle irreducible effective action. Hence we establish the one-loop perturbative equivalence of the mapped and original theories on the basis of the identity of the one-loop one-particle irreducible effective actions. Besides, we argue that the identity of the perturbative one-particle irreducible effective actions extends order by order in perturbation theory.
Quantum walks and non-Abelian discrete gauge theory
NASA Astrophysics Data System (ADS)
Arnault, Pablo; Di Molfetta, Giuseppe; Brachet, Marc; Debbasch, Fabrice
2016-07-01
A family of discrete-time quantum walks (DTQWs) on the line with an exact discrete U(N ) gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac fermion coupled to usual U(N ) gauge fields in two-dimensional spacetime. A discrete generalization of the usual U(N ) curvature is also constructed. An alternate interpretation of these results in terms of superimposed U(1 ) Maxwell fields and SU(N ) gauge fields is discussed in the Appendix. Numerical simulations are also presented, which explore the convergence of the DTQWs towards their continuous limit and which also compare the DTQWs with classical (i.e., nonquantum) motions in classical SU(2 ) fields. The results presented in this paper constitute a first step towards quantum simulations of generic Yang-Mills gauge theories through DTQWs.
Minimal Basis for Gauge Theory Amplitudes
Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Vanhove, Pierre
2009-10-16
Identities based on monodromy for integrations in string theory are used to derive relations between different color-ordered tree-level amplitudes in both bosonic and supersymmetric string theory. These relations imply that the color-ordered tree-level n-point gauge theory amplitudes can be expanded in a minimal basis of (n-3)exclamation amplitudes. This result holds for any choice of polarizations of the external states and in any number of dimensions.
Recursion equations in gauge field theories
NASA Astrophysics Data System (ADS)
Migdal, A. A.
An approximate recursion equation is formulated, describing the scale transformation of the effective action of a gauge field. In two-dimensional space-time the equation becomes exact. In four-dimensional theories it reproduces asymptotic freedom to an accuracy of 30% in the coefficients of the β-function. In the strong-coupling region the β-function remains negative and this results in an asymptotic prison in the infrared region. Possible generalizations and applications to the quark-gluon gauge theory are discussed.
Renormalized Polyakov loop in the deconfined phase of SU(N) gauge theory and gauge-string duality.
Andreev, Oleg
2009-05-29
We use gauge-string duality to analytically evaluate the renormalized Polyakov loop in pure Yang-Mills theories. For SU(3), the result is in quite good agreement with lattice simulations for a broad temperature range.
Gravity as the square of gauge theory
Bern, Zvi; Dennen, Tristan; Huang Yutin; Kiermaier, Michael
2010-09-15
We explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged to satisfy Jacobi-like identities in one-to-one correspondence to the associated color factors. Using on-shell recursion relations, we give a field-theory proof showing that the duality implies that diagrammatic numerators in gravity are just the product of two corresponding gauge-theory numerators, as previously conjectured. These squaring relations express gravity amplitudes in terms of gauge-theory ingredients, and are a recasting of the Kawai, Lewellen, and Tye relations. Assuming that numerators of loop amplitudes can be arranged to satisfy the duality, our tree-level proof immediately carries over to loop level via the unitarity method. We then present a Yang-Mills Lagrangian whose diagrams through five points manifestly satisfy the duality between color and kinematics. The existence of such Lagrangians suggests that the duality also extends to loop amplitudes, as confirmed at two and three loops in a concurrent paper. By ''squaring'' the novel Yang-Mills Lagrangian we immediately obtain its gravity counterpart. We outline the general structure of these Lagrangians for higher points. We also write down various new representations of gauge-theory and gravity amplitudes that follow from the duality between color and kinematics.
National Computational Infrastructure for Lattice Gauge Theory
Brower, Richard C.
2014-04-15
SciDAC-2 Project The Secret Life of Quarks: National Computational Infrastructure for Lattice Gauge Theory, from March 15, 2011 through March 14, 2012. The objective of this project is to construct the software needed to study quantum chromodynamics (QCD), the theory of the strong interactions of sub-atomic physics, and other strongly coupled gauge field theories anticipated to be of importance in the energy regime made accessible by the Large Hadron Collider (LHC). It builds upon the successful efforts of the SciDAC-1 project National Computational Infrastructure for Lattice Gauge Theory, in which a QCD Applications Programming Interface (QCD API) was developed that enables lattice gauge theorists to make effective use of a wide variety of massively parallel computers. This project serves the entire USQCD Collaboration, which consists of nearly all the high energy and nuclear physicists in the United States engaged in the numerical study of QCD and related strongly interacting quantum field theories. All software developed in it is publicly available, and can be downloaded from a link on the USQCD Collaboration web site, or directly from the github repositories with entrance linke http://usqcd-software.github.io
Gauge Field Theories, 2nd Edition
NASA Astrophysics Data System (ADS)
Frampton, Paul H.
2000-08-01
The first edition of Gauge Field Theories, published in 1985, quickly became widely used in universities and other institutions of higher learning around the world. Written by well-known physicist Paul Frampton, the new edition continues to offer a first-rate mathematical treatment of gauge field theories, while thoroughly updating all chapters to keep pace with developments in the field. Frampton emphasizes formalism rather than experiments and provides sufficient detail for readers wishing to do their own calculations or pursue theoretical physics research. Special features of the Second Edition include: * Improved, logical organization of the material on gauge invariance, quantization, and renormalization * Major revision of the chapter on electroweak interactions, incorporating the latest precision data and discovery of the top quark * Discussions of renormalization group and quantum chromodynamics * A completely new chapter on model building
Planar zeros in gauge theories and gravity
NASA Astrophysics Data System (ADS)
Jiménez, Diego Medrano; Vera, Agustín Sabio; Vázquez-Mozo, Miguel Á.
2016-09-01
Planar zeros are studied in the context of the five-point scattering amplitude for gauge bosons and gravitons. In the case of gauge theories, it is found that planar zeros are determined by an algebraic curve in the projective plane spanned by the three stereographic coordinates labelling the direction of the outgoing momenta. This curve depends on the values of six independent color structures. Considering the gauge group SU( N) with N = 2 , 3 , 5 and fixed color indices, the class of curves obtained gets broader by increasing the rank of the group. For the five-graviton scattering, on the other hand, we show that the amplitude vanishes whenever the process is planar, without imposing further kinematic conditions. A rationale for this result is provided using color-kinematics duality.
Induced gauge theories and W gravity
Schoutens, K. . Inst. for Theoretical Physics); Sevrin, A. ); van Nieuwenhuizen, P. . Theory Div. State Univ. of New York, Stony Brook, NY . Inst. for Theoretical Physics)
1991-11-01
We review some aspects of induced gauge theories in two dimensions. We focus on W{sub 3} gravity, paying particular attention to the treatment of the non-linearities inherent to W gravity. We show that the induced action {Gamma}{sub ind}(h,b) for chiral W{sub 3} in the c {yields} {plus minus}infinity limit is obtained from the induced action of a gauged Sl(3,R) Wess-Zumino-Witten model by imposing constraints on some of the affine currents. Subsequently we investigate the effective action, which is obtained by integrating the induced action over the gauge fields. We show perturbatively that certain subleading terms which appear in the induced action for finite c (and which are related to nonlocal terms in the Ward identifies) get canceled by similar terms due to loop corrections, and we propose an all-order result for the effective action.
Induced gauge theories and W gravity
Schoutens, K.; Sevrin, A.; van Nieuwenhuizen, P. |
1991-11-01
We review some aspects of induced gauge theories in two dimensions. We focus on W{sub 3} gravity, paying particular attention to the treatment of the non-linearities inherent to W gravity. We show that the induced action {Gamma}{sub ind}[h,b] for chiral W{sub 3} in the c {yields} {plus_minus}infinity limit is obtained from the induced action of a gauged Sl(3,R) Wess-Zumino-Witten model by imposing constraints on some of the affine currents. Subsequently we investigate the effective action, which is obtained by integrating the induced action over the gauge fields. We show perturbatively that certain subleading terms which appear in the induced action for finite c (and which are related to nonlocal terms in the Ward identifies) get canceled by similar terms due to loop corrections, and we propose an all-order result for the effective action.
Gauged supersymmetries in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Tissier, Matthieu; Wschebor, Nicolás
2009-03-01
In this paper we show that Yang-Mills theory in the Curci-Ferrari-Delbourgo-Jarvis gauge admits some up to now unknown local linear Ward identities. These identities imply some nonrenormalization theorems with practical simplifications for perturbation theory. We show, in particular, that all renormalization factors can be extracted from two-point functions. The Ward identities are shown to be related to supergauge transformations in the superfield formalism for Yang-Mills theory. The case of nonzero Curci-Ferrari mass is also addressed.
Gauged supersymmetries in Yang-Mills theory
Tissier, Matthieu; Wschebor, Nicolas
2009-03-15
In this paper we show that Yang-Mills theory in the Curci-Ferrari-Delbourgo-Jarvis gauge admits some up to now unknown local linear Ward identities. These identities imply some nonrenormalization theorems with practical simplifications for perturbation theory. We show, in particular, that all renormalization factors can be extracted from two-point functions. The Ward identities are shown to be related to supergauge transformations in the superfield formalism for Yang-Mills theory. The case of nonzero Curci-Ferrari mass is also addressed.
Local renormalizable gauge theories from nonlocal operators
Capri, M.A.L. Lemes, V.E.R. Sobreiro, R.F. Sorella, S.P. Thibes, R.
2008-03-15
The possibility that nonlocal operators might be added to the Yang-Mills action is investigated. We point out that there exists a class of nonlocal operators which lead to renormalizable gauge theories. These operators turn out to be localizable by means of the introduction of auxiliary fields. The renormalizability is thus ensured by the symmetry content exhibited by the resulting local theory. The example of the nonlocal operator Tr{integral}A{sub {mu}}1/(D{sup 2}) A{sub {mu}} is analyzed in detail. A few remarks on the possible role that these operators might have for confining theories are outlined.
Gauge theory of defects in continuous media I
NASA Astrophysics Data System (ADS)
Sahoo, D.
2006-11-01
We present a selective review of the gauge theory of defects in the elastic continuum. After introducing the essential geometric concepts of continuum mechanics in the presence of defects, the classical defect dynamics equations involving dislocation and disclination density tensors are introduced. The mathematical structure of gauge theories is briefly discussed. Typical recent works covering Yang-Mills type gauge theories and gravity type gauge theories are touched upon in a qualitative way.
Light-Front Quantization of Gauge Theories
Brodskey, Stanley
2002-12-01
Light-front wavefunctions provide a frame-independent representation of hadrons in terms of their physical quark and gluon degrees of freedom. The light-front Hamiltonian formalism provides new nonperturbative methods for obtaining the QCD spectrum and eigensolutions, including resolvant methods, variational techniques, and discretized light-front quantization. A new method for quantizing gauge theories in light-cone gauge using Dirac brackets to implement constraints is presented. In the case of the electroweak theory, this method of light-front quantization leads to a unitary and renormalizable theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions as well as the Goldstone boson equivalence theorem. Spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field leaving the light-front vacuum equal to the perturbative vacuum. I also discuss an ''event amplitude generator'' for automatically computing renormalized amplitudes in perturbation theory. The importance of final-state interactions for the interpretation of diffraction, shadowing, and single-spin asymmetries in inclusive reactions such as deep inelastic lepton-hadron scattering is emphasized.
Zero energy gauge fields and the phases of a gauge theory
Guendelman, E.I. )
1990-07-20
A new approach to the definition of the phases of a Poincare invariant gauge theory is developed. It is based on the role of gauge transformations that change the asymptotic value of the gauge fields from zero to a constant. In the context of theories without Higgs fields, this symmetry can be spontaneously broken when the gauge fields are massless particles, explicitly broken when the gauge fields develop a mass. Finally, the vacuum can be invariant under this transformation, this last case can be achieved when the theory has a violent infrared behavior, which in some theories can be connected to a confinement mechanism.
Light dilaton in walking gauge theories
Appelquist, Thomas; Bai Yang
2010-10-01
We analyze the existence of a dilaton in gauge theories with approximate infrared conformal symmetry. To the extent that these theories are governed in the infrared by an approximate fixed point (walking), the explicit breaking of the conformal symmetry at these scales is vanishingly small. If confinement and spontaneous chiral-symmetry breaking set in at some infrared scale, the resultant breaking of the approximate conformal symmetry can lead to the existence of a dilaton with mass parametrically small compared to the confinement scale, and potentially observable at the LHC.
Local subsystems in gauge theory and gravity
NASA Astrophysics Data System (ADS)
Donnelly, William; Freidel, Laurent
2016-09-01
We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of localized subsystems. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedom are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon.
Flavour singlets in gauge theory as permutations
NASA Astrophysics Data System (ADS)
Kimura, Yusuke; Ramgoolam, Sanjaye; Suzuki, Ryo
2016-12-01
Gauge-invariant operators can be specified by equivalence classes of permutations. We develop this idea concretely for the singlets of the flavour group SO( N f ) in U( N c ) gauge theory by using Gelfand pairs and Schur-Weyl duality. The singlet operators, when specialised at N f = 6, belong to the scalar sector of N=4 SYM. A simple formula is given for the two-point functions in the free field limit of g Y M 2 = 0. The free two-point functions are shown to be equal to the partition function on a 2-complex with boundaries and a defect, in a topological field theory of permutations. The permutation equivalence classes are Fourier transformed to a representation basis which is orthogonal for the two-point functions at finite N c , N f . Counting formulae for the gauge-invariant operators are described. The one-loop mixing matrix is derived as a linear operator on the permutation equivalence classes.
Gauge theories under incorporation of a generalized uncertainty principle
Kober, Martin
2010-10-15
There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of matter field equations like the Dirac equation. If there is postulated invariance of such a generalized field equation under local gauge transformations, the usual covariant derivative containing the gauge potential has to be replaced by a generalized covariant derivative. This leads to a generalized interaction between the matter field and the gauge field as well as to an additional self-interaction of the gauge field. Since the existence of a minimal length scale seems to be a necessary assumption of any consistent quantum theory of gravity, the gauge principle is a constitutive ingredient of the standard model, and even gravity can be described as gauge theory of local translations or Lorentz transformations, the presented extension of gauge theories appears as a very important consideration.
Group actions and anomalies in gauge theories
NASA Astrophysics Data System (ADS)
Catenacci, R.; Pirola, G. P.; Martellini, Maurizio; Reina, Cesare
1986-05-01
The transformation properties are studied of the vacuum functional W(A) for chiral fermions in a gauge potential A under the group A×U(1)×R+ of gauge, chiral and scale transformations. The vacuum functional W is identified with a section of a G×U(1)×R+ line bundle over the space A of all gauge potentials. Known results on bundles carrying group actions give a simple and unifying clue to non-abelian, abelian chiral anomalies, as well as to trace anomalies. While the first are due to the twisting of a line bundle on A/G, the abelian chiral and trace anomalies are related to characters of U(1) and R+ respectively. Characters of U(1) are basically controlled by ``winding numbers'', i.e. again by topology. Opposite to these, trace anomalies seem to have little to do with topology, with the exception of two-dimensional theories. Also at Gruppo Nazionale di Fisica Matematica, CNR.
Frobenius-Chern-Simons gauge theory
NASA Astrophysics Data System (ADS)
Bonezzi, Roberto; Boulanger, Nicolas; Sezgin, Ergin; Sundell, Per
2017-02-01
Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H , we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an {{{Z}}2} -graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in (arXiv:1505.04957) as an off-shell formulation of the minimal bosonic four-dimensional higher spin gravity theory. If F is unital and the {{{Z}}2} -grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in H\\otimes F . We give a new model of this type based on a twisting of {C}≤ft[{{{Z}}2}× {{{Z}}4}\\right] , which leads to self-dual complexified gauge fields on AdS 4. If F is 3-graded, the FCS model can be truncated consistently as to contain no zero-form constraints on-shell. Two examples thereof are a twisting of {C}[{{({{{Z}}2})}3}] that yields the original model, and the Clifford algebra C{{\\ell}2n} which provides an FCS formulation of the bosonic Konstein-Vasiliev model with gauge algebra hu≤ft({{4}n-1},0\\right) .
Chaos in Chiral Condensates in Gauge Theories
NASA Astrophysics Data System (ADS)
Hashimoto, Koji; Murata, Keiju; Yoshida, Kentaroh
2016-12-01
Assigning a chaos index for dynamics of generic quantum field theories is a challenging problem because the notion of a Lyapunov exponent, which is useful for singling out chaotic behavior, works only in classical systems. We address the issue by using the AdS /CFT correspondence, as the large Nc limit provides a classicalization (other than the standard ℏ→0 ) while keeping nontrivial quantum condensation. We demonstrate the chaos in the dynamics of quantum gauge theories: The time evolution of homogeneous quark condensates ⟨q ¯q ⟩ and ⟨q ¯γ5q ⟩ in an N =2 supersymmetric QCD with the S U (Nc) gauge group at large Nc and at a large 't Hooft coupling λ ≡NcgYM2 exhibits a positive Lyapunov exponent. The chaos dominates the phase space for energy density E ≳(6 ×1 02)×mq4(Nc/λ2), where mq is the quark mass. We evaluate the largest Lyapunov exponent as a function of (Nc,λ ,E ) and find that the N =2 supersymmetric QCD is more chaotic for smaller Nc.
Gauge invariance and radiative corrections in an extra dimensional theory
NASA Astrophysics Data System (ADS)
Novales-Sánchez, H.; Toscano, J. J.
2011-04-01
The gauge structure of the four dimensional effective theory originated in a pure five dimensional Yang-Mills theory compactified on the orbifold S1 /Z2, is discussed on the basis of the BRST symmetry. If gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields and the four dimensional theory is gauge invariant only if the compactification is carried out by using curvatures as fundamental objects. The four dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters and the other by the excited ones. Within this context, a gauge-fixing procedure to quantize the KK modes that is covariant under the first type of gauge transformations is shown and the ghost sector induced by the gauge-fixing functions is presented. If the gauge parameters are confined to the usual four dimensional space-time, the known result in the literature is reproduced with some minor variants, although it is emphasized that the excited KK modes are not gauge fields, but matter fields transforming under the adjoint representation of SU4(N). A calculation of the one-loop contributions of the excited KK modes of the SUL(2) gauge group on the off-shell W+W-V, with V a photon or a Z boson, is exhibited. Such contributions are free of ultraviolet divergences and well-behaved at high energies.
Nonquadratic gauge fixing and ghosts for gauge theories on the hypersphere
Brandt, F. T.; McKeon, D. G. C.
2011-10-15
It has been suggested that using a gauge fixing Lagrangian that is not quadratic in a gauge fixing condition is most appropriate for gauge theories formulated on a hypersphere. We reexamine the appropriate ghost action that is to be associated with gauge fixing, applying a technique that has been used for ensuring that the propagator for a massless spin-two field is transverse and traceless. It is shown that this nonquadratic gauge fixing Lagrangian leads to two pair of complex Fermionic ghosts and two Bosonic real ghosts.
Quantum cohomology and quantum hydrodynamics from supersymmetric quiver gauge theories
NASA Astrophysics Data System (ADS)
Bonelli, Giulio; Sciarappa, Antonio; Tanzini, Alessandro; Vasko, Petr
2016-11-01
We study the connection between N = 2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D-type and discuss how they describe the quantum cohomology of the corresponding Nakajima's quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix.
Two-dimensional lattice gauge theories with superconducting quantum circuits
Marcos, D.; Widmer, P.; Rico, E.; Hafezi, M.; Rabl, P.; Wiese, U.-J.; Zoller, P.
2014-01-01
A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability. PMID:25512676
Two-dimensional lattice gauge theories with superconducting quantum circuits
NASA Astrophysics Data System (ADS)
Marcos, D.; Widmer, P.; Rico, E.; Hafezi, M.; Rabl, P.; Wiese, U.-J.; Zoller, P.
2014-12-01
A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.
Two-dimensional lattice gauge theories with superconducting quantum circuits
Marcos, D.; Widmer, P.; Rico, E.; Hafezi, M.; Rabl, P.; Wiese, U.-J.; Zoller, P.
2014-12-15
A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.
Two-dimensional lattice gauge theories with superconducting quantum circuits.
Marcos, D; Widmer, P; Rico, E; Hafezi, M; Rabl, P; Wiese, U-J; Zoller, P
2014-12-01
A quantum simulator of [Formula: see text] lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.
Generating functionals for Green's functions in gauge field theories
Bordag, M.; Kaschlun, L.; Matveev, V.A.; Robaschik, D.
1987-09-01
The structure of the generating functional of the one-particle-irreducible Green's functions in gauge field theories is investigated. Both axial as well as covariant gauge conditions are considered. For both cases, the general structure of the functionals is obtained, and a functional expansion with respect to nonlocal operators is given. The appearance of gauge-dependent operators in the case of the covariant gauge follows in a natural manner from the structure of the corresponding functional.
SUPERSYMMETRIC INSTANTON CALCULUS: Gauge theories with matter
NASA Astrophysics Data System (ADS)
Novikov, V. A.; Shifman, M. A.; Vainshtein, A. I.; Zakharov, V. I.
Within the framework of gauge SUSY theories we discuss correlation functions of the type (W2(x),S2(0)) where S is the chiral matter superfield (in the one-flavor model). SUSY implies that these correlation functions do not depend on coordinates and vanish identically in perturbation theory. We develop a technique for the systematic calculation of instanton effects. It is shown that even in the limit x → 0 the correlation functions at hand are not saturated by small-size instantons with radius ρ ˜ x; a contribution of the same order of magnitude comes from the instantons of characteristic size ρ ˜ l/v (v is the vacuum expectation value of the scalar field, and we concentrate on the models with v > Λ where Λ is the scale parameter fixing the running gauge coupling constant). If v > Λ both types of instantons can be consistently taken into account. The computational formalism proposed is explicitly supersymmetric and uses the language of instanton-associated superfields. We demonstrate, in particular, that one can proceed to a new variable, ρinv, which can be naturally considered as a supersymmetric generalization of the instanton radius. Unlike the ordinary radius ρ, this variable is invariant under the SUSY transformations. If one uses ρinv instead of ρ the expressions for the instanton contribution can be rewritten in the form saturated by the domain ρ2inv=0. The cluster decomposition as well as x-independence of the correlation functions considered turn out to be obvious in this formalism.
Light-cone Wilson loop in classical lattice gauge theory
NASA Astrophysics Data System (ADS)
Laine, M.; Rothkopf, A.
2013-07-01
The transverse broadening of an energetic jet passing through a non-Abelian plasma is believed to be described by the thermal expectation value of a light-cone Wilson loop. In this exploratory study, we measure the light-cone Wilson loop with classical lattice gauge theory simulations. We observe, as suggested by previous studies, that there are strong interactions already at short transverse distances, which may lead to more efficient jet quenching than in leading-order perturbation theory. We also verify that the asymptotics of the Wilson loop do not change qualitatively when crossing the light cone, which supports arguments in the literature that infrared contributions to jet quenching can be studied with dimensionally reduced simulations in the space-like domain. Finally we speculate on possibilities for full four-dimensional lattice studies of the same observable, perhaps by employing shifted boundary conditions in order to simulate ensembles boosted by an imaginary velocity.
Fermion frontiers in vector lattice gauge theories: Proceedings. Volume 8
1998-11-01
The inclusion of fermions into simulations of lattice gauge theories is very difficult both theoretically and numerically. With the presence of Teraflops-scale computers for lattice gauge theory, the authors wanted a forum to discuss new approaches to lattice fermions. The workshop concentrated on approaches which are ripe for study on such large machines. Although lattice chiral fermions are vitally important to understand, there is not technique at hand which is viable on these Teraflops-scale machines for real-world problems. The discussion was therefore focused on recent developments and future prospects for QCD-like theories. For the well-known fermion formulations, the Aoki phase in Wilson fermions, novelties of U{sub A}(1) symmetry and the {eta}{prime} for staggered fermions and new approaches for simulating the determinant for Wilson fermions were discussed. The newer domain-wall fermion formulation was reviewed, with numerical results given by many speakers. The fermion proposal of Friedberg, Lee and Pang was introduced. They also were able to compare and contrast the dependence of QCD and QCD-like SUSY theories on the number of quark flavors. These proceedings consist of several transparencies and a summary page from each speaker. This should serve to outline the major points made in each talk.
Exact partition functions for gauge theories on Rλ3
NASA Astrophysics Data System (ADS)
Wallet, Jean-Christophe
2016-11-01
The noncommutative space Rλ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of Rλ3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.
Parity anomalies in gauge theories in 2 + 1 dimensions
Rao, S.; Yahalom, R.
1986-01-01
We show that the introduction of massless fermions in an abelian gauge theory in 2+1 dimensions does not lead to any parity anomaly despite a non-commutativity of limits in the structure function of the odd part of the vacuum polarization tensor. However, parity anomaly does exist in non-abelian theories due to a conflict between gauge invariance under large gauge transformations and the parity symmetry. 6 refs.
Non-Abelian gauge theory on q-Quantum spaces
Schraml, Stefan L.
2002-08-23
Gauge theories on q-deformed spaces are constructed using covariant derivatives. For this purpose a ''vielbein'' is introduced, which transforms under gauge transformations. The non-Abelian case is treated by establishing a connection to gauge theories on commutative spaces, i.e. by a Seiberg-Witten map. As an example we consider the Manin plane. Remarks are made concerning the relation between covariant coordinates and covariant derivatives.
Origin of Mass Hierarchies in Gauge Theories
NASA Astrophysics Data System (ADS)
Cvetic, Mirjam
composites which carry four flavors. We study the origin of this hierarchy in the context of a supersymmetric vector-like gauge theory. We show that for the case of such a supersymmetric vector-like theory, the Vafa-Witten constraint for the conservation of the global symmetries does not apply. Within the elementary Higgs field approach we show that the desired solution for the mass matrix emerges as an interplay between certain hard terms of the Higgs potential, which respect the global symmetry SU(4)(,L) x SU(4)(,R) of four flavors, and the soft terms, which respect the gauge symmetry SU(2)(,L)('e+(mu)) x SU(2)(,R)('e+(mu)). Some of the soft terms are of nonperturbative origin, while some are induced radiatively. The proper inter- and intra -family hierarchy as well as the desired Cabibbo mixing angles can be reproduced, but the results depends on the parameters of the Higgs potential.
Canonical Bose gas simulations with stochastic gauges.
Drummond, P D; Deuar, P; Kheruntsyan, K V
2004-01-30
A technique to simulate the grand canonical ensembles of interacting Bose gases is presented. Results are generated for many temperatures by averaging over energy-weighted stochastic paths, each corresponding to a solution of coupled Gross-Pitaevskii equations with phase noise. The stochastic gauge method used relies on an off-diagonal coherent-state expansion, thus taking into account all quantum correlations. As an example, the second-order spatial correlation function and momentum distribution for an interacting 1D Bose gas are calculated.
National Computational Infrastructure for Lattice Gauge Theory
Reed, Daniel, A
2008-05-30
In this document we describe work done under the SciDAC-1 Project National Computerational Infrastructure for Lattice Gauge Theory. The objective of this project was to construct the computational infrastructure needed to study quantim chromodynamics (QCD). Nearly all high energy and nuclear physicists in the United States working on the numerical study of QCD are involved in the project, as are Brookhaven National Laboratory (BNL), Fermi National Accelerator Laboratory (FNAL), and Thomas Jefferson National Accelerator Facility (JLab). A list of the serior participants is given in Appendix A.2. The project includes the development of community software for the effective use of the terascale computers, and the research and development of commodity clusters optimized for the study of QCD. The software developed as part of this effort is pubicly available, and is being widely used by physicists in the United States and abroad. The prototype clusters built with SciDAC-1 fund have been used to test the software, and are available to lattice guage theorists in the United States on a peer reviewed basis.
Phase transitions in Abelian lattice gauge theories
NASA Astrophysics Data System (ADS)
Cheluvaraja, Srinath
2000-02-01
We study the phase transition in the U (1) lattice gauge theory using the Wilson-Polyakov line as the order parameter. The Wilson-Polyakov line remains very small at strong coupling and becomes non-zero at weak coupling, signalling a confinement-to-deconfinement phase transition. The decondensation of monopole loops is responsible for this phase transition. A finite size scaling analysis of the susceptibility of the Wilson line gives a ratio for icons/Journals/Common/gamma" ALT="gamma" ALIGN="TOP"/> /icons/Journals/Common/nu" ALT="nu" ALIGN="TOP"/> which is quite close to the corresponding value in the three-dimensional planar model. A scaling behaviour of the monopole loop distribution function is also established at the point of the second-order phase transition. A measurement of the plaquette susceptibility at the transition point shows that it does not scale with the four-dimensional volume as is expected of a first-order bulk transition.
Aspects of supersymmetric gauge theory and string theory
NASA Astrophysics Data System (ADS)
Huang, Minxin
This thesis consists of two parts. In the first part we study some topics in N = 1 supersymmeric gauge theory and the relation to matrix models. We review the relevant non-perturbative techniques for computing effective superpotential, such as Seiberg-Witten curve. Then we review the proposal of Dijkgraaf and Vafa that relates the glueball superpotentials to the computation in matrix models. We then consider a case of multi-trace superpotential. We perform the perturbative computation of glueball superpotential in this case and explain the subtlety in identifying the glueball superfield. We also use these techniques to study phases of N = 1 gauge theory with flavors. In the second part we study topics in AdS/CFT correspondence and its plane wave limit. We review the plane wave geometry and BMN operators that corresponding to string modes. Then we study string interactions in the case of a highly curved plane wave background, and demonstrate the agreements between calculations of string interaction amplitudes in the two dual theories. Finally we study D3-brane giant gravitons and open string attached to them. Giant gravitons are non-perturbative objects that have very large R-charge.
Lepton violating double β decay in modern gauge theories
NASA Astrophysics Data System (ADS)
Vergados, J. D.
1981-08-01
The neutrinoless lepton violating double β decay is investigated in the context of modern gauge theories, whereby it is mediated by a Majorana neutrino. Transition operators appropriate for calculations of the relevant nuclear matrix elements are constructed. In addition, some of the approximations of the pregauge theories of double β decay are investigated. Explicit shell model calculations are performed in the case of the A=48 system. [RADIOACTIVITY Double β decay. Gauge theories. Majorana neutrinos. Lepton nonconservation. Shell model calculations.
Localization of Gauge Theories on the Three-Sphere
NASA Astrophysics Data System (ADS)
Yaakov, Itamar
We describe the application of localization techniques to the path integral for supersymmetric gauge theories in three dimensions. The localization procedure reduces the computation of the expectation value of BPS observables to a calculation in a matrix model. We describe the ingredients of this model for a general quiver gauge theory and the incorporation of supersymmetric deformations and observables. We use the matrix model expressions to test several duality conjectures for supersymmetric gauge theories. We perform tests of mirror symmetry of three-dimensional quiver gauge theories and of Seiberg-like dualities. Specifically, we explicitly show that the partition functions of the dual pairs, which are highly nontrivial functions of the deformations, agree. We describe extensions of these dualities which can be inferred from the form of the partition functions. We review the application of the matrix model to the study of renormalization group flow and the space of conformal field theories in three dimensions.
Tensor Networks for Lattice Gauge Theories with Continuous Groups
NASA Astrophysics Data System (ADS)
Tagliacozzo, L.; Celi, A.; Lewenstein, M.
2014-10-01
We discuss how to formulate lattice gauge theories in the tensor-network language. In this way, we obtain both a consistent-truncation scheme of the Kogut-Susskind lattice gauge theories and a tensor-network variational ansatz for gauge-invariant states that can be used in actual numerical computations. Our construction is also applied to the simplest realization of the quantum link models or gauge magnets and provides a clear way to understand their microscopic relation with the Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge-invariant operators that modify continuously Rokhsar-Kivelson wave functions and can be used to extend the phase diagrams of known models. As an example, we characterize the transition between the deconfined phase of the Z2 lattice gauge theory and the Rokhsar-Kivelson point of the U (1 ) gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.
Solution of quantum integrable systems from quiver gauge theories
NASA Astrophysics Data System (ADS)
Dorey, Nick; Zhao, Peng
2017-02-01
We construct new integrable systems describing particles with internal spin from four-dimensional N = 2 quiver gauge theories. The models can be quantized and solved exactly using the quantum inverse scattering method and also using the Bethe/Gauge correspondence.
Finite-size scaling tests for SU(3) lattice gauge theory with color sextet fermions
DeGrand, Thomas
2009-12-01
The observed slow running of the gauge coupling in SU(3) lattice gauge theory with two flavors of color sextet fermions naturally suggests it is a theory with one relevant coupling, the fermion mass, and that at zero mass correlation functions decay algebraically. I perform a finite-size scaling study on simulation data at two values of the bare gauge coupling with this assumption and observe a common exponent for the scaling of the correlation length with the fermion mass, y{sub m}{approx}1.5. An analysis of the scaling of valence Dirac eigenvalues at one of these bare couplings produces a similar number.
NASA Astrophysics Data System (ADS)
Roiban, Radu; Spradlin, Marcus; Volovich, Anastasia
2011-11-01
This issue aims to serve as an introduction to our current understanding of the structure of scattering amplitudes in gauge theory, an area which has seen particularly rapid advances in recent years following decades of steady progress. The articles contained herein provide a snapshot of the latest developments which we hope will serve as a valuable resource for graduate students and other scientists wishing to learn about the current state of the field, even if our continually evolving understanding of the subject might soon render this compilation incomplete. Why the fascination with scattering amplitudes, which have attracted the imagination and dedicated effort of so many physicists? Part of it stems from the belief, supported now by numerous examples, that unexpected simplifications of otherwise apparently complicated calculations do not happen by accident. Instead they provide a strong motivation to seek out an underlying explanation. The insight thereby gained can subsequently be used to make the next class of seemingly impossible calculations not only possible, but in some cases even trivial. This two-pronged strategy of exploring and exploiting the structure of gauge theory amplitudes appeals to a wide audience from formal theorists interested in mathematical structure for the sake of its own beauty to more phenomenologically-minded physicists eager to speed up the next generation of analysis software. Understandably it is the maximally supersymmetric 𝒩 = 4 Yang-Mills theory (SYM) which has the simplest structure and has correspondingly received the most attention. Rarely in theoretical physics are we fortunate enough to encounter a toy model which is simple enough to be solved completely yet rich enough to possess interesting non-trivial structure while simultaneously, and most importantly, being applicable (even if only as a good approximation) to a wide range of 'real' systems. The canonical example in quantum mechanics is of course the harmonic
Scale-invariant gauge theories of gravity: Theoretical foundations
NASA Astrophysics Data System (ADS)
Lasenby, A. N.; Hobson, M. P.
2016-09-01
We consider the construction of gauge theories of gravity, focussing in particular on the extension of local Poincaré invariance to include invariance under local changes of scale. We work exclusively in terms of finite transformations, which allow for a more transparent interpretation of such theories in terms of gauge fields in Minkowski spacetime. Our approach therefore differs from the usual geometrical description of locally scale-invariant Poincaré gauge theory (PGT) and Weyl gauge theory (WGT) in terms of Riemann-Cartan and Weyl-Cartan spacetimes, respectively. In particular, we reconsider the interpretation of the Einstein gauge and also the equations of motion of matter fields and test particles in these theories. Inspired by the observation that the PGT and WGT matter actions for the Dirac field and electromagnetic field have more general invariance properties than those imposed by construction, we go on to present a novel alternative to WGT by considering an "extended" form for the transformation law of the rotational gauge field under local dilations, which includes its "normal" transformation law in WGT as a special case. The resulting "extended" Weyl gauge theory (eWGT) has a number of interesting features that we describe in detail. In particular, we present a new scale-invariant gauge theory of gravity that accommodates ordinary matter and is defined by the most general parity-invariant eWGT Lagrangian that is at most quadratic in the eWGT field strengths, and we derive its field equations. We also consider the construction of PGTs that are invariant under local dilations assuming either the "normal" or "extended" transformation law for the rotational gauge field, but show that they are special cases of WGT and eWGT, respectively.
Generally covariant vs. gauge structure for conformal field theories
Campigotto, M.; Fatibene, L.
2015-11-15
We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must be introduced as gauge transformations (affecting fields but not spacetime point) and then discuss special structures implied by the splitting of the conformal group. -- Highlights: •Both a natural and a gauge natural structure for conformal gravity are defined. •Global properties and natural lift of spacetime transformations are described. •The possible definitions of physical state are considered and discussed. •The gauge natural theory has less physical states than the corresponding natural one. •The dynamics forces to prefer the gauge natural structure over the natural one.
Non-Abelian gauge field theory in scale relativity
Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry
2006-03-15
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ''scale-space.'' We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.
A classical theory of continuous spin and hidden gauge invariance
Zoller, D.
1991-12-31
We present a classical higher derivative point particle theory whose quantization gives Wigner`s continuous spin representation of the Poincare group. Although the theory is not reparameterization invariant in the usual sense, it does possess a hidden gauge invariance that provides a non-local representation of the reparameterization group. The Hamiltonian of the theory does not vanish and its value is the continuous spin parameter. The theory presented here represents the simplest example of a wide class of higher derivative theories possessing a hidden gauge invariance.
A classical theory of continuous spin and hidden gauge invariance
Zoller, D.
1991-01-01
We present a classical higher derivative point particle theory whose quantization gives Wigner's continuous spin representation of the Poincare group. Although the theory is not reparameterization invariant in the usual sense, it does possess a hidden gauge invariance that provides a non-local representation of the reparameterization group. The Hamiltonian of the theory does not vanish and its value is the continuous spin parameter. The theory presented here represents the simplest example of a wide class of higher derivative theories possessing a hidden gauge invariance.
Large field inflation models from higher-dimensional gauge theories
NASA Astrophysics Data System (ADS)
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-01
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model turns out to be the most preferred model in this framework.
Large field inflation models from higher-dimensional gauge theories
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-23
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante’s Inferno model turns out to be the most preferred model in this framework.
SU{sub {ital q}}(2) lattice gauge theory
Bimonte, G.; Stern, A.; Vitale, P.
1996-07-01
We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, the symmetry gets promoted to a quantum group gauge symmetry. The theory depends on two parameters: the deformation parameter {lambda} and the lattice spacing {ital a}. We show that the system of Kogut and Susskind is recovered when {lambda}{r_arrow}0, while QCD is recovered in the continuum limit (for any {lambda}). We, thus, have the possibility of having a two-parameter regularization of QCD. {copyright} {ital 1996 The American Physical Society.}
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
NASA Astrophysics Data System (ADS)
Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp; Nigg, Daniel; Erhard, Alexander; Heyl, Markus; Hauke, Philipp; Dalmonte, Marcello; Monz, Thomas; Zoller, Peter; Blatt, Rainer
2016-06-01
Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman’s idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments—the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer.
Martinez, Esteban A; Muschik, Christine A; Schindler, Philipp; Nigg, Daniel; Erhard, Alexander; Heyl, Markus; Hauke, Philipp; Dalmonte, Marcello; Monz, Thomas; Zoller, Peter; Blatt, Rainer
2016-06-23
Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman's idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments-the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.
Loop calculus for lattice gauge theories
Gambini, R.; Leal, L.; Trias, A.
1989-05-15
Hamiltonian calculations are performed using a loop-labeled basis where the full set of identities for the SU(/ital N/) gauge models has been incorporated. The loops are classified as clusterlike structures and the eigenvalue problem leads to a linear set of finite-difference equations easily amenable to numerical treatment. Encouraging results are reported for SU(2) at spatial dimension 2.
Conformal Orbifold Partition Functions from Topologically Massive Gauge Theory
NASA Astrophysics Data System (ADS)
Castelo Ferreira, Pedro; Kogan, Ian I.; Szabo, Richard J.
2002-04-01
We continue the development of the topological membrane approach to open and unoriented string theories. We study orbifolds of topologically massive gauge theory defined on the geometry [0,1] × Σ, where Σ is a generic compact Riemann surface. The orbifold operations are constructed by gauging the discrete symmetries of the bulk three-dimensional field theory. Multi-loop bosonic string vacuum amplitudes are thereby computed as bulk correlation functions of the gauge theory. It is shown that the three-dimensional correlators naturally reproduce twisted and untwisted sectors in the case of closed worldsheet orbifolds, and Neumann and Dirichlet boundary conditions in the case of open ones. The bulk wavefunctions are used to explicitly construct the characters of the underlying extended Kac-Moody group for arbitrary genus. The correlators for both the original theory and its orbifolds give the expected modular invariant statistical sums over the characters.
Perturbative quantum gravity as a double copy of gauge theory.
Bern, Zvi; Carrasco, John Joseph M; Johansson, Henrik
2010-08-06
In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.
Relational mechanics as a gauge theory
NASA Astrophysics Data System (ADS)
Ferraro, Rafael
2016-02-01
Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. The procedure implies the addition of compensating terms to the kinetic energy, in such a way that the resulting equations of motion are valid in any frame. The compensating terms provide inertial forces depending on the total momentum P, intrinsic angular momentum J and intrinsic inertia tensor I. Therefore, the privileged frames where Newton's equations are valid ( Newtonian frames) are completely determined by the matter distribution of the universe ( Machianization). At the Hamiltonian level, the gauge invariance leads to first class constraints that remove those degrees of freedom that make no sense once the absolute space has been eliminated. This reformulation of classical mechanics is entirely relational, since it is a dynamics for the distances between particles. It is also Machian, since the rotation of the rest of the universe produces centrifugal effects. It then provides a new perspective to consider the foundational ideas of general relativity, like Mach's principle and the weak equivalence principle. With regard to the concept of time, the absence of an absolute time is known to be a characteristic of parametrized systems. Furthermore, the scale invariance of those parametrized systems whose potentials are inversely proportional to the squared distances can be also gauged by introducing another compensating term associated with the intrinsic virial G ( shape-dynamics).
Gauge theories on hyperbolic spaces and dual wormhole instabilities
Buchel, Alex
2004-09-15
We study supergravity duals of strongly coupled four-dimensional gauge theories formulated on compact quotients of hyperbolic spaces. The resulting background geometries are represented by Euclidean wormholes, which complicate establishing the precise gauge theory/string theory correspondence dictionary. These backgrounds suffer from the nonperturbative instabilities arising from the D3D3-bar pair-production in the background four-form potential. We discuss conditions for suppressing this Schwingerlike instability. We find that Euclidean wormholes arising in this construction develop a naked singularity before they can be stabilized.
The Seiberg-Witten map for noncommutative gauge theories
Cerchiai, B.L.; Pasqua, A.F.; Zumino, B.
2002-06-26
The Seiberg-Witten map for noncommutative Yang-Mills theories is studied and methods for its explicit construction are discussed which are valid for any gauge group. In particular the use of the evolution equation is described in some detail and its relation to the cohomological approach is elucidated. Cohomological methods which are applicable to gauge theories requiring the Batalin-Vilkoviskii antifield formalism are briefly mentioned. Also, the analogy of the Weyl-Moyal star product with the star product of opestring field theory and possible ramifications of this analogy are briefly mentioned.
NASA Astrophysics Data System (ADS)
Pinto, Carlos
2016-03-01
We analyze the interplay between gauge fixing and boundary conditions in two-dimensional U(1) lattice gauge theory. We show on the basis of a general argument that periodic boundary conditions result in an ill-defined weak coupling approximation but that the approximation can be made well-defined if the boundaries are fixed to zero. We confirm this result in the particular case of the Feynman gauge. We show that the zero momentum mode divergence in the propagator that appears in the Feynman gauge vanishes when the weak coupling approximation is well-defined. In addition we obtain exact results (for arbitrary coupling), including finite size corrections, for the partition function and for general one-point and two-point functions in the axial gauge under both periodic and zero boundary conditions and confirm these results numerically. The dependence of these objects on both lattice size and coupling constant is investigated using specific examples. These exact results may provide insight into similar gauge fixing issues in more complex models.
Ice limit of Coulomb gauge Yang-Mills theory
Heinzl, T.; Ilderton, A.; Langfeld, K.; Lavelle, M.; McMullan, D.
2008-10-01
In this paper we describe gauge invariant multiquark states generalizing the path integral framework developed by Parrinello, Jona-Lasinio, and Zwanziger to amend the Faddeev-Popov approach. This allows us to produce states such that, in a limit which we call the ice limit, fermions are dressed with glue exclusively from the fundamental modular region associated with Coulomb gauge. The limit can be taken analytically without difficulties, avoiding the Gribov problem. This is illustrated by an unambiguous construction of gauge invariant mesonic states for which we simulate the static quark-antiquark potential.
RIKEN BNL RESEARCH CENTER WORKSHOP ON GAUGE-INVARIANT VARIABLES IN GAUGE THEORIES, VOLUME 20
VAN BAAL,P.; ORLAND,P.; PISARSKI,R.
2000-06-01
This four-day workshop focused on the wide variety of approaches to the non-perturbative physics of QCD. The main topic was the formulation of non-Abelian gauge theory in orbit space, but some other ideas were discussed, in particular the possible extension of the Maldacena conjecture to nonsupersymmetric gauge theories. The idea was to involve most of the participants in general discussions on the problem. Panel discussions were organized to further encourage debate and understanding. Most of the talks roughly fell into three categories: (1) Variational methods in field theory; (2) Anti-de Sitter space ideas; (3) The fundamental domain, gauge fixing, Gribov copies and topological objects (both in the continuum and on a lattice). In particular some remarkable progress in three-dimensional gauge theories was presented, from the analytic side by V.P. Nair and mostly from the numerical side by O. Philipsen. This work may ultimately have important implications for RHIC experiments on the high-temperature quark-gluon plasma.
Discretized Abelian Chern-Simons gauge theory on arbitrary graphs
NASA Astrophysics Data System (ADS)
Sun, Kai; Kumar, Krishna; Fradkin, Eduardo
2015-09-01
In this paper, we show how to discretize the Abelian Chern-Simons gauge theory on generic planar lattices/graphs (with or without translational symmetries) embedded in arbitrary two-dimensional closed orientable manifolds. We find that, as long as a one-to-one correspondence between vertices and faces can be defined on the graph such that each face is paired up with a neighboring vertex (and vice versa), a discretized Abelian Chern-Simons theory can be constructed consistently. We further verify that all the essential properties of the Chern-Simons gauge theory are preserved in the discretized setup. In addition, we find that the existence of such a one-to-one correspondence is not only a sufficient condition for discretizing a Chern-Simons gauge theory but, for the discretized theory to be nonsingular and to preserve some key properties of the topological field theory, this correspondence is also a necessary one. A specific example will then be provided, in which we discretize the Abelian Chern-Simons gauge theory on a tetrahedron.
Theory and renormalization of the gauge-invariant effective action
NASA Astrophysics Data System (ADS)
Hart, C. F.
1983-10-01
The different methods for constructing a gauge-invariant effective action (GIEA) for quantum non-Abelian gauge field theories proposed by 't Hooft, DeWitt, Boulware, and Abbott are all shown to be equivalent. In the course of proving this equivalence we show how to extend the usual background-field method so as to construct what may be considered the prototypical GIEA and discuss in some detail the invariance and gauge transformation properties of both the usual theory and the new theory using the GIEA. All solutions to the GIEA field equations are shown to be physical-being solutions to the usual field equations with an arbitrary gauge condition. The renormalization program based upon the GIEA is shown to differ from the standard theory and we outline the modifications which are needed in the present proof of renormalizability. In particular we prove that the physical renormalization is independent of any gauge-fixing choice. Finally, we prove that the S-matrix elements derived from the GIEA for an arbitrary background-field solution to the field equations are the same as those derived using the usual effective action.
Equivariant dimensional reduction and quiver gauge theories
NASA Astrophysics Data System (ADS)
Dolan, Brian P.; Szabo, Richard J.
2011-09-01
We review recent applications of equivariant dimensional reduction techniques to the construction of Yang-Mills-Higgs-Dirac theories with dynamical mass generation and exactly massless chiral fermions.
Modified coupling procedure for the Poincare gauge theory of gravity
Kazmierczak, Marcin
2009-06-15
The minimal coupling procedure, which is employed in standard Yang-Mills theories, appears to be ambiguous in the case of gravity. We propose a slight modification of this procedure, which removes the ambiguity. Our modification justifies some earlier results concerning the consequences of the Poincare gauge theory of gravity. In particular, the predictions of the Einstein-Cartan theory with fermionic matter are rendered unique.
Algebraic isomorphism in two-dimensional anomalous gauge theories
Carvalhaes, C.G.; Natividade, C.P.
1997-08-01
The operator solution of the anomalous chiral Schwinger model is discussed on the basis of the general principles of Wightman field theory. Some basic structural properties of the model are analyzed taking a careful control on the Hilbert space associated with the Wightman functions. The isomorphism between gauge noninvariant and gauge invariant descriptions of the anomalous theory is established in terms of the corresponding field algebras. We show that (i) the {Theta}-vacuum representation and (ii) the suggested equivalence of vector Schwinger model and chiral Schwinger model cannot be established in terms of the intrinsic field algebra. {copyright} 1997 Academic Press, Inc.
BRST formulation of Chern-Simons gauge theory coupled to matter fields
Shin, H.; Kim, W.; Kim, J. ); Park, Y. )
1992-09-15
We study the Abelian Chern-Simons gauge theory coupled to a complex scalar field in the covariant gauge. By introducing the Becchi-Rouet-Stora-Tyutin formulation, it is shown that fractional spin also appears in the covariant gauge.
Coulomb branches for rank 2 gauge groups in 3 d N=4 gauge theories
NASA Astrophysics Data System (ADS)
Hanany, Amihay; Sperling, Marcus
2016-08-01
The Coulomb branch of 3-dimensional N=4 gauge theories is the space of bare and dressed BPS monopole operators. We utilise the conformal dimension to define a fan which, upon intersection with the weight lattice of a GNO-dual group, gives rise to a collection of semi-groups. It turns out that the unique Hilbert bases of these semi-groups are a sufficient, finite set of monopole operators which generate the entire chiral ring. Moreover, the knowledge of the properties of the minimal generators is enough to compute the Hilbert series explicitly. The techniques of this paper allow an efficient evaluation of the Hilbert series for general rank gauge groups. As an application, we provide various examples for all rank two gauge groups to demonstrate the novel interpretation.
Runoff simulation using radar and rain gauge data
NASA Astrophysics Data System (ADS)
Liu, X. Y.; Mao, J. T.; Zhu, Y. J.; Li, J. R.
2003-03-01
The conceptual rainfall-runoff model TOPMODEL is used to simulate runoffs of the Meishan and Nianyushan catchments during the summers of 1998 and 1999 in the GAME/HUBEX (GEWEX Asia Monsoon Experiment /HUAIHE River Basin Experiment) project. The rainfall distributions are estimated by weather radar and rain gauge networks according to different methods. Observed and simulated runoffs are compared and analyzed for both catchments. Results show that (1) the runoff of the catchment is best simulated by radar data combined with rain gauge network data from inside the catchment, and (2) the rainfall estimated by radar adjusted by a few rain gauges outside the catchment can be used to simulate runoff equally as well as using the dense rain gauge network alone.
Worldsheet theory of light-cone gauge noncritical strings on higher genus Riemann surfaces
NASA Astrophysics Data System (ADS)
Ishibashi, Nobuyuki; Murakami, Koichi
2016-06-01
It is possible to formulate light-cone gauge string field theory in noncritical dimensions. Such a theory corresponds to conformal gauge worldsheet theory with nonstandard longitudinal part. We study the longitudinal part of the worldsheet theory on higher genus Riemann surfaces. The results in this paper shall be used to study the dimensional regularization of light-cone gauge string field theory.
BRST detour quantization: Generating gauge theories from constraints
Cherney, D.; Waldron, A.; Latini, E.
2010-06-15
We present the Becchi-Rouet-Stora-Tyutin (BRST) cohomologies of a class of constraint (super) Lie algebras as detour complexes. By interpreting the components of detour complexes as gauge invariances, Bianchi identities, and equations of motion, we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. Along with general results, we give details for three of these theories which correspond to gauge invariant spinning particle models of totally symmetric, antisymmetric, and Kaehler antisymmetric forms. In particular, we give details of our recent announcement of a (p,q)-form Kaehler electromagnetism. We also discuss how our results generalize to other special geometries.
Renormalization of vacuum expectation values in spontaneously broken gauge theories
NASA Astrophysics Data System (ADS)
Sperling, Marcus; Stöckinger, Dominik; Voigt, Alexander
2013-07-01
We compute one-loop and two-loop β-functions for vacuum expectation values (VEVs) in gauge theories. In R ξ gauge the VEVs renormalize differently from the respective scalar fields. We focus particularly on the origin and behaviour of this difference and show that it can be interpreted as the anomalous dimension of a certain scalar background field, leading to simple direct computation and qualitative understanding. The results are given for generic as well as supersymmetric gauge theories. These complement the set of well-known γ- and β-functions of Machacek/Vaughn. As an application, we compute the β-functions for VEVs and tan β in the MSSM, NMSSM, and E6SSM.
Abelian gauge theories on compact manifolds and the Gribov ambiguity
Kelnhofer, Gerald
2008-05-15
We study the quantization of Abelian gauge theories of principal torus bundles over compact manifolds with and without boundary. It is shown that these gauge theories suffer from a Gribov ambiguity originating in the nontriviality of the bundle of connections whose geometrical structure will be analyzed in detail. Motivated by the stochastic quantization approach, we propose a modified functional integral measure on the space of connections that takes the Gribov problem into account. This functional integral measure is used to calculate the partition function, Green's functions, and the field strength correlating functions in any dimension by using the fact that the space of inequivalent connections itself admits the structure of a bundle over a finite dimensional torus. Green's functions are shown to be affected by the nontrivial topology, giving rise to nonvanishing vacuum expectation values for the gauge fields.
Perturbation theory in supersymmetric QED: Infrared divergences and gauge invariance
NASA Astrophysics Data System (ADS)
Dine, Michael; Draper, Patrick; Haber, Howard E.; Haskins, Laurel Stephenson
2016-11-01
We study some aspects of perturbation theory in N =1 supersymmetric Abelian gauge theories with massive charged matter. In general gauges, infrared (IR) divergences and nonlocal behavior arise in one particle irreducible (1PI) diagrams, associated with a 1 /k4 term in the propagator for the vector superfield. We examine this structure in supersymmetric QED. The IR divergences are gauge dependent and must cancel in physical quantities like the electron pole mass. We demonstrate that cancellation takes place in a nontrivial way, amounting to a reorganization of the perturbative series from powers of e2 to powers of e . We also show how these complications are avoided in cases where a Wilsonian effective action can be defined.
Quantized vortices in interacting gauge theories
NASA Astrophysics Data System (ADS)
Butera, Salvatore; Valiente, Manuel; Ohberg, Patrik
2015-05-01
We consider a two-dimensional weakly interacting ultracold Bose gas whose constituents are two-level atoms. We study the effects of a synthetic density-dependent gauge field that arises from laser-matter coupling in the adiabatic limit with a laser configuration such that the single-particle vector potential corresponds to a constant synthetic magnetic field. We find a new type of current non-linearity in the Gross-Pitaevskii equation which affects the dynamics of the order parameter of the condensate. We investigate on the physical conditions that make the nucleation of a quantized vortex in the system energetically favourable with respect to the non rotating solution. Two different physical interpretations can be given to this new non linearity: firstly it can be seen as a local modification of the mean field coupling constant, whose value depends on the angular momentum of the condensate. Secondly, it can be interpreted as a density modulated angular velocity given to the cloud. We analyze the physical conditions that make a single vortex state energetically favourable. In the Thomas-Fermi limit, we show that the effect of the new nonlinearity is to induce a rotation to the condensate, where the transition from non-rotating to rotating depends on the density of the cloud. The authors acknowledge support from CM-DTC and EPSRC.
Quantized vortices in interacting gauge theories
NASA Astrophysics Data System (ADS)
Butera, Salvatore; Valiente, Manuel; Öhberg, Patrik
2016-01-01
We consider a two-dimensional weakly interacting ultracold Bose gas whose constituents are two-level atoms. We study the effects of a synthetic density-dependent gauge field that arises from laser-matter coupling in the adiabatic limit with a laser configuration such that the single-particle zeroth-order vector potential corresponds to a constant synthetic magnetic field. We find a new exotic type of current nonlinearity in the Gross-Pitaevskii equation which affects the dynamics of the order parameter of the condensate. We investigate the rotational properties of this system in the Thomas-Fermi limit, focusing in particular on the physical conditions that make the existence of a quantized vortex in the system energetically favourable with respect to the non-rotating solution. We point out that two different physical interpretations can be given to this new nonlinearity: firstly it can be seen as a local modification of the mean field coupling constant, whose value depends on the angular momentum of the condensate. Secondly, it can be interpreted as a density modulated angular velocity given to the cloud. Looking at the problem from both of these viewpoints, we show that the effect of the new nonlinearity is to induce a rotation to the condensate, where the transition from non-rotating to rotating states depends on the density of the cloud.
On the solvability of two dimensional semigroup gauge theories
Varga, Peter
2010-06-15
We study the solvability of two dimensional semigroup gauge theories by Migdal's link elimination method. We determine certain conditions that ensure that the partition sum corresponding to the join of two plaquettes depends only on the holonomy around the boundary of the joined plaquettes. These conditions are checked for a few types of semigroups: 0-groups, cyclic, inverse symmetric, and Brandt semigroups.
Vacuum stability of asymptotically safe gauge-Yukawa theories
NASA Astrophysics Data System (ADS)
Litim, Daniel F.; Mojaza, Matin; Sannino, Francesco
2016-01-01
We study the phase diagram and the stability of the ground state for certain four-dimensional gauge-Yukawa theories whose high-energy behaviour is controlled by an interacting fixed point. We also provide analytical and numerical results for running couplings, their crossover scales, the separatrix, and the Coleman-Weinberg effective potential. Classical and quantum stability of the vacuum is established.
Hamiltonian flow in Coulomb gauge Yang-Mills theory
Leder, Markus; Reinhardt, Hugo; Pawlowski, Jan M.; Weber, Axel
2011-01-15
We derive a new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge. The flow equations for the static gluon and ghost propagators are solved under the assumption of ghost dominance within different diagrammatic approximations. The results are compared to those obtained in the variational approach and the reliability of the approximations is discussed.
Perturbative Quantum Gravity and its Relation to Gauge Theory.
Bern, Zvi
2002-01-01
In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on D-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input the gravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.
A gauge theory of gravity in curved phase-spaces
NASA Astrophysics Data System (ADS)
Castro, Carlos
2016-06-01
After a cursory introduction of the basic ideas behind Born’s Reciprocal Relativity theory, the geometry of the cotangent bundle of spacetime is studied via the introduction of nonlinear connections associated with certain nonholonomic modifications of Riemann-Cartan gravity within the context of Finsler geometry. A novel gauge theory of gravity in the 8D cotangent bundle T∗M of spacetime is explicitly constructed and based on the gauge group SO(6, 2) ×sR8 which acts on the tangent space to the cotangent bundle T(x,p)T∗M at each point (x,p). Several gravitational actions involving curvature and torsion tensors and associated with the geometry of curved phase-spaces are presented. We conclude with a brief discussion of the field equations, the geometrization of matter, quantum field theory (QFT) in accelerated frames, T-duality, double field theory, and generalized geometry.
Gauge Theories on the Coulomb Branch
NASA Astrophysics Data System (ADS)
Schwarz, John H.
We construct the world-volume action of a probe D3-brane in AdS5 × S5 with N units of flux. It has the field content, symmetries, and dualities of the U(1) factor of 𝒩 = 4 U(N + 1) super Yang-Mills theory, spontaneously broken to U(N) × U(1) by being on the Coulomb branch, with the massive fields integrated out. This motivates the conjecture that it is the exact effective action, called a highly effective action (HEA). We construct an SL(2, Z) multiplet of BPS soliton solutions of the D3-brane theory (the conjectured HEA) and show that they reproduce the electrically charged massive states that have been integrated out as well as magnetic monopoles and dyons. Their charges are uniformly spread on a spherical surface, called a soliton bubble, which is interpreted as a phase boundary.
Stringy Instantons and Quiver Gauge Theories
Florea, Bogdan; Kachru, Shamit; McGreevy, John; Saulina, Natalia
2006-10-24
We explore contributions to the 4D effective superpotential which arise from Euclidean D3 branes (''instantons'') that intersect space-filling D-branes. These effects can perturb the effective field theory on the space-filling branes by nontrivial operators composed of charged matter fields, changing the vacuum structure in a qualitative way in some examples. Our considerations are exemplified throughout by a careful study of a fractional brane configuration on a del Pezzo surface.
Gauge Theories and Spontaneous Symmetry Breaking.
1980-11-01
breaking spontaneous symmetric breaking , Higgs mechanism bifurcation problem RATr0ACT’fwwdhn om pea71 Ul nonmevi dumad #~lyb block Im.,) his report is a...field theories. It was felt that the symmetry breaking used by the physicists LiI (a procedure known as the Higgs mechanism) is not precisely a...feeling, after some discussions, that the symmctry breaking used by the phyalciuts (a procedure known as the Higgs mechanism) is not precisely a
Gauge theory in deformed mathcal{N} = (1, 1) superspace
NASA Astrophysics Data System (ADS)
Buchbinder, I. L.; Ivanov, E. A.; Lechtenfeld, O.; Samsonov, I. B.; Zupnik, B. M.
2008-09-01
We review the non-anticommutative Q-deformations of mathcal{N} = (1, 1) supersymmetric theories in four-dimensional Euclidean harmonic superspace. These deformations preserve chirality and harmonic Grassmann analyticity. The associated field theories arise as a low-energy limit of string theory in specific backgrounds and generalize the Moyal-deformed supersymmetric field theories. A characteristic feature of the Q-deformed theories is the half-breaking of supersymmetry in the chiral sector of the Euclidean superspace. Our main focus is on the chiral singlet Q-deformation, which is distinguished by preserving the SO(4) ˜ Spin(4) “Lorentz” symmetry and the SU(2) R-symmetry. We present the superfield and component structures of the deformed mathcal{N} = (1, 0) supersymmetric gauge theory as well as of hypermultiplets coupled to a gauge superfield: invariant actions, deformed transformation rules, and so on. We discuss quantum aspects of these models and prove their renormalizability in the Abelian case. For the charged hypermultiplet in an Abelian gauge superfield background we construct the deformed holomorphic effective action.
Gauge theories from D7-branes over vanishing 4-cycles
Franco, Sebastian; Torroba, Gonzalo; /SLAC /Stanford U., Phys. Dept.
2010-12-16
We study quiver gauge theories on D7-branes wrapped over vanishing holomorphic 4-cycles. We investigate how to incorporate O7-planes and/or flavor D7-branes, which are necessary to cancel anomalies. These theories are chiral, preserve four supercharges and exhibit very rich infrared dynamics. Geometric transitions and duality in the presence of O-planes are analyzed. We study the Higgs branch of these quiver theories, showing the emergence of fuzzy internal dimensions. This branch is related to noncommutative instantons on the divisor wrapped by the seven-branes. Our results have a natural application to the recently introduced F(uzz) limit of F-theory.
Euclidean quantum field theory: Curved spacetimes and gauge fields
NASA Astrophysics Data System (ADS)
Ritter, William Gordon
This thesis presents a new formulation of quantum field theory (QFT) on curved spacetimes, with definite advantages over previous formulations, and an introduction to the millennium prize problem on four-dimensional gauge theory. Our constructions are completely rigorous, making QFT on curved spacetimes into a subfield of mathematics, and we achieve the first analytic control over nonperturbative aspects of interacting theories on curved spacetimes. The success of Euclidean path integrals to capture nonperturbative aspects of QFT has been striking. The Euclidean path integral is the most accurate method of calculating strong-coupling effects in gauge theory (such as glueball masses). Euclidean methods are also useful in the study of black holes, as evidenced by the Hartle-Hawking calculation of black-hole radiance. From a mathematical point of view, on flat spacetimes the Euclidean functional integral provides the most elegant method of constructing examples of interacting relativistic field theories. Yet until now, the incredibly-useful Euclidean path integral had never been given a definitive mathematical treatment on curved backgrounds. It is our aim to rectify this situation. Along the way, we discover that the Dirac operator on an arbitrary Clifford bundle has a resolvent kernel which is the Laplace transform of a positive measure. In studying spacetime symmetries, we discover a new way of constructing unitary representations of noncompact Lie groups. We also define and explore an interesting notion of convergence for Laplacians. The same mathematical framework applies to scalar fields, fermions, and gauge fields. The later chapters are devoted to gauge theory. We present a rigorous, self-contained introduction to the subject, aimed at mathematicians and using the language of modern mathematics, with a view towards nonperturbative renormalization in four dimensions. The latter ideas are unfinished. A completion of the final chapter would imply the construction
Banerjee, D; Dalmonte, M; Müller, M; Rico, E; Stebler, P; Wiese, U-J; Zoller, P
2012-10-26
Using a Fermi-Bose mixture of ultracold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.
Fusion basis for lattice gauge theory and loop quantum gravity
NASA Astrophysics Data System (ADS)
Delcamp, Clement; Dittrich, Bianca; Riello, Aldo
2017-02-01
We introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2 + 1) dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin-network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel'd double of the gauge group, and can be readily "fused" together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi-local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse-graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin-network basis, in which it is much more complicated to account for electric excitations, i.e. for Gauß constraint violations, emerging at larger scales. Moreover, since the fusion basis comes equipped with a hierarchical structure, it readily provides the language to design states with sophisticated multi-scale structures. Another way to employ this hierarchical structure is to encode a notion of subsystems for lattice gauge theories and (2 + 1) gravity coupled to point particles. In a follow-up work, we have exploited this notion to provide a new definition of entanglement entropy for these theories.
The effective potential in nonconformal gauge theories
NASA Astrophysics Data System (ADS)
Brandt, F. T.; Chishtie, F. A.; McKeon, D. G. C.
2017-01-01
By using the renormalization group (RG) equation it has proved possible to sum logarithmic corrections to quantities that arise due to quantum effects in field theories. In particular, the effective potential V in the Standard Model in the limit that there are no massive parameters in the classical action (the “conformal limit”) has been subject to this analysis, as has the effective potential in a scalar theory with a quartic self-coupling and in massless scalar electrodynamics. Having multiple coupling constants and/or mass parameters in the initial action complicates this analysis, as then several mass scales arise. We show how to address this problem by considering the effective potential in a Yukawa model when the scalar field has a tree-level mass term. In addition to summing logarithmic corrections by using the RG equation, we also consider the consequences of the condition V‧(v) = 0 where v is the vacuum expectation value of the scalar. If V is expanded in powers of logarithms that arise, then it proves possible to show that either v is zero or that V is independent of the scalar. (That is, either there is no spontaneous symmetry breaking or the vacuum expectation value is not determined by minimizing V as V is “flat”.)
Spontaneous parity violation and SUSY strong gauge theory
Haba, Naoyuki; Ohki, Hiroshi
2012-07-27
We suggest simple models of spontaneous parity violation in supersymmetric strong gauge theory. We focus on left-right symmetric model and investigate vacuum with spontaneous parity violation. Non-perturbative effects are calculable in supersymmetric gauge theory, and we suggest new models. Our models show confinement, so that we try to understand them by using a dual description of the theory. The left-right symmetry breaking and electroweak symmetry breaking are simultaneously occurred with the suitable energy scale hierarchy. This structure has several advantages compared to the MSSM. The scale of the Higgs mass (left-right breaking scale) and that of VEVs are different, so the SUSY little hierarchy problems are absent. The second model also induces spontaneous supersymmetry breaking.
Cosmological consequences of noncommutative gauge theories
NASA Astrophysics Data System (ADS)
Lambiase, G.; Vilasi, G.; Yoshioka, A.
2017-01-01
Cosmological consequence of non commutative electrodynamics are investigated. In particular we consider the case in which the Lagrangian of the standard electrodynamics is modified by the introduction of terms of the form {θα β}{{F}μ ν}{{F}ρ σ}{{F}ω τ} , where {θα β} are the parameters characterizing the non commutative nature of the theory, and {{F}α β} are the components of the electromagnetic field represented by the Faraday 2-differential form. We shall study the consequences of the modified electrodynamics working in the context of the radiation dominated era of the early Universe. We focus on the possibility to generate the matter–antimatter asymmetry in the Universe by using the present upper bounds on the parameter θ provided by CMB and Lamb shift experiments.
NASA Astrophysics Data System (ADS)
Najima, R.; Hiroki, A.; Kawasaki, S.; Kimura, T.
1986-01-01
Gauge theories of antisymmetric tensor-spinor fields of higher ranks are investigated. The manifestly covariant BRS and anti-BRS invariant theories of these spinor gauge fields are formulated in Bonora and Tonin's superspace formalism.
Effective Lagrangian Models for gauge theories of fundamental interactions
NASA Astrophysics Data System (ADS)
Sannino, Francesco
The non abelian gauge theory which describes, in the perturbative regime, the strong interactions is Quantum Chromodynamics (QCD). Quarks and gluons are the fundamental degrees of freedom of the theory. A key feature of the theory (due to quantum corrections) is asymptotic freedom, i.e. the strong coupling constant increases as the energy scale of interest decreases. The perturbative approach becomes unreliable below a characteristic scale of the theory (Λ). Quarks and gluons confine themselves into colorless particles called hadrons (pions, protons,/...). The latter are the true physical states of the theory. We need to investigate alternative ways to describe strong interactions, and in general any asymptotically free theory, in the non perturbative regime. This is the fundamental motivation of the present thesis. Although the underlying gauge theory cannot be easily treated in the non perturbative regime we can still use its global symmetries as a guide to build Effective Lagrangian Models. These models will be written directly in terms of the colorless physical states of the theory, i.e. hadrons.
Flux compactifications, dual gauge theories and supersymmetry breaking
NASA Astrophysics Data System (ADS)
Torroba, Gonzalo
The nonholomorphic sector of four dimensional theories with N = 1 supersymmetry that arises from string compactifications is analyzed, and new models of supersymmetry breaking (both in string and field theory) are presented. The dissertation combines three complementary viewpoints. First, space-time effects in 4d supergravity are studied from type IIB string theory compactified on warped Calabi-Yau manifolds with fluxes. The vacuum structure of supersymmetric flux compactifications is well understood and our aim is to extend this to include space-time dependence in the presence of nontrivial warping. Going beyond the static limit is required in order to compute kinetic terms and masses. We develop formalism for identifying the microscopic 10d fluctuations that give rise to fields in the low energy 4d theory, and we present a general formula for their kinetic terms. As an application, the effective theories for the universal Kahler modulus and the complex modulus of the warped deformed conifold are determined. The full effective action for warped compactifications is calculated to quadratic order, including both 4d zero modes and their light Kaluza-Klein excitations. Next, using gauge/gravity dualities, we consider the previous results from the gauge theory side. The focus is on the warped deformed conifold, which is dual to the Klebanov-Strassler gauge theory. In the infrared it reduces to four dimensional pure super Yang-Mills, corresponding to D5 branes in the resolved conifold. The closed string analysis reveals a new term in the Kahler potential for the complex modulus, which has important effects on the low energy theory. It is suggested that this term has a natural interpretation in the dual gauge theory, in terms of the composite nature of the gaugino condensate. Finally, new models of supersymmetry breaking are developed. From the string theory side, we analyze supersymmetry breaking by anti-self-dual flux in the deformed conifold. The theory develops a
Space-Time Diffeomorphisms in Noncommutative Gauge Theories
NASA Astrophysics Data System (ADS)
Rosenbaum, Marcos; Vergara, J. David; Juarez, L. Román
2008-07-01
In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007), 10367-10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics) where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985), 288-315, 316-333]. Nonetheless, such an homomorphic mapping can be rec! uperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987), 319-328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.
The Corolla Polynomial for Spontaneously Broken Gauge Theories
NASA Astrophysics Data System (ADS)
Prinz, David
2016-09-01
In Kreimer and Yeats (Electr. J. Comb. 41-41, 2013), Kreimer et al. (Annals Phys. 336, 180-222, 2013) and Sars (2015) the Corolla Polynomial C ({Γ }) in C [a_{h1}, ldots , a_{h_{ \\vert {Γ }^{[1/2]} \\vert }}] was introduced as a graph polynomial in half-edge variables {ah}_{h in {Γ }^{[1/2]}} over a 3-regular scalar quantum field theory (QFT) Feynman graph Γ. It allows for a covariant quantization of pure Yang-Mills theory without the need for introducing ghost fields, clarifies the relation between quantum gauge theory and scalar QFT with cubic interaction and translates back the problem of renormalizing quantum gauge theory to the problem of renormalizing scalar QFT with cubic interaction (which is super renormalizable in 4 dimensions of spacetime). Furthermore, it is, as we believe, useful for computer calculations. In Prinz (2015) on which this paper is based the formulation of Kreimer and Yeats (Electr. J. Comb. 41-41, 2013), Kreimer et al. (Annals Phys. 336, 180-222, 2013) and Sars (2015) gets slightly altered in a fashion specialized in the case of the Feynman gauge. It is then formulated as a graph polynomial C ({Γ } ) in C [a_{h_{1 ± }}, ldots , a_{h_{ \\vert {Γ }^{[1/2]} \\vert } {h}_{± }}, b_{h1}, ldots , b_{h_{ \\vert {Γ }^{[1/2]} \\vert }}] in three different types of half-edge variables {a_{h+} , a_{h-} , bh}_{h in {Γ }^{[1/2]}} . This formulation is also suitable for the generalization to the case of spontaneously broken gauge theories (in particular all bosons from the Standard Model), as was first worked out in Prinz (2015) and gets reviewed here.
Lorentz violating p-form gauge theories in superspace
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker; Shah, Mushtaq B.; Ganai, Prince A.
2017-03-01
Very special relativity (VSR) keeps the main features of special relativity but breaks rotational invariance due to an intrinsic preferred direction. We study the VSR-modified extended BRST and anti-BRST symmetry of the Batalin-Vilkovisky (BV) actions corresponding to the p=1,2,3-form gauge theories. Within the VSR framework, we discuss the extended BRST invariant and extended BRST and anti-BRST invariant superspace formulations for these BV actions. Here we observe that the VSR-modified extended BRST invariant BV actions corresponding to the p=1,2,3-form gauge theories can be written in a manifestly covariant manner in a superspace with one Grassmann coordinate. Moreover, two Grassmann coordinates are required to describe the VSR-modified extended BRST and extended anti-BRST invariant BV actions in a superspace. These results are consistent with the Lorentz-invariant (special relativity) formulation.
Reflections on the renormalization procedure for gauge theories
NASA Astrophysics Data System (ADS)
't Hooft, Gerard
2016-11-01
Various pieces of insight were needed to formulate the rules for working with gauge theories of the electro-magnetic, weak and strong forces. First, it was needed to understand how to formulate the Feynman rules. We had to learn that there are many different ways to derive them, and it was needed to know how different formulations of the gauge constraint lead to the same final results: the calculated values of the scattering amplitudes. The rules for dealing with the infinities that had to be subtracted were a big challenge, culminating in the discovery of the Becchi-Rouet-Stora-Tyutin symmetry. Fond recollections of the numerous discussions the author had with Raymond Stora on this topic are memorised here. We end with some reflections on the mathematical status of quantum field theories, and the transcription of a letter by R. Stora to the author.
N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
Boucher-Veronneau, C.; Dixon, L.J.; /SLAC
2012-02-15
We present the full two-loop four-graviton amplitudes in N = 4, 5, 6 supergravity. These results were obtained using the double-copy structure of gravity, which follows from the recently conjectured color-kinematics duality in gauge theory. The two-loop four-gluon scattering amplitudes in N = 0, 1, 2 supersymmetric gauge theory are a second essential ingredient. The gravity amplitudes have the expected infrared behavior: the two-loop divergences are given in terms of the squares of the corresponding one-loop amplitudes. The finite remainders are presented in a compact form. The finite remainder for N = 8 supergravity is also presented, in a form that utilizes a pure function with a very simple symbol.
Phases of N=1 Supersymmetric Chiral Gauge Theories
Craig, Nathaniel; Essig, Rouven; Hook, Anson; Torroba, Gonzalo; /SLAC /Stanford U., Phys. Dept.
2012-02-17
We analyze the phases of supersymmetric chiral gauge theories with an antisymmetric tensor and (anti)fundamental flavors, in the presence of a classically marginal superpotential deformation. Varying the number of flavors that appear in the superpotential reveals rich infrared chiral dynamics and novel dualities. The dualities are characterized by an infinite family of magnetic duals with arbitrarily large gauge groups describing the same fixed point, correlated with arbitrarily large classical global symmetries that are truncated nonperturbatively. At the origin of moduli space, these theories exhibit a phase with confinement and chiral symmetry breaking, an interacting nonabelian Coulomb phase, and phases where an interacting sector coexists with a sector that either s-confines or is in a free magnetic phase. Properties of these intriguing 'mixed phases' are studied in detail using duality and a-maximization, and the presence of superpotential interactions provides further insights into their formation.
Bound states in gauge theories as the Poincare group representations
Cherny, A. Yu.; Dorokhov, A. E.; Han, Nguyen Suan; Pervushin, V. N. Shilin, V. I.
2013-03-15
The bound-state generating functional is constructed in gauge theories. This construction is based on the Dirac Hamiltonian approach to gauge theories, the Poincare group classification of fields and their nonlocal bound states, and the Markov-Yukawa constraint of irreducibility. The generating functional contains additional anomalous creations of pseudoscalar bound states: para-positronium in QED and mesons inQCDin the two-gamma processes of the type of {gamma} + {gamma} {yields} {pi}{sub 0} +para-positronium. The functional allows us to establish physically clear and transparent relations between the perturbativeQCD to its nonperturbative low-energy model by means of normal ordering and the quark and gluon condensates. In the limit of small current quark masses, the Gell-Mann-Oakes-Renner relation is derived from the Schwinger-Dyson and Bethe-Salpeter equations. The constituent quark masses can be calculated from a self-consistent nonlinear equation.
Geometrical Effective Action: Gauge Field Theory Without Ghosts.
NASA Astrophysics Data System (ADS)
Paris, Carmen Molina
Ghosts were invented by Feynman (1) in 1962 while trying to construct a quantum theory of gravity. Having convinced himself that there was no way in which the gravitational field could consistently escape quantization in a universe where everything else is subject to the laws of quantum mechanics, he was trying to see how these laws would work when applied to spacetime curvature. The first obstacle he faced was the non-Abelian character of the diffeomorphism group (the gauge group of gravity) which forces the gravitational field to act partly as its own source. In the language of Feynman graphs this means that gravitational charge (stress-energy) is carried by graviton lines as well as by all other lines and hence leaks all over every graph. Feynman's key idea for solving the problem was to replace every Feynman propagator by its equivalent, an advanced Green's function minus a positive-frequency Wightman function, and to throw away all noncausal loops of advanced Green's functions^1, obtaining thereby a mode sum over tree functions. It is easy to show that tree functions are gauge invariant provided the external lines bear only physical mode functions. Feynman therefore proposed to restrict the mode sums to physical modes, a procedure that not only secures gauge invariance but unitarity as well. But there is a difficulty: Because the physical mode functions are defined in a special frame, the procedure is not manifestly Lorentz invariant ^2. Feynman was able to show that deletion of the nonphysical modes is equivalent to subtracting, from the contribution of every closed loop, that of another (Lorentz invariant) loop propagating a particle having spin 1 (or one less than that of the gauge field). This is the ghost. Because its contribution is subtracted, it is a fermion. Feynman's discovery, and the work that it stimulated, made it seem as if the quantum theory of gauge fields cannot even be formulated without ghosts. It is the purpose of this dissertation to show
Neutrinoless ββ-decay in gauge theories
NASA Astrophysics Data System (ADS)
Vergados, J. D.
1983-06-01
The lepton violating neutrinoless ββ-decay is investigated in the context of fashionable gauge theories. Various mechanisms are examined e.g. light or heavy neutrinos, with or without righ-handed currents, intermediate doubly charged Higgs Particles, Majoran emisison etc. Numberical results have been obtained for the transitions 48Ca→8Ti(β-β-) and 58Ni→58Fe (β+B+, electron capture, double electron capture) employing realistic nuclear models.
Supersymmetric gauge theories on the five-sphere
NASA Astrophysics Data System (ADS)
Hosomichi, Kazuo; Seong, Rak-Kyeong; Terashima, Seiji
2012-12-01
We construct Euclidean 5d supersymmetric gauge theories on the five-sphere with vector and hypermultiplets. The SUSY transformation and the action are explicitly determined from the standard Noether procedure as well as from off-shell supergravity. Using localization techniques, the path-integral is shown to be restricted to the integration over a generalization of instantons on CP2 and the Coulomb moduli.
Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory
NASA Astrophysics Data System (ADS)
Grady, Michael
2013-11-01
Further evidence is presented for the existence of a non-confining phase at weak coupling in SU(2) lattice gauge theory. Using Monte Carlo simulations with the standard Wilson action, gauge-invariant SO(3)-Z2 monopoles, which are strong-coupling lattice artifacts, have been seen to undergo a percolation transition exactly at the phase transition previously seen using Coulomb gauge methods, with an infinite lattice critical point near β=3.2. The theory with both Z2 vortices and monopoles and SO(3)-Z2 monopoles eliminated is simulated in the strong-coupling (β=0) limit on lattices up to 604. Here, as in the high-β phase of the Wilson-action theory, finite size scaling shows it spontaneously breaks the remnant symmetry left over after Coulomb gauge fixing. Such a symmetry breaking precludes the potential from having a linear term. The monopole restriction appears to prevent the transition to a confining phase at any β. Direct measurement of the instantaneous Coulomb potential shows a Coulombic form with moderately running coupling possibly approaching an infrared fixed point of α˜1.4. The Coulomb potential is measured to 50 lattice spacings and 2 fm. A short-distance fit to the 2-loop perturbative potential is used to set the scale. High precision at such long distances is made possible through the use of open boundary conditions, which was previously found to cut random and systematic errors of the Coulomb gauge fixing procedure dramatically. The Coulomb potential agrees with the gauge-invariant interquark potential measured with smeared Wilson loops on periodic lattices as far as the latter can be practically measured with similar statistics data.
Behavior in strong fields of Euclidean gauge theories. II
NASA Astrophysics Data System (ADS)
Haba, Z.
1984-04-01
Functional determinants resulting from functional integration in quantum gauge theories are studied. We derive an expansion around the constant field strength for the (renormalized) spinor determinant detMF in QED. We show that, if the field strength F is large and its derivatives are bounded, then detMF≡exp(-W)~exp(cF2lnF2), where c>0. Hence, the effective action W in (four-dimensional) QED is unbounded from below. Moreover, we prove that exp(-W) is not integrable. A similar result is established in the Yukawa model [detMY~exp(φ4lnφ4)]. We estimate the scalar determinant detMA2 for a non-Abelian gauge field. We show that (like in the Abelian case studied earlier) detMA2=exp[c|F|2ln|F|2+r2(F,DF,DDF)], where c>0 and r2 is bounded by a quadratic form of the gauge-invariant variables |F|, |DF|, and |DDF|. We investigate the effect of gluon self-interaction on the stability of models with broken gauge symmetry G-->H (we discuss in detail the Georgi-Glashow model). We sum up (in an approximation) the contribution of massive gluons to the O(2)-invariant effective action. It is shown that this effective action is bounded from below for slowly varying fields, if the couplings are asymptotically free at the one-loop level.
C, P, and T invariance of noncommutative gauge theories
Sheikh-Jabbari
2000-06-05
In this paper we study the invariance of the noncommutative gauge theories under C, P, and T transformations. For the noncommutative space (when only the spatial part of straight theta is nonzero) we show that noncommutative QED (NCQED) is parity invariant. In addition, we show that under charge conjugation the theory on noncommutative R(4)(straight theta) is transformed to the theory on R(4)(-straight theta), so NCQED is a CP violating theory. The theory remains invariant under time reversal if, together with proper changes in fields, we also change straight theta by -straight theta. Hence altogether NCQED is CPT invariant. Moreover, we show that the CPT invariance holds for general noncommutative space-time.
[Investigations in dynamics of gauge theories in theoretical particle physics
Not Available
1993-02-01
The major theme of the theoretical physics research conducted under DOE support over the past several years has been within the rubric of the standard model, and concerned the interplay between symmetries and dynamics. The research was thus carried out mostly in the context of gauge field theories, and usually in the presence of chiral fermions. Dynamical symmetry breaking was examined both from the point of view of perturbation theory, as well as from non-perturbative techniques associated with certain characteristic features of specific theories. Among the topics of research were: the implications of abelian and non-abelian anomalies on the spectrum and possible dynamical symmetry breaking in any theory, topological and conformal properties of quantum fields in two and higher dimensions, the breaking of global chiral symmetries by vector-like gauge theories such as QCD, the phenomenological implications of a strongly interacting Higgs sector in the standard model, and the application of soliton ideas to the physics to be explored at the SSC.
Quantum Chromodynamics -- The Perfect Yang-Mills Gauge Field Theory
NASA Astrophysics Data System (ADS)
Gross, David
David Gross: My talk today is about the most beautiful of all Yang-Mills Theories (non-Abelian gauge theories), the theory of the strong nuclear interactions, Quantum Chromodynamics, QCD. We are celebrating 60 years of the publication of a remarkable paper which introduced the concept of non-Abelian local gauge symmetries, now called the Yang-Mills theory, to physics. In the introduction to this paper it is noted that the usual principle of isotopic spin symmetry is not consistent with the concept of localized fields. This sentence has drawn attention over the years because the usual principle of isotopic spin symmetry is consistent, it is just not satisfactory. The authors, Yang and Mills, introduced a more satisfactory notion of local symmetry which did not require one to rotate (in isotopic spin space) the whole universe at once to achieve the symmetry transformation. Global symmetries are thus are similar to `action at a distance', whereas Yang-Mills theory is manifestly local...
Moyal deformations of Clifford gauge theories of gravity
NASA Astrophysics Data System (ADS)
Castro, Carlos
2016-12-01
A Moyal deformation of a Clifford Cl(3, 1) Gauge Theory of (Conformal) Gravity is performed for canonical noncommutativity (constant Θμν parameters). In the very special case when one imposes certain constraints on the fields, there are no first-order contributions in the Θμν parameters to the Moyal deformations of Clifford gauge theories of gravity. However, when one does not impose constraints on the fields, there are first-order contributions in Θμν to the Moyal deformations in variance with the previous results obtained by other authors and based on different gauge groups. Despite that the generators of U(2, 2),SO(4, 2),SO(2, 3) can be expressed in terms of the Clifford algebra generators this does not imply that these algebras are isomorphic to the Clifford algebra. Therefore one should not expect identical results to those obtained by other authors. In particular, there are Moyal deformations of the Einstein-Hilbert gravitational action with a cosmological constant to first-order in Θμν. Finally, we provide a mechanism which furnishes a plausible cancellation of the huge vacuum energy density.
Yang-Mills gauge theory and Higgs particle
NASA Astrophysics Data System (ADS)
Wu, Tai Tsun; Wu, Sau Lan
2015-12-01
Motivated by the experimental data on the Higgs particle from the ATLAS Collaboration and the CMS Collaboration at CERN, the standard model, which is a Yang-Mills non-Abelian gauge theory with the group U(1) × SU(2) × SU(3), is augmented by scalar quarks and scalar leptons without changing the gauge group and without any additional Higgs particle. Thus there is fermion-boson symmetry between these new particles and the known quarks and leptons. In a simplest scenario, the cancellation of the quadratic divergences in this augmented standard model leads to a determination of the masses of all these scalar quarks and scalar leptons. All these masses are found to be less than 100 GeV/c2, and the right-handed scalar neutrinos are especially light. Alterative procedures are given with less reliance on the experimental data, leading to the same conclusions.
Yang-Mills Gauge Theory and Higgs Particle
NASA Astrophysics Data System (ADS)
Wu, Tai Tsun; Wu, Sau Lan
Motivated by the experimental data on the Higgs particle from the ATLAS Collaboration and the CMS Collaboration at CERN, the standard model, which is a Yang-Mills non-Abelian gauge theory with the group U(1) × SU (2) × SU (3), is augmented by scalar quarks and scalar leptons without changing the gauge group and without any additional Higgs particle. Thus there is fermion-boson symmetry between these new particles and the known quarks and leptons. In a simplest scenario, the cancellation of the quadratic divergences in this augmented standard model leads to a determination of the masses of all these scalar quarks and scalar leptons. All these masses are found to be less than 100 GeV/c2, and the right-handed scalar neutrinos are especially light. Alterative procedures are given with less reliance on the experimental data, leading to the same conclusions.
Three-loop calculations in non-abelian gauge theories
NASA Astrophysics Data System (ADS)
Tarasov, O. V.; Vladimirov, A. A.
2013-09-01
A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous dimensions for non-Abelian gauge theories with fermions in the three-loop approximation. A three-loop expression for the effective charge of QCD is given. Charge renormalization effects in the SU(4)-supersymmetric gauge model is shown to vanish at this level. A complete list of required formulas is given in Appendix. The above-mentioned results of three-loop calculations were published by the present authors (with A.Yu. Zharkov and L.V. Avdeev) in 1980 in Physics Letters B. The present text, which treats the subject in more details and contains a lot of calculational techniques, was also published in 1980 as the JINR Communication E2-80-483.
Pauli-Villars Regularization of Non-Abelian Gauge Theories
NASA Astrophysics Data System (ADS)
Hiller, J. R.
2016-07-01
As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev-Popov ghosts then establishes a residual BRST symmetry. Although there are drawbacks to the approach, in particular the computational load of a large number of PV fields and a nonlocal interaction of the ghost fields, this formulation could provide a foundation for renormalizable nonperturbative solutions of light-front QCD in an arbitrary covariant gauge.
Gauge Theory on Twisted kappa-Minkowski: Old Problems and Possible Solutions
NASA Astrophysics Data System (ADS)
Dimitrijević, Marija; Jonke, Larisa; Pachoł, Anna
2014-06-01
We review the application of twist deformation formalism and the construction of noncommutative gauge theory on κ-Minkowski space-time. We compare two different types of twists: the Abelian and the Jordanian one. In each case we provide the twisted differential calculus and consider {U}(1) gauge theory. Different methods of obtaining a gauge invariant action and related problems are thoroughly discussed.
Comments on twisted indices in 3d supersymmetric gauge theories
NASA Astrophysics Data System (ADS)
Closset, Cyril; Kim, Heeyeon
2016-08-01
We study three-dimensional {N} = 2 supersymmetric gauge theories on Σ g × S 1 with a topological twist along Σ g , a genus- g Riemann surface. The twisted supersymmetric index at genus g and the correlation functions of half-BPS loop operators on S 1 can be computed exactly by supersymmetric localization. For g = 1, this gives a simple UV computation of the 3d Witten index. Twisted indices provide us with a clean derivation of the quantum algebra of supersymmetric Wilson loops, for any Yang-Mills-Chern-Simons-matter theory, in terms of the associated Bethe equations for the theory on {{R}}^2× {S}^1 . This also provides a powerful and simple tool to study 3d {N} = 2 Seiberg dualities. Finally, we study A- and B-twisted indices for {N} = 4 supersymmetric gauge theories, which turns out to be very useful for quantitative studies of three-dimensional mirror symmetry. We also briefly comment on a relation between the S 2 × S 1 twisted indices and the Hilbert series of {N} = 4 moduli spaces.
Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
NASA Astrophysics Data System (ADS)
Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.
2009-03-01
We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques on its noncommutative deformation. As a result the gauge theory localizes on noncommutative instantons which can be classified in terms of N-coloured three-dimensional Young diagrams. We give to these noncommutative instantons a geometrical description in terms of certain stable framed coherent sheaves on projective space by using a higher-dimensional generalization of the ADHM formalism. From this formalism we construct a topological matrix quantum mechanics which computes an index of BPS states and provides an alternative approach to the six-dimensional gauge theory.
Reissner—Nordström-de—Sitter-type Solution by a Gauge Theory of Gravity
NASA Astrophysics Data System (ADS)
Enache, V.; Camelia, Popa; Păun, V.; Agop, M.
2008-10-01
We use the theory based on a gravitational gauge group (Wu's model) to obtain a spherical symmetric solution of the Geld equations for the gravitational potential on a Minkowski spacetime. The gauge group, the gauge covariant derivative, the strength tensor of the gauge Held, the gauge invariant Lagrangean with the cosmological constant, the Geld equations of the gauge potentials with a gravitational energy-momentum tensor as well as with a tensor of the Geld of a point like source are determined. Finally, a Reissner-Nordstrom-de Sitter-type metric on the gauge group space is obtained.
Proton Stability in Grand Unified Theories and Discrete Gauge Symmetries
Mohapatra, R. N.
2008-05-13
Most supersymmetric grand unified theories face the problem of rapid proton decay coming either from R-parity violating interactions and/or from Planck scale induced R-parity conserving operators, possibly induced by non-perturbative Planck scale effects such as black holes or wormholes. In this talk, I argue in favor of the possibility that a natural way to resolve this problem is to assume that there are new discrete or continuous gauge symmetries accompanying these theories that resolve these problems while at the same time allowing enough flexibility to have a viable model. I discuss this for left-right and SO(10) theories and discuss the profound impact such considerations have on the construction of realistic GUT models. I then discuss a recently proposed SO(10) model which has only apparently string inspired multiplets and has enough structure to be a realistic model.
Torsional Newton-Cartan geometry from Galilean gauge theory
NASA Astrophysics Data System (ADS)
Banerjee, Rabin; Mukherjee, Pradip
2016-11-01
Using the recently advanced Galilean gauge theory (GGT) we give a comprehensive construction of torsional Newton-Cartan (NC) geometry. The coupling of a Galilean symmetric model with background NC geometry following GGT is illustrated by a free nonrelativistic scalar field theory. The issue of spatial diffeomorphism (Son and Wingate 2006 Ann. Phys. 321 197-224 Banerjee et al 2015 Phys. Rev. D 91 084021) is focussed from a new angle. The expression of the torsionful connection is worked out, which is in complete parallel with the relativistic theory. Also, smooth transition of the connection to its well known torsionless expression is demonstrated. A complete (implicit) expression of the torsion tensor for the NC spacetime is provided where the first-order variables occur in a suggestive way. The well known result for the temporal part of torsion is reproduced from our expression.
Lattice gaugefixing and other optics in lattice gauge theory
Yee, Ken.
1992-06-01
We present results from four projects. In the first, quark and gluon propagators and effective masses and {Delta}I = 1/2 Rule operator matching coefficients are computed numerically in gaugefixed lattice QCD. In the second, the same quantities are evaluated analytically in the strong coupling, N {yields} {infinity} limit. In the third project, the Schwinger model is studied in covariant gauges, where we show that the effective electron mass varies with the gauge parameter and that longitudinal gaugefixing ambiguities affect operator product expansion coefficients (analogous to {Delta}I = 1/2 Rule matching coefficients) determined by matching gauge variant matrix elements. However, we find that matching coefficients even if shifted by the unphysical modes are {xi} invariant. In the fourth project, we show that the strong coupling parallelogram lattice Schwinger model as a different thermodynamic limit than the weak coupling continuum limit. As a function of lattice skewness angle these models span the {Delta} = {minus}1 critical line of 6-vertex models which, in turn, have been identified as c = 1 conformal field theories.
Non-abelian higher gauge theory and categorical bundle
NASA Astrophysics Data System (ADS)
Viennot, David
2016-12-01
A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is an attempt to generalize the bundle structure in order to describe horizontal lifts of surfaces. A such attempt is particularly difficult for the non-abelian case. Some structures have been proposed to realize this goal (twisted bundle, gerbes with connection, bundle gerbe, 2-bundle). Each of them uses a category in place of the total space manifold of the usual principal bundle structure. Some of them replace also the structure group by a category (more precisely a Lie crossed module viewed as a category). But the base space remains still a simple manifold (possibly viewed as a trivial category with only identity arrows). We propose a new principal categorical bundle structure, with a Lie crossed module as structure groupoid, but with a base space belonging to a bigger class of categories (which includes non-trivial categories), that we called affine 2-spaces. We study the geometric structure of the categorical bundles built on these categories (which are a more complicated structure than the 2-bundles) and the connective structures on these bundles. Finally we treat an example interesting for quantum dynamics which is associated with the Bloch wave operator theory.
Lattice Gauge Theory and the Origin of Mass
Kronfeld, Andreas S.
2013-08-01
Most of the mass of everyday objects resides in atomic nuclei/ the total of the electrons' mass adds up to less than one part in a thousand. The nuclei are composed of nucleons---protons and neutrons---whose nuclear binding energy, though tremendous on a human scale, is small compared to their rest energy. The nucleons are, in turn, composites of massless gluons and nearly massless quarks. It is the energy of these confined objects, via $M=E/c^2$, that is responsible for everyday mass. This article discusses the physics of this mechanism and the role of lattice gauge theory in establishing its connection to quantum chromodynamics.
Gauge-fields and integrated quantum-classical theory
Stapp, H.P.
1986-01-01
Physical situations in which quantum systems communicate continuously to their classically described environment are not covered by contemporary quantum theory, which requires a temporary separation of quantum degrees of freedom from classical ones. A generalization would be needed to cover these situations. An incomplete proposal is advanced for combining the quantum and classical degrees of freedom into a unified objective description. It is based on the use of certain quantum-classical structures of light that arise from gauge invariance to coordinate the quantum and classical degrees of freedom. Also discussed is the question of where experimenters should look to find phenomena pertaining to the quantum-classical connection. 17 refs.
Lattice gauge theory on the Intel parallel scientific computer
NASA Astrophysics Data System (ADS)
Gottlieb, Steven
1990-08-01
Intel Scientific Computers (ISC) has just started producing its third general of parallel computer, the iPSC/860. Based on the i860 chip that has a peak performance of 80 Mflops and with a current maximum of 128 nodes, this computer should achieve speeds in excess of those obtainable on conventional vector supercomputers. The hardware, software and computing techniques appropriate for lattice gauge theory calculations are described. The differences between a staggered fermion conjugate gradient program written under CANOPY and for the iPSC are detailed.
Kasamatsu, Kenichi; Ichinose, Ikuo; Matsui, Tetsuo
2013-09-13
Recently, the possibility of quantum simulation of dynamical gauge fields was pointed out by using a system of cold atoms trapped on each link in an optical lattice. However, to implement exact local gauge invariance, fine-tuning the interaction parameters among atoms is necessary. In the present Letter, we study the effect of violation of the U(1) local gauge invariance by relaxing the fine-tuning of the parameters and showing that a wide variety of cold atoms is still a faithful quantum simulator for a U(1) gauge-Higgs model containing a Higgs field sitting on sites. The clarification of the dynamics of this gauge-Higgs model sheds some light upon various unsolved problems, including the inflation process of the early Universe. We study the phase structure of this model by Monte Carlo simulation and also discuss the atomic characteristics of the Higgs phase in each simulator.
Quantum Field Theory Tools:. a Mechanism of Mass Generation of Gauge Fields
NASA Astrophysics Data System (ADS)
Flores-Baez, F. V.; Godina-Nava, J. J.; Ordaz-Hernandez, G.
We present a simple mechanism for mass generation of gauge fields for the Yang-Mills theory, where two gauge SU(N)-connections are introduced to incorporate the mass term. Variations of these two sets of gauge fields compensate each other under local gauge transformations with the local gauge transformations of the matter fields, preserving gauge invariance. In this way the mass term of gauge fields is introduced without violating the local gauge symmetry of the Lagrangian. Because the Lagrangian has strict local gauge symmetry, the model is a renormalizable quantum model. This model, in the appropriate limit, comes from a class of universal Lagrangians which define a new massive Yang-Mills theories without Higgs bosons.
Geometric Quantization of Chern-Simons Gauge Theory
NASA Astrophysics Data System (ADS)
Axelrod, Scott Elliot
1991-02-01
We present a new construction of the quantum Hilbert space of Chern-Simons gauge theory using methods which are natural from the three dimensional point of view. We describe a generalization of Lagrangian field theory which is an appropriate classical starting point for topological quantum field theories. It is explained how classical Chern-Simons theory with arbitrary gauge group G fits in this framework. Given G compact, an element of H ^4(BG,doubz), and a principal G-bundle E on a closed 2-manifold Sigma, we arrive at a prequantum line bundle on the moduli space of flat G-connections on E. Equipping Sigma with a complex structure, we obtain by Kahler quantization a quantum Hilbert space. To show that this Hilbert space is independent of the choice of complex structure, and so is acted on by the mapping class group, we construct a natural projectively flat connection on the quantum Hilbert bundle over Teichmuller space. This connection has been previously constructed in the context of two dimensional conformal field theory where it is interpreted as the stress energy tensor. Our construction thus gives a 2 + 1 dimensional derivation of the basic properties of 1 + 1 dimensional current algebra. To construct the connection we show generally that for affine symplectic quotients the natural projectively flat connection on the quantum Hilbert bundle may be expressed purely in terms of the intrinsic Kahler geometry of the quotient and the Quillen connection on a certain determinant line bundle. The proof of most of the properties of the connection we construct follows surprisingly simply from the index theorem identities for the curvature of the Quillen connection. As an example, we treat the case when Sigma has genus one explicitly. We also make some preliminary comments concerning the Hilbert space structure.
AGT relations for abelian quiver gauge theories on ALE spaces
NASA Astrophysics Data System (ADS)
Pedrini, Mattia; Sala, Francesco; Szabo, Richard J.
2016-05-01
We construct level one dominant representations of the affine Kac-Moody algebra gl̂k on the equivariant cohomology groups of moduli spaces of rank one framed sheaves on the orbifold compactification of the minimal resolution Xk of the Ak-1 toric singularity C2 /Zk. We show that the direct sum of the fundamental classes of these moduli spaces is a Whittaker vector for gl̂k, which proves the AGT correspondence for pure N = 2 U(1) gauge theory on Xk. We consider Carlsson-Okounkov type Ext-bundles over products of the moduli spaces and use their Euler classes to define vertex operators. Under the decomposition gl̂k ≃ h ⊕sl̂k, these vertex operators decompose as products of bosonic exponentials associated to the Heisenberg algebra h and primary fields of sl̂k. We use these operators to prove the AGT correspondence for N = 2 superconformal abelian quiver gauge theories on Xk.
Surface charge algebra in gauge theories and thermodynamic integrability
NASA Astrophysics Data System (ADS)
Barnich, Glenn; Compère, Geoffrey
2008-04-01
Surface charges and their algebra in interacting Lagrangian gauge field theories are constructed out of the underlying linearized theory using techniques from the variational calculus. In the case of exact solutions and symmetries, the surface charges are interpreted as a Pfaff system. Integrability is governed by Frobenius' theorem and the charges associated with the derived symmetry algebra are shown to vanish. In the asymptotic context, we provide a generalized covariant derivation of the result that the representation of the asymptotic symmetry algebra through charges may be centrally extended. Comparison with Hamiltonian and covariant phase space methods is made. All approaches are shown to agree for exact solutions and symmetries while there are differences in the asymptotic context.
Creating a monopole in 4D gauge theories
NASA Astrophysics Data System (ADS)
Khvedelidze, A.; Kovner, A.; McMullan, David
2008-05-01
The problem of defining the second quantized monopole creation operator in non-Abelian gauge theories is discussed and exemplified by the (3 + 1)-dimensional Georgi-Glashow model. We construct the “coherent state” operator M( x) that creates the Coulomb magnetic field in terms of the Dirac singular electromagnetic potential. Our calculation of the vacuum expectation value of this operator < M( x)> in the confining phase indicates that it is free from the singularity along the Dirac string and in the leading order of perturbation theory the < M( x)> vanishes as a power of the volume of the system. This supports the conception that inclusion of the nonperturbative effects introduces an effective infrared cutoff on the calculation providing the finiteness of vacuum expectation value < M( x)>.
On S-Duality in Abelian Gauge Theory
NASA Astrophysics Data System (ADS)
Witten, Edward
1995-09-01
U(1) gauge theory on R4 is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action of SL(2,Z). In this paper, the duality is studied on a general four-manifold and it is shown that the partition function is not a modular-invariant function but transforms as a modular form. This result plays an essential role in determining a new low-energy interaction that arises when N=2 supersymmetric Yang-Mills theory is formulated on a four-manifold; the determination of this interaction gives a new test of the solution of the model and would enter in computations of the Donaldson invariants of four-manifolds with b+2≤1. Certain other aspects of abelian duality, relevant to matters such as the dependence of Donaldson invariants on the second Stieffel-Whitney class, are also analyzed.
Higher gauge theories from Lie n-algebras and off-shell covariantization
NASA Astrophysics Data System (ADS)
Carow-Watamura, Ursula; Heller, Marc Andre; Ikeda, Noriaki; Kaneko, Yukio; Watamura, Satoshi
2016-07-01
We analyze higher gauge theories in various dimensions using a supergeometric method based on a differential graded symplectic manifold, called a QP-manifold, which is closely related to the BRST-BV formalism in gauge theories. Extensions of the Lie 2-algebra gauge structure are formulated within the Lie n-algebra induced by the QP-structure. We find that in 5 and 6 dimensions there are special extensions of the gauge algebra. In these cases, a restriction of the gauge symmetry by imposing constraints on the auxiliary gauge fields leads to a covariantized theory. As an example we show that we can obtain an off-shell covariantized higher gauge theory in 5 dimensions, which is similar to the one proposed in [1].
New gauge-invariant formulation of the Chern-Simons gauge theory
Park, M.; Park, Y.
1998-11-01
A new gauge invariant formulation of the relativistic scalar field interacting with Chern-Simons gauge fields is considered. This formulation is consistent with the gauge fixed formulation. Furthermore, we find that canonical (Noether) Poincar{acute e} generators are not gauge invariant even on the constraints surface and do not satisfy the (classical) Poincar{acute e} algebra. It is the improved generators, constructed from the symmetric energy-momentum tensor, which are (manifestly) gauge invariant and obey the classical Poincar{acute e} algebra. {copyright} {ital 1998} {ital The American Physical Society}
Theory Modeling and Simulation
Shlachter, Jack
2012-08-23
Los Alamos has a long history in theory, modeling and simulation. We focus on multidisciplinary teams that tackle complex problems. Theory, modeling and simulation are tools to solve problems just like an NMR spectrometer, a gas chromatograph or an electron microscope. Problems should be used to define the theoretical tools needed and not the other way around. Best results occur when theory and experiments are working together in a team.
Deconfinement Phase Transition in a 3D Nonlocal U(1) Lattice Gauge Theory
Arakawa, Gaku; Ichinose, Ikuo; Matsui, Tetsuo; Sakakibara, Kazuhiko
2005-06-03
We introduce a 3D compact U(1) lattice gauge theory having nonlocal interactions in the temporal direction, and study its phase structure. The model is relevant for the compact QED{sub 3} and strongly correlated electron systems like the t-J model of cuprates. For a power-law decaying long-range interaction, which simulates the effect of gapless matter fields, a second-order phase transition takes place separating the confinement and deconfinement phases. For an exponentially decaying interaction simulating matter fields with gaps, the system exhibits no signals of a second-order transition.
Perturbation theory in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
Campagnari, Davide R.; Reinhardt, Hugo; Weber, Axel
2009-07-15
We study the Hamiltonian approach to Yang-Mills theory in Coulomb gauge in Rayleigh-Schroedinger perturbation theory. The static gluon and ghost propagator as well as the potential between static color sources are calculated to one-loop order. Furthermore, the one-loop {beta} function is calculated from both the ghost-gluon vertex and the static potential and found to agree with the result of covariant perturbation theory.
Finite and Gauge-Yukawa unified theories: Theory and predictions
Kobayashi, T.; Kubo, J.; Mondragon, M.; Zoupanos, G.
1999-10-25
All-loop Finite Unified Theories (FUTs) are very interesting N=1 GUTs in which a complete reduction of couplings has been achieved. FUTs realize an old field theoretical dream and have remarkable predictive power. Reduction of dimensionless couplings in N=1 GUTs is achieved by searching for renormalization group invariant (RGI) relations among them holding beyond the unification scale. Finiteness results from the fact that there exists RGI relations among dimensionless couplings that guarantee the vanishing of the {beta}- functions in certain N=1 supersymmetric GUTS even to all orders. Recent developments in the soft supersymmetry breaking (SSB) sector of N=1 GUTs and FUTs lead to exact RGI relations also in this sector of the theories. Of particular interest is a RGI sum rule for the soft scalar masses holding to all orders. The characteristic features of SU(5) models that have been constructed based on the above tools are: a) the old agreement of the top quark prediction with the measured value remains unchanged, b) the lightest Higgs boson is predicted to be around 120 GeV, c) the s-spectrum starts above several hundreds of GeV.
Field theory on R×S 3 topology. V: SU 2 gauge theory
NASA Astrophysics Data System (ADS)
Carmeli, M.; Malin, S.
1987-02-01
A gauge theory on R×S 3 topology is developed. It is a generalization to the previously obtained field theory on R×S 3 topology and in which equations of motion were obtained for a scalar particle, a spin one-half particle, the electromagnetic field of magnetic moments, and a Shrödinger-type equation, as compared to ordinary field equations defined on a Minkowskian manifold. The new gauge field equations are presented and compared to the ordinary Yang-Mills field equations, and the mathematical and physical differences between them are discussed.
Infrared singularities in Landau gauge Yang-Mills theory
Alkofer, Reinhard; Huber, Markus Q.; Schwenzer, Kai
2010-05-15
We present a more detailed picture of the infrared regime of Landau-gauge Yang-Mills theory. This is done within a novel framework that allows one to take into account the influence of finite scales within an infrared power counting analysis. We find that there are two qualitatively different infrared fixed points of the full system of Dyson-Schwinger equations. The first extends the known scaling solution, where the ghost dynamics is dominant and gluon propagation is strongly suppressed. It features in addition to the strong divergences of gluonic vertex functions in the previously considered uniform scaling limit, when all external momenta tend to zero, also weaker kinematic divergences, when only some of the external momenta vanish. The second solution represents the recently proposed decoupling scenario where the gluons become massive and the ghosts remain bare. In this case we find that none of the vertex functions is enhanced, so that the infrared dynamics is entirely suppressed. Our analysis also provides a strict argument why the Landau-gauge gluon dressing function cannot be infrared divergent.
CERN Winter School on Supergravity, Strings, and Gauge Theory 2010
None
2016-07-12
The CERN Winter School on Supergravity, Strings, and Gauge Theory is the analytic continuation of the yearly training school of the former EC-RTN string network "Constituents, Fundamental Forces and Symmetries of the Universe". The 2010 edition of the school is supported and organized by the CERN Theory Divison, and will take place from Monday January 25 to Friday January 29, at CERN. As its predecessors, this school is meant primarily for training of doctoral students and young postdoctoral researchers in recent developments in theoretical high-energy physics and string theory. The programme of the school will consist of five series of pedagogical lectures, complemented by tutorial discussion sessions in the afternoons. Previous schools in this series were organized in 2005 at SISSA in Trieste, and in 2006, 2007, 2008, and 2009 at CERN, Geneva. Other similar schools have been organized in the past by the former related RTN network "The Quantum Structure of Spacetime and the Geometric Nature of Fundamental Interactions". This edition of the school is not funded by the European Union. The school is funded by the CERN Theory Division, and the Arnold Sommerfeld Center at Ludwig-Maximilians University of Munich. Scientific committee: M. Gaberdiel, D. Luest, A. Sevrin, J. Simon, K. Stelle, S. Theisen, A. Uranga, A. Van Proeyen, E. Verlinde Local organizers: A. Uranga, J. Walcher
CERN Winter School on Supergravity, Strings, and Gauge Theory 2010
2010-01-22
The CERN Winter School on Supergravity, Strings, and Gauge Theory is the analytic continuation of the yearly training school of the former EC-RTN string network "Constituents, Fundamental Forces and Symmetries of the Universe". The 2010 edition of the school is supported and organized by the CERN Theory Divison, and will take place from Monday January 25 to Friday January 29, at CERN. As its predecessors, this school is meant primarily for training of doctoral students and young postdoctoral researchers in recent developments in theoretical high-energy physics and string theory. The programme of the school will consist of five series of pedagogical lectures, complemented by tutorial discussion sessions in the afternoons. Previous schools in this series were organized in 2005 at SISSA in Trieste, and in 2006, 2007, 2008, and 2009 at CERN, Geneva. Other similar schools have been organized in the past by the former related RTN network "The Quantum Structure of Spacetime and the Geometric Nature of Fundamental Interactions". This edition of the school is not funded by the European Union. The school is funded by the CERN Theory Division, and the Arnold Sommerfeld Center at Ludwig-Maximilians University of Munich. Scientific committee: M. Gaberdiel, D. Luest, A. Sevrin, J. Simon, K. Stelle, S. Theisen, A. Uranga, A. Van Proeyen, E. Verlinde Local organizers: A. Uranga, J. Walcher
More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
Maas, Axel
2009-01-01
Fixing a gauge in the nonperturbative domain of Yang-Mills theory is a nontrivial problem due to the presence of Gribov copies. In particular, there are different gauges in the nonperturbative regime which all correspond to the same definition of a gauge in the perturbative domain. Gauge-dependent correlation functions may differ in these gauges. Two such gauges are the minimal Landau gauge and the absolute Landau gauge, both corresponding to the perturbative Landau gauge. These, and their numerical implementation, are described and presented in detail. Other choices will also be discussed. This investigation is performed, using numerical lattice gauge theory calculations, by comparing the propagators of gluons and ghosts for the minimal Landau gauge and the absolute Landau gauge in SU(2) Yang-Mills theory. It is found that the propagators are different in the far infrared and even at energy scales of the order of half a GeV. In particular, the finite-volume effects are also modified. This is observed in two and three dimensions. Some remarks on the four-dimensional case are provided as well.
Integrability of classical strings dual for noncommutative gauge theories
NASA Astrophysics Data System (ADS)
Matsumoto, Takuya; Yoshida, Kentaroh
2014-06-01
We derive the gravity duals of noncommutative gauge theories from the Yang-Baxter sigma model description of the AdS5 × S5 superstring with classical r-matrices. The corresponding classical r-matrices are 1) solutions of the classical Yang-Baxter equation (CYBE), 2) skew-symmetric, 3) nilpotent and 4) abelian. Hence these should be called abelian Jordanian deformations. As a result, the gravity duals are shown to be integrable deformations of AdS5 × S5. Then, abelian twists of AdS5 are also investigated. These results provide a support for the gravity/CYBE correspondence proposed in arXiv:1404.1838.
NASA Astrophysics Data System (ADS)
Kuno, Yoshihito; Kasamatsu, Kenichi; Takahashi, Yoshiro; Ichinose, Ikuo; Matsui, Tetsuo
2015-06-01
Lattice gauge theory has provided a crucial non-perturbative method in studying canonical models in high-energy physics such as quantum chromodynamics. Among other models of lattice gauge theory, the lattice gauge-Higgs model is a quite important one because it describes a wide variety of phenomena/models related to the Anderson-Higgs mechanism, such as superconductivity, the standard model of particle physics, and the inflation process of the early Universe. In this paper, we first show that atomic description of the lattice gauge model allows us to explore real-time dynamics of the gauge variables by using the Gross-Pitaevskii equations. Numerical simulations of the time development of an electric flux reveal some interesting characteristics of the dynamic aspect of the model and determine its phase diagram. Next, to realize a quantum simulator of the U(1) lattice gauge-Higgs model on an optical lattice filled by cold atoms, we propose two feasible methods: (i) Wannier states in the excited bands and (ii) dipolar atoms in a multilayer optical lattice. We pay attention to the constraint of Gauss's law and avoid nonlocal gauge interactions.
Phase transitions in higher derivative gravity and gauge theory: R-charged black holes
NASA Astrophysics Data System (ADS)
Dey, Tanay K.; Mukherji, Sudipta; Mukhopadhyay, Subir; Sarkar, Swarnendu
2007-09-01
This is a continuation of our earlier work where we constructed a phenomenologically motivated effective action of the boundary gauge theory at finite temperature and finite gauge coupling on S3 × S1. In this paper, we argue that this effective action qualitatively reproduces the gauge theory representing various bulk phases of R-charged black hole with Gauss-Bonnet correction. We analyze the system both in canonical and grand canonical ensemble.
Twisted gauge theories in three-dimensional Walker-Wang models
NASA Astrophysics Data System (ADS)
Wang, Zitao; Chen, Xie
2017-03-01
Three-dimensional gauge theories with a discrete gauge group can emerge from spin models as a gapped topological phase with fractional point excitations (gauge charge) and loop excitations (gauge flux). It is known that 3D gauge theories can be "twisted," in the sense that the gauge flux loops can have nontrivial braiding statistics among themselves and such twisted gauge theories are realized in models discovered by Dijkgraaf and Witten. A different framework to systematically construct three-dimensional topological phases was proposed by Walker and Wang and a series of examples have been studied. Can the Walker-Wang construction be used to realize the topological order in twisted gauge theories? This is not immediately clear because the Walker-Wang construction is based on a loop condensation picture while the Dijkgraaf-Witten theory is based on a membrane condensation picture. In this paper, we show that the answer to this question is Yes, by presenting an explicit construction of the Walker-Wang models which realize both the twisted and untwisted gauge theories with gauge group Z2×Z2 . We identify the topological order of the models by performing modular transformations on the ground-state wave functions and show that the modular matrices exactly match those for the Z2×Z2 gauge theories. By relating the Walker-Wang construction to the Dijkgraaf-Witten construction, our result opens up a way to study twisted gauge theories with fermonic charges, and correspondingly strongly interacting fermionic symmetry protected topological phases and their surface states, through exactly solvable models.
Maximum-likelihood approach to topological charge fluctuations in lattice gauge theory
NASA Astrophysics Data System (ADS)
Brower, R. C.; Cheng, M.; Fleming, G. T.; Lin, M. F.; Neil, E. T.; Osborn, J. C.; Rebbi, C.; Rinaldi, E.; Schaich, D.; Schroeder, C.; Voronov, G.; Vranas, P.; Weinberg, E.; Witzel, O.
2014-07-01
We present a novel technique for the determination of the topological susceptibility (related to the variance of the distribution of global topological charge) from lattice gauge theory simulations, based on maximum-likelihood analysis of the Markov-chain Monte Carlo time series. This technique is expected to be particularly useful in situations where relatively few tunneling events are observed. Restriction to a lattice subvolume on which topological charge is not quantized is explored, and may lead to further improvement when the global topology is poorly sampled. We test our proposed method on a set of lattice data, and compare it to traditional methods.
Monopoles and Confinement in U(1) Lattice Gauge Theory
NASA Astrophysics Data System (ADS)
Copeland, Timothy John
Available from UMI in association with The British Library. Requires signed TDF. Confinement in U(1) gauge theory is investigated, with particular emphasis on the role of monopoles. Starting from the work of Polyakov, the theoretical aspects are considered first, in some detail. This leads to the conclusion that the conventional techniques for analysing Monte Carlo data may not be adequate, and motivates the development of an alternative interpretation based on the theoretical insight gained. This takes more account of the expected physical properties of the theory, and does not assume beforehand that one type of behaviour (perturbative, or monopole driven) dominates. It is found that better fits to the Monte Carlo data can be achieved this way than by using the conventional methods, although different string tensions are found. The small distance behaviour is found to be best explained in terms of Coulomb effects, rather than the Luscher vibrating string picture sometimes used before. Perturbative calculations are made of Wilson loops on lattices of different shapes, and some comparisons with Monte Carlo data are made. Comments are made on the significance of these results for four dimensions, and for SU(2) and SU(3).
NASA Astrophysics Data System (ADS)
Gattringer, Christof; Marchis, Carlotta
2017-03-01
We propose a new approach to strong coupling series and dual representations for non-abelian lattice gauge theories using the SU(2) case as an example. The Wilson gauge action is written as a sum over ;abelian color cycles; (ACC) which correspond to loops in color space around plaquettes. The ACCs are complex numbers which can be commuted freely such that the strong coupling series and the dual representation can be obtained as in the abelian case. Using a suitable representation of the SU(2) gauge variables we integrate out all original gauge links and identify the constraints for the dual variables in the SU(2) case. We show that the construction can be generalized to the case of SU(2) gauge fields with staggered fermions. The result is a strong coupling series where all gauge integrals are known in closed form and we discuss its applicability for possible dual simulations. The abelian color cycle concept can be generalized to other non-abelian gauge groups such as SU(3).
Generalized mixing angles in gauge theories with natural flavor conservation
Rothman, Arthur C.; Kang, Kyungsik
1981-01-01
A number of theorems, relating Natural Flavor Conservation and Calculability are proven for general gauge models of the weak and electromagnetic interactions with an unbroken U(1) symmetry. The concept of nontriviality - a necessary condition that all naturally flavor conserving gauge models must obey in order to have nontrivial mixing angles - is introduced. It is found that naturality groups guaranteeing Natural Flavor Conservation cannot generate meaningful mixing angles in any gauge model.
Topics in Lattice Gauge Theory and Theoretical Physics
NASA Astrophysics Data System (ADS)
Komijani, Javad
This dissertation contains two completely independent parts. In Part 1, I investigate effective field theories and their applications in lattice gauge theory. Quantum chromodynamics (QCD) as a part of the standard model (SM) describes the physics of quarks and gluons. There are several numerical and analytical methods to tackle the QCD problems. Lattice QCD is the dominant numerical method. Effective field theories, on the other hand, provide analytic methods to describe the low-energy dynamics of QCD. To use the effective theories in lattice QCD, I develop chiral perturbation theory for heavy-light mesons with staggered quarks---an implementation of fermions on lattice. I use this effective chiral theory to study the pattern of taste splitting in masses of the mesons with staggered quarks. I also calculate the leptonic decay constant of the heavy-light mesons with staggered quarks to one-loop order in the chiral expansion. The resulting chiral formula provides a suitable fit form to combine and analyze a large number of decay constants of heavy-light mesons computed from different lattice ensembles with various choices of input parameters. I perform a comprehensive chiral fit to the lattice data for D mesons computed by the MILC collaboration. Consequently, I determine the physical values of the decay constants of D mesons. These precise results place narrow restrictions on the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements. In Part 2, I introduce the concept of a nonlinear eigenvalue problem by investigating three nonlinear differential equations. First, equation y'(x) = cos[pixy(x)] is investigated. A discrete set of initial conditions y(0) = an, leading to unstable separatrix behavior, are identified as the eigenvalues of the problem. I calculate the asymptotic behavior of the initial conditions an and their corresponding solutions for large n by reducing the equation to a linear one-dimensional random-walk problem. Second, I investigate equation y''(x)=6[y( x
Six-dimensional (1,0) superconformal models and higher gauge theory
Palmer, Sam; Sämann, Christian
2013-11-15
We analyze the gauge structure of a recently proposed superconformal field theory in six dimensions. We find that this structure amounts to a weak Courant-Dorfman algebra, which, in turn, can be interpreted as a strong homotopy Lie algebra. This suggests that the superconformal field theory is closely related to higher gauge theory, describing the parallel transport of extended objects. Indeed we find that, under certain restrictions, the field content and gauge transformations reduce to those of higher gauge theory. We also present a number of interesting examples of admissible gauge structures such as the structure Lie 2-algebra of an abelian gerbe, differential crossed modules, the 3-algebras of M2-brane models, and string Lie 2-algebras.
Gauging the twisted Poincare symmetry as a noncommutative theory of gravitation
Chaichian, M.; Tureanu, A.; Oksanen, M.; Zet, G.
2009-02-15
Einstein's theory of general relativity was formulated as a gauge theory of Lorentz symmetry by Utiyama in 1956, while the Einstein-Cartan gravitational theory was formulated by Kibble in 1961 as the gauge theory of Poincare transformations. In this framework, we propose a formulation of the gravitational theory on canonical noncommutative space-time by covariantly gauging the twisted Poincare symmetry, in order to fulfil the requirement of covariance under the general coordinate transformations, an essential ingredient of the theory of general relativity. It appears that the twisted Poincare symmetry cannot be gauged by generalizing the Abelian twist to a covariant non-Abelian twist, nor by introducing a more general covariant twist element. The advantages of such a formulation as well as the related problems are discussed and possible ways out are outlined.
On p -form theories with gauge invariant second order field equations
NASA Astrophysics Data System (ADS)
Deffayet, Cédric; Mukohyama, Shinji; Sivanesan, Vishagan
2016-04-01
We explore field theories of a single p -form with equations of motions of order strictly equal to 2 and gauge invariance. We give a general method for the classification of such theories which are extensions to the p -forms of the Galileon models for scalars. Our classification scheme allows us to compute an upper bound on the number of different such theories depending on p and on the space-time dimension. We are also able to build a nontrivial Galileon-like theory for a 3-form with gauge invariance and an action which is polynomial into the derivatives of the form. This theory has gauge invariant field equations but an action which is not, like a Chern-Simons theory. Hence the recently discovered no-go theorem stating that there are no nontrivial gauge invariant vector Galileons (which we are also able here to confirm with our method) does not extend to other odd-p cases.
Topics in Nonsupersymmetric Scattering Amplitudes in Gauge and Gravity Theories
NASA Astrophysics Data System (ADS)
Nohle, Joshua David
In Chapters 1 and 2, we introduce and review the duality between color and kinematics in Yang-Mills theory uncovered by Bern, Carrasco and Johansson (BCJ). In Chapter 3, we provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions. In Chapter 4, we extend the four-point one-loop nonsupersymmetric pure Yang-Mills discussion of Chapter 3 to include fermions and scalars circulating in the loop with all external gluons. This gives another nontrivial loop-level example showing that the duality between color and kinematics holds in nonsupersymmetric gauge theory. The construction is valid in any spacetime dimension and written in terms of formal polarization vectors. We also convert these expressions into a four-dimensional form with explicit external helicity states. Using this, we compare our results to one-loop duality-satisfying amplitudes that are already present in literature. In Chapter 5, we switch from the topic of color-kinematics duality to discuss the recently renewed interest in the soft behavior of gravitons and gluons. Specifically, we discuss the subleading low-energy behavior. Cachazo and Strominger recently proposed an extension of the soft-graviton theorem found by Weinberg. In addition, they proved the validity of their extension at
Cold Atoms in Non-Abelian Gauge Potentials: From the Hofstadter Moth to Lattice Gauge Theory
Osterloh, K.; Baig, M.; Santos, L.; Zoller, P.; Lewenstein, M.
2005-07-01
We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary kxk matrices. The single-particle dynamics in the case of intense U(2) vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.
Time-Dependent Variational Approach to the pure Gauge Theory for Evaluating the Shear Viscosity
NASA Astrophysics Data System (ADS)
Tsue, Yasuhiko; Lee, Tong-Gyu; Ishii, Hiroshi
2009-10-01
The time-dependent variational approach to the pure Yang-Mills gauge theory, especially a color su(3) gauge theory, is formulated in the functional Schr"odinger picture with a Gaussian wave functional approximation. The equations of motion for the quantum gauge fields are formulated in the Liouville-von Neumann form. This variational approach is applied in order to derive the shear viscosity, which is one of the transport coefficients for the pure gluonic matter, by using the linear response theory. As a result, the contribution to the shear viscosity from the quantum gluons is zero up to the lowest order of the coupling g in the quantum gluonic matter.
Abe, Sumiyoshi; Kobayashi, Tsunehiro
2003-03-01
Microcanonical ensemble theory of free bosons is derived from quantum mechanics by making use of the hidden gauge structure. The relative phase interaction associated with this gauge structure, described by the Pegg-Barnett formalism, is shown to lead to perfect decoherence in the thermodynamic limit and the principle of equal a priori probability, simultaneously.
Covariant gauges without Gribov ambiguities in Yang-Mills theories
NASA Astrophysics Data System (ADS)
Serreau, J.; Tissier, M.; Tresmontant, A.
2014-06-01
We propose a one-parameter family of nonlinear covariant gauges which can be formulated as an extremization procedure that may be amenable to lattice implementation. At high energies, where the Gribov ambiguities can be ignored, this reduces to the Curci-Ferrari-Delbourgo-Jarvis gauges. We further propose a continuum formulation in terms of a local action which is free of Gribov ambiguities and avoids the Neuberger zero problem of the standard Faddeev-Popov construction. This involves an averaging over Gribov copies with a nonuniform weight, which introduces a new gauge-fixing parameter. We show that the proposed gauge-fixed action is perturbatively renormalizable in four dimensions and we provide explicit expressions of the renormalization factors at one loop. We discuss the possible implications of the present proposal for the calculation of Yang-Mills correlators.
The energy-momentum tensor(s) in classical gauge theories
Blaschke, Daniel N.; Gieres, François; Reboud, Méril; ...
2016-07-12
We give an introduction to, and review of, the energy-momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy-momentum tensor. In conclusion, the relationship with the Einstein-Hilbert tensor following from the coupling to a gravitational field is also discussed.
Probing the W-Z-Higgs sector of electroweak gauge theories at the superconducting super collider
Gunion, J.F.
1986-10-01
We review and summarize the procedures for exploring at the SSC the W-Z-Higgs sector of SU(2)/sub L/ x U(1) and extended gauge theory versions thereof, including supersymmetric and left-right symmetric models.
Gauge invariant perturbation theory and non-critical string models of Yang-Mills theories
NASA Astrophysics Data System (ADS)
Lugo, Adrián R.; Sturla, Mauricio B.
2010-04-01
We carry out a gauge invariant analysis of certain perturbations of D - 2-branes solutions of low energy string theories. We get generically a system of second order coupled differential equations, and show that only in very particular cases it is possible to reduce it to just one differential equation. Later, we apply it to a multi-parameter, generically singular family of constant dilaton solutions of non-critical string theories in D dimensions, a generalization of that recently found in arXiv:0709.0471 [hep-th]. According to arguments coming from the holographic gauge theory-gravity correspondence, and at least in some region of the parameters space, we obtain glue-ball spectra of Yang-Mills theories in diverse dimensions, putting special emphasis in the scalar metric perturbations not considered previously in the literature in the non critical setup. We compare our numerical results to those studied previously and to lattice results, finding qualitative and in some cases, tuning properly the parameters, quantitative agreement. These results seem to show some kind of universality of the models, as well as an irrelevance of the singular character of the solutions. We also develop the analysis for the T-dual, non trivial dilaton family of solutions, showing perfect agreement between them.
Duality and gauge invariance of non-commutative spacetime Podolsky electromagnetic theory
NASA Astrophysics Data System (ADS)
Abreu, Everton M. C.; Fernandes, Rafael L.; Mendes, Albert C. R.; Neto, Jorge Ananias; Neves, Mario, Jr.
2017-01-01
The interest in higher derivative field theories has its origin mainly in their influence concerning the renormalization properties of physical models and to remove ultraviolet divergences. In this paper, we have introduced the non-commutative (NC) version of the Podolsky theory and we investigated the effect of the non-commutativity over its original gauge invariance property. We have demonstrated precisely that the non-commutativity spoiled the primary gauge invariance of the original action under this primary gauge transformation. After that we have used the Noether dualization technique to obtain a dual and gauge invariant action. We have demonstrated that through the introduction of a Stueckelberg field in this NC model, we can also recover the primary gauge invariance. In this way, we have accomplished a comparison between both methods.
Ward identities and gauge flow for M-theory in N =3 superspace
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker
2015-09-01
We derive the Becchi-Rouet-Stora-Tyutin (BRST) symmetry, Slavnov-Taylor identities, and Nielsen identities for the Aharony-Bergman-Jafferis-Maldacena theories in N =3 harmonic superspace. Further, the gauge dependence of one-particle irreducible amplitudes in this superconformal Chern-Simons theory is shown to be generated by a canonical flow with respect to the extended Slavnov-Taylor identity, induced by the extended BRST transformations (including the BRST transformations of the gauge parameters).
Renormalization In Quantum Gauge Theory Using Zeta-Function Method
Chiritoiu, Viorel; Zet, Gheorghe
2009-05-22
It is possible to consider space-time symmetries (for example Poincare or de Sitter) as purely inner symmetries. A formulation of the de Sitter symmetry as purely inner symmetry defined on a fixed Minkowski space-time is presented. We define the generators of the de Sitter group and write the equations of structure using a constant deformation parameter {lambda}. Local gauge transformations and corresponding covariant derivative depending on gauge fields are obtained. The method of generalized zeta-function is used to realize the renormalization. An effective integral of action is obtained and a comparison with other results is given.
Gauge coupling unification and light exotica in string theory.
Raby, Stuart; Wingerter, Akin
2007-08-03
In this Letter we consider the consequences for the CERN Large Hadron Collider of light vectorlike exotica with fractional electric charge. It is shown that such states are found in orbifold constructions of the heterotic string. Moreover, these exotica are consistent with gauge coupling unification at one loop, even though they do not come in complete multiplets of SU(5).
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2015-05-01
We prove the Adler-Bardeen theorem in a large class of general gauge theories, including nonrenormalizable ones. We assume that the gauge symmetries are general covariance, local Lorentz symmetry, and Abelian and non-Abelian Yang-Mills symmetries, and that the local functionals of vanishing ghost numbers satisfy a variant of the Kluberg-Stern-Zuber conjecture. We show that if the gauge anomalies are trivial at one loop, for every truncation of the theory there exists a subtraction scheme where they manifestly vanish to all orders, within the truncation. Outside the truncation the cancellation of gauge anomalies can be enforced by fine-tuning local counterterms. The framework of the proof is worked out by combining a recently formulated chiral dimensional regularization with a gauge invariant higher-derivative regularization. If the higher-derivative regularizing terms are placed well beyond the truncation, and the energy scale Λ associated with them is kept fixed, the theory is superrenormalizable and has the property that, once the gauge anomalies are canceled at one loop, they manifestly vanish from two loops onwards by simple power counting. When the Λ divergences are subtracted away and Λ is sent to infinity, the anomaly cancellation survives in a manifest form within the truncation and in a nonmanifest form outside. The standard model coupled to quantum gravity satisfies all the assumptions, so it is free of gauge anomalies to all orders.
Introduction to gauge theories of the strong, weak, and electromagnetic interactions
Quigg, C.
1980-07-01
The plan of these notes is as follows. Chapter 1 is devoted to a brief evocative review of current beliefs and prejudices that form the context for the discussion to follow. The idea of Gauge Invariance is introduced in Chapter 2, and the connection between conservation laws and symmetries of the Lagrangian is recalled. Non-Abelian gauge field theories are constructed in Chapter 3, by analogy with the familiar case of electromagnetism. The Yang-Mills theory based upon isospin symmetry is constructed explicitly, and the generalization is made to other gauge groups. Chapter 4 is concerned with spontaneous symmetry breaking and the phenomena that occur in the presence or absence of local gauge symmetries. The existence of massless scalar fields (Goldstone particles) and their metamorphosis by means of the Higgs mechanism are illustrated by simple examples. The Weinberg-Salam model is presented in Chapter 5, and a brief resume of applications to experiment is given. Quantum Chromodynamics, the gauge theory of colored quarks and gluons, is developed in Chapter 6. Asymptotic freedom is derived schematically, and a few simple applications of perturbative QCD ae exhibited. Details of the conjectured confinement mechanism are omitted. The strategy of grand unified theories of the strong, weak, and electromagnetic interactions is laid out in Chapter 7. Some properties and consequences of the minimal unifying group SU(5) are presented, and the gauge hierarchy problem is introduced in passing. The final chapter contains an essay on the current outlook: aspirations, unanswered questions, and bold scenarios.
Non-anticommutative chiral singlet deformation of N=(1,1) gauge theory
NASA Astrophysics Data System (ADS)
Ferrara, S.; Ivanov, E.; Lechtenfeld, O.; Sokatchev, E.; Zupnik, B.
2005-01-01
We study the SO(4)×SU(2) invariant Q-deformation of Euclidean N=(1,1) gauge theories in the harmonic superspace formulation. This deformation preserves chirality and Grassmann harmonic analyticity but breaks N=(1,1) to N=(1,0) supersymmetry. The action of the deformed gauge theory is an integral over the chiral superspace, and only the purely chiral part of the covariant superfield strength contributes to it. We give the component form of the N=(1,0) supersymmetric action for the gauge groups U(1) and U(n>1). In the U(1) and U(2) cases, we find the explicit nonlinear field redefinition (Seiberg-Witten map) relating the deformed N=(1,1) gauge multiplet to the undeformed one. This map exists in the general U(n) case as well, and we use this fact to argue that the deformed U(n) gauge theory can be nonlinearly reduced to a theory with the gauge group SU(n).
Comments on Worldsheet Theories Dual to Free Large N Gauge Theories
Aharony, Ofer; David, Justin R.; Gopakumar, Rajesh; Komargodski, Zohar; Razamat, Shlomo S.; /Technion
2007-03-21
We continue to investigate properties of the worldsheet conformal field theories (CFTs) which are conjectured to be dual to free large N gauge theories, using the mapping of Feynman diagrams to the worldsheet suggested in [1]. The modular invariance of these CFTs is shown to be built into the formalism. We show that correlation functions in these CFTs which are localized on subspaces of the moduli space may be interpreted as delta-function distributions, and that this can be consistent with a local worldsheet description given some constraints on the operator product expansion coefficients. We illustrate these features by a detailed analysis of a specific four-point function diagram. To reliably compute this correlator we use a novel perturbation scheme which involves an expansion in the large dimension of some operators.
Gauge Mechanics of Deformable Bodies: a Theory of Something.
NASA Astrophysics Data System (ADS)
Shapere, Alfred Dudley
The treatment of the motion of deformable bodies requires a specification of axes for each shape. We present a natural kinematic formulation of this problem in terms of a gauge structure over the space of shapes that the body may assume. Our first and simplest application is to a freely -falling self-deforming body. We show how deformations of a body with angular momentum zero can result in a change in orientation, and we give a general expression for the gauge potential describing the net rotation due to an arbitrary change of shape. The problem of swimming at low Reynolds number may also be formulated in terms of a gauge potential. Effective methods for computing it, by solving a linear boundary value problem, are described. We employ conformal mapping techniques to calculate swimming motions for cylinders with a variety of cross-sections. We also determine the net translational motions due to arbitrary infinitesimal deformations of the sphere and the circular cylinder. The solution is compactly expressed in terms of the field strength tensor of the gauge potential. Having solved for all cyclic swimming motions of a nearly spherical body, it makes sense to ask which motions are the best. We define a notion of efficiency and use it to determine optimal swimming strokes. These strokes are composed of propagating waves, symmetric about the axis of propulsion. Qualitatively, they resemble the swimming strokes of ciliated micro-organisms, such as the Paramecium. The solution of Stokes' equations is not feasible analytically, except for the simplest shapes. Two approximation schemes may help in studying more general swimming strokes. We discuss and test a short-wavelength analytic approximation, valid when the scales associated with a deformation are small relative to the radius of curvature of the average shape. The complementary domain of large deformations is probably best dealt with on a computer. We sketch a general method for solving Stokes' equations numerically.
Lectures on the plane-wave string/gauge theory duality
NASA Astrophysics Data System (ADS)
Plefka, J. C.
2004-02-01
These lectures give an introduction to the novel duality relating type IIB string theory in a maximally supersymmetric plane-wave background to = 4, d = 4, U(N) super Yang-Mills theory in a particular large N and large R-charge limit due to Berenstein, Maldacena and Nastase. In the first part of these lectures the duality is derived from the AdS/CFT correspondence by taking a Penrose limit of the AdS5 × S5 geometry and studying the corresponding double-scaling limit on the gauge theory side. The resulting free plane-wave superstring is then quantized in light-cone gauge. On the gauge theory side of the correspondence the composite super Yang-Mills operators dual to string excitations are identified, and it is shown how the string spectrum can be mapped to the planar scaling dimensions of these operators. In the second part of these lectures we study the correspondence at the interacting respectively non-planar level. On the gauge theory side it is demonstrated that the large N large R-charge limit in question preserves contributions from Feynman graphs of all genera through the emergence of a new genus counting parameter - in agreement with the string genus expansion for non-zero gs. Effective quantum mechanical tools to compute higher genus contributions to the scaling dimensions of composite operators are developed and explicitly applied in a genus one computation. We then turn to the interacting string theory side and give an elementary introduction into light-cone superstring field theory in a plane-wave background and point out how the genus one prediction from gauge theory can be reproduced. Finally, we summarize the present status of the plane-wave string/gauge theory duality.
Gauge invariances of higher derivative Maxwell-Chern-Simons field theory: A new Hamiltonian approach
NASA Astrophysics Data System (ADS)
Mukherjee, Pradip; Paul, Biswajit
2012-02-01
A new method of abstracting the independent gauge invariances of higher derivative systems, recently introduced in [R. Banerjee, P. Mukherjee, and B. Paul, J. High Energy Phys.JHEPFG1029-8479 08 (2011) 085.10.1007/JHEP08(2011)085], has been applied to higher derivative field theories. This has been discussed taking the extended Maxwell-Chern-Simons model as an example. A new Hamiltonian analysis of the model is provided. This Hamiltonian analysis has been used to construct the independent gauge generator. An exact mapping between the Hamiltonian gauge transformations and the U(1) symmetries of the action has been established.
Perturbative quantization of Yang-Mills theory with classical double as gauge algebra
NASA Astrophysics Data System (ADS)
Ruiz Ruiz, F.
2016-02-01
Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary.
Group-theoretic relations for amplitudes in gauge theories with orthogonal and symplectic groups
NASA Astrophysics Data System (ADS)
Huang, Jia-Hui
2017-01-01
It is important to find nontrivial constraint relations for color-ordered amplitudes in gauge theories. In the past several years, a pure group-theoretic iterative method has been proposed for deriving linear constraints on color-ordered amplitudes in S U (N ) gauge theories. In this paper, we use the same method to derive linear constraints on four-point gluon amplitudes in S O (N ) and S p (2 N ) gauge theories. These constraints are derived up to four-loop order. It is found that there are n =1 , 6, 10, 13, 16 constraint relations at L =0 , 1, 2, 3, 4 loop orders in both S O (N ) and S p (2 N ) cases. Correspondingly, there are 2,3,5,8, and 11 independent four-point color-ordered amplitudes at L =0 , 1, 2, 3, 4 loop orders in both theories.
Canonical quantization of four- and five-dimensional U(1) gauge theories
NASA Astrophysics Data System (ADS)
Shnerb, N.; Horwitz, L. P.
1993-12-01
We discuss the canonical quantization of an interacting massless U(1) gauge field using a bosonic gauge-fixing method. We present a way to make the transformation between the Lorentz and the Coulomb gauge of such theories, without using an explicit representation of the fields in terms of creation-annihilation operators. We demonstrate this method in the case of Maxwell photons interacting with Schrödinger electrons and then we treat, with the same methods, a system of higher-dimensional equations appearing in the framework of a manifestly covariant relativistic quantum theory. The nonrelativistic limit of the Coulomb term for such a theory is discussed and compared to the Fokker action appearing in the Wheeler-Feynman action-at-a-distance theory for electromagnetic interactions.
Heavy quark free energy in QCD and in gauge theories with gravity duals
Noronha, Jorge
2010-09-15
Recent lattice results in pure glue SU(3) theory at high temperatures have shown that the expectation value of the renormalized Polyakov loop approaches its asymptotic limit at high temperatures from above. We show that this implies that the 'heavy quark free energy' obtained from the renormalized loop computed on the lattice does not behave like a true thermodynamic free energy. While this should be expected to occur in asymptotically free gauge theories such as QCD, we use the gauge/string duality to show that in a large class of strongly coupled gauge theories with nontrivial UV fixed points the Polyakov loop reaches its asymptotic value from above only if the dimension of the relevant operator used to deform the conformal field theory is greater than or equal to 3.
Operator counting and eigenvalue distributions for 3D supersymmetric gauge theories
NASA Astrophysics Data System (ADS)
Gulotta, Daniel R.; Herzog, Christopher P.; Pufu, Silviu S.
2011-11-01
We give further support for our conjecture relating eigenvalue distributions of the Kapustin-Willett-Yaakov matrix model in the large N limit to numbers of operators in the chiral ring of the corresponding supersymmetric three-dimensional gauge theory. We show that the relation holds for non-critical R-charges and for examples with mathcal{N} = {2} instead of mathcal{N} = {3} supersymmetry where the bifundamental matter fields are nonchiral. We prove that, for non-critical R-charges, the conjecture is equivalent to a relation between the free energy of the gauge theory on a three sphere and the volume of a Sasaki manifold that is part of the moduli space of the gauge theory. We also investigate the consequences of our conjecture for chiral theories where the matrix model is not well understood.
Predicting the singlet vector channel in a partially broken gauge-Higgs theory
NASA Astrophysics Data System (ADS)
Maas, A.; Törek, P.
2017-01-01
We study a toy version of a grand-unified theory on the lattice: An S U (3 ) gauge theory, which experiences a Brout-Englert-Higgs effect due to a single Higgs field in the fundamental representation. This yields a perturbative breaking pattern S U (3 )→S U (2 ). We investigate the singlet vector channel, finding a nondegenerate and massive ground state. This is in contradistinction to the perturbative prediction of three massless and five massive vector states, even though the correlation functions of the gauge bosons exhibit a weak-coupling behavior, being almost tree-level-like. However, a combination of perturbation theory with the Fröhlich-Morchio-Strocchi mechanism, and thus passing to gauge-invariant perturbation theory, allows one to predict the physical spectrum in this channel.
Analytic approach to phase transitions and observables in Abelian gauge theories
Di Bartolo, C.; Gambini, R.; Trias, A.
1989-05-15
The Hamiltonian formulation of the /ital Z/(2) gauge theory at spatial dimension 2 is analyzed in gauge-invariant geometric terms by working in the loop-labeled basis of the /ital C/ representation. A consistent behavior of physical quantities near the critical point and a reasonable estimation of the transition point and the critical exponents are obtained by using a set of variables that improves the collective description proposed in previous related work.
Gauge theory of fermions on R X S{sup 3} spacetime
Dariescu, M.A.; Dariescu, C.; Gottlieb, I.
1995-06-01
A Lorentz-invariant gauge theory for massive fermions on R X S{sup 3} spacetime is built up. Using the symmetry of S{sup 3}, the authors obtain Dirac-type equations and derive the expression of the fermionic propagator. Finally, starting from the SU(N) gauge-invariant Lagrangian, they obtain the set of Dirac-Yang-Mills equations on R X S{sup 3} spacetime, pointing out major differences from the Minkowskian case.
Gravity as a double copy of gauge theory: from amplitudes to black holes
NASA Astrophysics Data System (ADS)
Monteiro, Ricardo; O'Connell, Donal; White, Chris D.
2015-05-01
We discuss the relation between perturbative gauge theory and perturbative gravity, and look at how this relation extends to some exact classical solutions. First, we give an overview of the double copy prescription that takes gauge theory amplitudes into gravity amplitudes, which has been crucial to progress in perturbative studies of supergravity. Then, we review how the self-dual sectors provide an important insight into the relation between the theories. A key role is played by a kinematic algebraic structure mirroring the color structure. Finally, we review how these ideas extend to some exact classical solutions, namely black holes and plane waves.
Beyond gauge theory: positivity and causal localization in the presence of vector mesons
NASA Astrophysics Data System (ADS)
Schroer, Bert
2016-07-01
The Hilbert space formulation of interacting s=1 vector-potentials stands is an interesting contrast with the point-local Krein space setting of gauge theory. Already in the absence of interactions the Wilson loop in a Hilbert space setting has a topological property which is missing in the gauge-theoretic description (Haag duality, Aharonov-Bohm effect); the conceptual differences increase in the presence of interactions. The Hilbert space positivity weakens the causal localization properties of interacting fields, which results in the replacement of the gauge-variant point-local matter fields in Krein space by string-local physical fields in Hilbert space. The gauge invariance of the perturbative S-matrix corresponds to its independence of the space-like string direction of its interpolating fields. In contrast to gauge theory, whose direct physical range is limited to a gauge-invariant perturbative S-matrix and local observables, its Hilbert space string-local counterpart is a full-fledged quantum field theory (QFT). The new setting reveals that the Lie structure of self-coupled vector mesons results from perturbative implementation of the causal localization principles of QFT.
Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence
NASA Astrophysics Data System (ADS)
Luo, Yuan; Tan, Meng-Chwan; Yagi, Junya; Zhao, Qin
2015-02-01
We study Ω-deformation of B-twisted gauge theories in two dimensions. As an application, we construct an Ω-deformed, topologically twisted five-dimensional maximally supersymmetric Yang-Mills theory on the product of a Riemann surface Σ and a three-manifold M, and show that when Σ is a disk, this theory is equivalent to analytically continued Chern-Simons theory on M. Based on these results, we establish a correspondence between three-dimensional = 2 superconformal theories and analytically continued Chern-Simons theory. Furthermore, we argue that there is a mirror symmetry between Ω-deformed two-dimensional theories.
Three-dimensional gauge theory in Dirac formalism
NASA Astrophysics Data System (ADS)
Kamimura, Kiyoshi
1986-08-01
The Hagen model [C. R. Hagen, Ann. Phys. (NY) 157, 342 (1984); Phys. Rev. D 31, 331 (1985)] is studied using the method of constrained Hamiltonian formalism developed by Dirac [P. A. M. Dirac, Can. J. Math. 2, 129 (1950); Lectures on Quantum Mechanics (Yeshiva U. P., New York, 1964)]. The results recently obtained by Burnel and Van Der Rest-Jaspers [A. Burnel and M. Van Der Rest-Jaspers, J. Math. Phys. 26, 3155 (1985)] are reexamined and modified. There appear two second-class constraints and their choice is not crucial. The equivalence of different gauges is proved without referring to the current conservation law.
Gauge formulation of gravitation theories. I. The Poincaré, de Sitter, and conformal cases
NASA Astrophysics Data System (ADS)
Ivanov, E. A.; Niederle, J.
1982-02-01
The gauge formulations of various gravitation theories are discussed. They are based on the approach in which we have the group Diff R4 acting on xμ and in which we attach to every xμ a tangent space with the group of action H. Group H does not act on xμ and plays the role of an internal (global) symmetry group in the standard Yang-Mills theory. The matter fields in the theory transform according to representations of H and are assumed to be scalars of Diff R4. The full invariance group of the Lagrangian is then of the form Hloc⊗Diff R4. Here Hloc is a local gauge group obtained from H exactly as in the Yang-Mills theory. The approach has two characteristic features: (i) The group Hloc must be spontaneously broken in order to exclude redundant gauge fields (the Lorentz connections) from the theory in a way covariant with respect to the gauge transformations. (ii) To different H there correspond different gravitational theories, all invariant under Diff R4 but differing in backgrounds. Thus if H is isomorphic to the Poincaré group the corresponding gauge theory turns out to be equivalent to the usual Einstein or Einstein-Cartan theory of gravity in the Minkowski space as a background. The other choices for H considered in the paper are the de Sitter groups and the conformal group. They yield the Einstein theory with a negative (or positive) cosmological term in the corresponding de Sitter space and the Weyl or Cartan-Weyl theory (depending on realization of the conformal group), respectively.
NASA Astrophysics Data System (ADS)
Huang, Changyu; Huang, Yong-Chang; Zhou, Bao-Hua
2015-09-01
We investigate the inner structure of a general S U (2 ) [naturally including S O (3 )] symmetry system—the fermion-gauge field interaction system—and achieve naturally a set of gauge-invariant spin and orbital angular momentum operators of fermion and gauge fields by Noether's theorem in general field theory. Some new relations concerning non-Abelian field strengths are discovered, e.g., the covariant transverse condition, covariant parallel condition (i.e., non-Abelian divergence, non-Abelian curl), and simplified S U (2 ) Coulomb theorem. And we show that the condition that Chen et al. obtained to construct their gauge-invariant angular momentum operators is a result of some fundamental equations in the general field theory. The results obtained in this paper present a new perspective for looking at the overall structure of the gauge field, and provide a new viewpoint to the final resolution of the nucleon spin crisis in the general field theory. Especially, the achieved theory in this paper can calculate the strong interactions with isospin symmetry and solves the serious problem without gauge-invariant angular momenta in strong interaction systems with isospin symmetry, and then the achieved predictions in the calculations can be exactly measured by particle physics experiments due to their gauge invariant properties.
Entanglement entropy for pure gauge theories in 1+1 dimensions using the lattice regularization
NASA Astrophysics Data System (ADS)
Aoki, Sinya; Itou, Etsuko; Nagata, Keitaro
2016-12-01
We study the entanglement entropy (EE) for pure gauge theories in 1+1 dimensions with the lattice regularization. Using the definition of the EE for lattice gauge theories proposed in a previous paper,1 we calculate the EE for arbitrary pure as well as mixed states in terms of eigenstates of the transfer matrix in (1+1)-dimensional lattice gauge theory. We find that the EE of an arbitrary pure state does not depend on the lattice spacing, thus giving the EE in the continuum limit, and show that the EE for an arbitrary pure state is independent of the real (Minkowski) time evolution. We also explicitly demonstrate the dependence of EE on the gauge fixing at the boundaries between two subspaces, which was pointed out for general cases in the paper. In addition, we calculate the EE at zero as well as finite temperature by the replica method, and show that our result in the continuum limit corresponds to the result obtained before in the continuum theory, with a specific value of the counterterm, which is otherwise arbitrary in the continuum calculation. We confirm the gauge dependence of the EE also for the replica method.
All-order results for infrared and collinear singularities in massless gauge theories
Dixon, Lance J.; Gardi, Einan; Magnea, Lorenzo; /CERN
2010-05-26
We review recent results concerning the all-order structure of infrared and collinear divergences in massless gauge theory amplitudes. While the exponentiation of these divergences for nonabelian gauge theories has been understood for a long time, in the past couple of years we have begun to unravel the all-order structure of the anomalous dimensions that build up the perturbative exponent. In the large-N{sub c} limit, all infrared and collinear divergences are determined by just three functions; one of them, the cusp anomalous dimension, plays a key role also for non-planar contributions. Indeed, all infrared and collinear divergences of massless gauge theory amplitudes with any number of hard partonsmay be captured by a surprisingly simple expression constructed as a sum over color dipoles. Potential corrections to this expression, correlating four or more hard partons at three loops or beyond, are tightly constrained and are currently under study.
The ADHM-like constructions for instantons on CP2 and three-dimensional gauge theories
NASA Astrophysics Data System (ADS)
Mekareeya, Noppadol; Rodríguez-Gómez, Diego
2015-02-01
We study the moduli spaces of self-dual instantons on CP2 in a simple group G. When G is a classical group, these instanton solutions can be realized using ADHM-like constructions which can be naturally embedded into certain three-dimensional quiver gauge theories with four supercharges. The topological data for such instanton bundles and their relations to the quiver gauge theories are described. Based on such gauge theory constructions, we compute the Hilbert series of the moduli spaces of instantons that correspond to various configurations. The results turn out to be equal to the Hilbert series of their counterparts on C2 upon an appropriate mapping. We check the former against the Hilbert series derived from the blowup formula for the Hirzebruch surface F1 and find an agreement. The connection between the moduli spaces of instantons on such two spaces is explained in detail.
Optimization of pressure gauge locations for water distribution systems using entropy theory.
Yoo, Do Guen; Chang, Dong Eil; Jun, Hwandon; Kim, Joong Hoon
2012-12-01
It is essential to select the optimal pressure gauge location for effective management and maintenance of water distribution systems. This study proposes an objective and quantified standard for selecting the optimal pressure gauge location by defining the pressure change at other nodes as a result of demand change at a specific node using entropy theory. Two cases are considered in terms of demand change: that in which demand at all nodes shows peak load by using a peak factor and that comprising the demand change of the normal distribution whose average is the base demand. The actual pressure change pattern is determined by using the emitter function of EPANET to reflect the pressure that changes practically at each node. The optimal pressure gauge location is determined by prioritizing the node that processes the largest amount of information it gives to (giving entropy) and receives from (receiving entropy) the whole system according to the entropy standard. The suggested model is applied to one virtual and one real pipe network, and the optimal pressure gauge location combination is calculated by implementing the sensitivity analysis based on the study results. These analysis results support the following two conclusions. Firstly, the installation priority of the pressure gauge in water distribution networks can be determined with a more objective standard through the entropy theory. Secondly, the model can be used as an efficient decision-making guide for gauge installation in water distribution systems.
Perturbations of matter fields in the second-order gauge-invariant cosmological perturbation theory
NASA Astrophysics Data System (ADS)
Nakamura, Kouji
2009-12-01
To show that the general framework of the second-order gauge-invariant perturbation theory developed by K. Nakamura [Prog. Theor. Phys. 110, 723 (2003)PTPKAV0033-068X10.1143/PTP.110.723; Prog. Theor. Phys. 113, 481 (2005)PTPKAV0033-068X10.1143/PTP.113.481] is applicable to a wide class of cosmological situations, some formulas for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe, which is developed in Prog. Theor. Phys. 117, 17 (2007)PTPKAV0033-068X10.1143/PTP.117.17. We derive the formulas for the perturbations of the energy-momentum tensors and equations of motion for a perfect fluid, an imperfect fluid, and a single scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing. Through these formulas, we may say that the decomposition formulas for the perturbations of any tensor field into gauge-invariant and gauge-variant parts, which are proposed in the above papers, are universal.
2d Affine XY-Spin Model/4d Gauge Theory Duality and Deconfinement
Anber, Mohamed M.; Poppitz, Erich; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept. /San Francisco State U.
2012-08-16
We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2) = Z{sub 2} gauge theories, compactified on a small spatial circle R{sup 1,2} x S{sup 1}, and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on R{sup 2} x T{sup 2}. Similarly, thermal gauge theories of higher rank are dual to new families of 'affine' XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU(N{sub c}) gauge theories with n{sub f} {ge} 1 adjoint Weyl fermions.
Confinement Driven by Scalar Field in 4d Non Abelian Gauge Theories
Chabab, Mohamed
2007-01-12
We review some of the most recent work on confinement in 4d gauge theories with a massive scalar field (dilaton). Emphasis is put on the derivation of confining analytical solutions to the Coulomb problem versus dilaton effective couplings to gauge terms. It is shown that these effective theories can be relevant to model quark confinement and may shed some light on confinement mechanism. Moreover, the study of interquark potential, derived from Dick Model, in the heavy meson sector proves that phenomenological investigation of tmechanism is more than justified and deserves more efforts.
Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions
NASA Astrophysics Data System (ADS)
Chernodub, M. N.; Goy, V. A.; Molochkov, A. V.
2016-11-01
We propose a general numerical method to study the Casimir effect in lattice gauge theories. We illustrate the method by calculating the energy density of zero-point fluctuations around two parallel wires of finite static permittivity in Abelian gauge theory in two spatial dimensions. We discuss various subtle issues related to the lattice formulation of the problem and show how they can successfully be resolved. Finally, we calculate the Casimir potential between the wires of a fixed permittivity, extrapolate our results to the limit of ideally conducting wires and demonstrate excellent agreement with a known theoretical result.
Hamiltonian Approach to Yang-Mills Theory in Coulomb Gauge--Revisited
Reinhardt, Hugo; Campagnari, Davide R.; Leder, Markus; Burgio, Giuseppe; Quandt, Markus; Pawlowski, Jan M.; Weber, Axel
2011-05-24
I briefly review results obtained within the variational Hamiltonian approach to Yang-Mills theory in Coulomb gauge and confront them with recent lattice data. The variational approach is extended to non-Gaussian wave functionals including three- and four-gluon kernels in the exponential of the vacuum wave functional and used to calculate the three-gluon vertex. A new functional renormalization group flow equation for Hamiltonian Yang-Mills theory in Coulomb gauge is solved for the gluon and ghost propagator under the assumption of ghost dominance. The results are compared to those obtained in the variational approach.
Atomic quantum simulation of a three-dimensional U(1) gauge-Higgs model
NASA Astrophysics Data System (ADS)
Kuno, Yoshihito; Sakane, Shinya; Kasamatsu, Kenichi; Ichinose, Ikuo; Matsui, Tetsuo
2016-12-01
In this paper, we study theoretically atomic quantum simulations of a U(1) gauge-Higgs model on a three-dimensional (3D) spatial lattice by using an extended Bose-Hubbard model with intersite repulsions on a 3D optical lattice. Here, the phase and density fluctuations of the boson variable on each site of the optical lattice describe the vector potential and the electric field on each link of the gauge-model lattice, respectively. The target gauge model is different from the standard Wilson-type U(1) gauge-Higgs model because it has plaquette and Higgs interactions with asymmetric couplings in the space-time directions. Nevertheless, the corresponding quantum simulation is still important as it provides us with a platform to study unexplored time-dependent phenomena characteristic of each phase in the general gauge-Higgs models. To determine the phase diagram of the gauge-Higgs model at zero temperature, we perform Monte Carlo simulations of the corresponding 3+1-dimensional U(1) gauge-Higgs model, and obtain the confinement and Higgs phases. To investigate the dynamical properties of the gauge-Higgs model, we apply the Gross-Pitaevskii equations to the extended Bose-Hubbard model. We simulate the time evolution of an electric flux that initially is put on a straight line connecting two external point charges. We also calculate the potential energy between this pair of charges and obtain the string tension in the confinement phase. Finally, we propose a feasible experimental setup for the atomic simulations of this quantum gauge-Higgs model on the 3D optical lattice. These results may serve as theoretical guides for future experiments.
Aharonov-Bohm order parameters for non-Abelian gauge theories
Lo, H.
1995-12-15
The Aharonov-Bohm effect has been invoked to probe the phase structure of a gauge theory. Yet in the case of non-Abelian gauge theories, it proves difficult to formulate a general procedure that unambiguously specifies the realization of the gauge symmetry, e.g., the unbroken subgroup. In this paper we propose a set of order parameters that will do the job. We articulate the fact that any useful Aharonov-Bohm experiment necessarily proceeds in two stages: calibration and measurement. World sheets of virtual cosmic string loops can wrap around test charges, thus changing their states relative to other charges in the universe. Consequently, repeated flux measurements with test charges will not necessarily agree. This was the main stumbling block to previous attempts to construct order parameters for non-Abelian gauge theories. In those works, the particles that one uses for calibration and subsequent measurement are stored in {ital separate} ``boxes.`` By storing all test particles in the {ital same} ``box`` we show how quantum fluctuations can be overcome. The importance of gauge fixing is also emphasized. {copyright} 1995 The American Physical Society.
Simulating Dirac fermions with Abelian and non-Abelian gauge fields in optical lattices
Alba, E.; Fernandez-Gonzalvo, X.; Mur-Petit, J.; Garcia-Ripoll, J.J.; Pachos, J.K.
2013-01-15
In this work we present an optical lattice setup to realize a full Dirac Hamiltonian in 2+1 dimensions. We show how all possible external potentials coupled to the Dirac field can arise from perturbations of the existing couplings of the honeycomb lattice pattern. This greatly simplifies the proposed implementations, requiring only spatial modulations of the intensity of the laser beams to induce complex non-Abelian potentials. We finally suggest several experiments to observe the properties of the quantum field theory in the setup. - Highlights: Black-Right-Pointing-Pointer This work provides a very flexible setup for simulating Dirac fermions. Black-Right-Pointing-Pointer The manuscript contains a detailed study of optical lattice deformations. Black-Right-Pointing-Pointer The link between lattice deformations and effective gauge Hamiltonians is studied.
Light-cone analysis of ungauged and topologically gauged BLG theories
NASA Astrophysics Data System (ADS)
Nilsson, Bengt E. W.
2009-09-01
We consider three-dimensional maximally superconformal Bagger-Lambert-Gustavsson (BLG) theory and its topologically gauged version (constructed recently in Gran and Nilsson (2009 J. High Energy Phys. JHEP03(2009)074 (arXiv:0809.4478 [hep-th]))) in the light-cone gauge. After eliminating the entire Chern-Simons gauge field, the ungauged BLG light-cone theory looks more conventional and, apart from the order of the interaction terms, resembles \\mathcal N=4 super-Yang-Mills theory in four dimensions. The light-cone superspace version of the BLG theory is given at the quadratic order together with a suggested form for the quartic terms. Some problems with constructing the sixth-order interaction terms are also discussed. In the topologically gauged case, we analyze the field equations related to the three Chern-Simons-type terms of \\mathcal N=8 conformal supergravity and discuss some of the special features of this theory and its couplings to BLG.
Large N phase transitions in massive N = 2 gauge theories
Russo, J. G.
2014-07-23
Using exact results obtained from localization on S{sup 4}, we explore the large N limit of N = 2 super Yang-Mills theories with massive matter multiplets. In this talk we discuss two cases: N = 2* theory, describing a massive hypermultiplet in the adjoint representation, and super QCD with massive quarks. When the radius of the four-sphere is sent to infinity these theories are described by solvable matrix models, which exhibit a number of interesting phenomena including quantum phase transitions at finite 't Hooft coupling.
Azuma, Takehiro; Morita, Takeshi; Takeuchi, Shingo
2014-08-29
It is expected that the Gregory-Laflamme (GL) instability in the black string in gravity is related to the Rayleigh-Plateau instability in fluid mechanics. Especially, the orders of the phase transitions associated with these instabilities depend on the number of the transverse space dimensions, and they are of first and second order below and above the critical dimension. Through the gauge-gravity correspondence, the GL instability is conjectured to be thermodynamically related to the Hagedorn instability in large-N gauge theories, and it leads to a prediction that the order of the confinement-deconfinement transition associated with the Hagedorn instability may depend on the transverse dimension. We test this conjecture in the D-dimensional bosonic D0-brane model using numerical simulation and the 1/D expansion, and confirm the expected D dependence.
The algebra of physical observables in non-linearly realized gauge theories
NASA Astrophysics Data System (ADS)
Quadri, Andrea
2010-11-01
We classify the physical observables in spontaneously broken non-linearly realized gauge theories in the recently proposed loopwise expansion governed by the Weak Power-Counting (WPC) and the Local Functional Equation. The latter controls the non-trivial quantum deformation of the classical non-linearly realized gauge symmetry, to all orders in the loop expansion. The Batalin-Vilkovisky (BV) formalism is used. We show that the dependence of the vertex functional on the Goldstone fields is obtained via a canonical transformation w.r.t. the BV bracket associated with the BRST symmetry of the model. We also compare the WPC with strict power-counting renormalizability in linearly realized gauge theories. In the case of the electroweak group we find that the tree-level Weinberg relation still holds if power-counting renormalizability is weakened to the WPC condition.
Decorated tensor network renormalization for lattice gauge theories and spin foam models
NASA Astrophysics Data System (ADS)
Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian
2016-05-01
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.
Dual variables for lattice gauge theories and the phase structure of Z (N) systems
Ukawa, A.; Windey, P.; Guth, A.H.
1980-02-15
The 't Hooft disorder parameters are constructed within the framework of SU(N) lattice gauge theories in three or four dimensions. It is found that these operators arise naturally from a duality transformation which is similar to the standard transformation for Z (N) gauge theories. To illustrate the behavior of dual variables in a simpler context, we study the Villain form of the Z (N) gauge system in three and four dimensions. The techniques include duality, strong-coupling expansions, and the electrodynamic representation. In four dimensions it is found that for N>N/sub c/ approx. = 4, the system possesses at least three phases: a strong-coupling phase with electric confinement, a weak-coupling phase with magnetic confinement, and an intermediate phase which resembles QED, with a massless photon and no confinement. We also study an SU(N) -Higgs system, which interpolates between the Z (N) and SU(N) systems.
Gauge theories on A(dS) space and Killing vectors
Banerjee, Rabin Majhi, Bibhas Ranjan
2008-03-15
We provide a general technique for collectively analysing a manifestly covariant formulation of non-abelian gauge theories on both anti-de Sitter as well as de Sitter spaces. This is done by stereographically projecting the corresponding theories, defined on a flat Minkowski space, onto the surface of the A(dS) hyperboloid. The gauge and matter fields in the two descriptions are mapped by conformal Killing vectors and conformal Killing spinors, respectively. A bilinear map connecting the spinors with the vector is established. Different forms of gauge fixing conditions and their equivalence are discussed. The U(1) axial anomaly as well as the non-abelian covariant and consistent chiral anomalies on A(dS) space are obtained. Electric-magnetic duality is demonstrated. The zero curvature limit is shown to yield consistent findings.
Zhang, Zhen-Lu; Huang, Yong-Chang
2014-03-15
Quantization theory gives rise to transverse phonons for the traditional Coulomb gauge condition and to scalar and longitudinal photons for the Lorentz gauge condition. We describe a new approach to quantize the general singular QED system by decomposing a general gauge potential into two orthogonal components in general field theory, which preserves scalar and longitudinal photons. Using these two orthogonal components, we obtain an expansion of the gauge-invariant Lagrangian density, from which we deduce the two orthogonal canonical momenta conjugate to the two components of the gauge potential. We then obtain the canonical Hamiltonian in the phase space and deduce the inherent constraints. In terms of the naturally deduced gauge condition, the quantization results are exactly consistent with those in the traditional Coulomb gauge condition and superior to those in the Lorentz gauge condition. Moreover, we find that all the nonvanishing quantum commutators are permanently gauge-invariant. A system can only be measured in physical experiments when it is gauge-invariant. The vanishing longitudinal vector potential means that the gauge invariance of the general QED system cannot be retained. This is similar to the nucleon spin crisis dilemma, which is an example of a physical quantity that cannot be exactly measured experimentally. However, the theory here solves this dilemma by keeping the gauge invariance of the general QED system. -- Highlights: •We decompose the general gauge potential into two orthogonal parts according to general field theory. •We identify a new approach for quantizing the general singular QED system. •The results obtained are superior to those for the Lorentz gauge condition. •The theory presented solves dilemmas such as the nucleon spin crisis.
Plasmon mass scale in classical nonequilibrium gauge theory
NASA Astrophysics Data System (ADS)
Lappi, T.; Peuron, J.
2017-01-01
Classical lattice Yang-Mills calculations provide a good way to understand different nonequilibrium phenomena in nonperturbatively overoccupied systems. Above the Debye scale the classical theory can be matched smoothly to kinetic theory. The aim of this work is to study the limits of this quasiparticle picture by determining the plasmon mass in classical real-time Yang-Mills theory on a lattice in three spatial dimensions. We compare three methods to determine the plasmon mass: a hard thermal loop expression in terms of the particle distribution, an effective dispersion relation constructed from fields and their time derivatives, and the measurement of oscillations between electric and magnetic field modes after artificially introducing a homogeneous color electric field. We find that a version of the dispersion relation that uses electric fields and their time derivatives agrees with the other methods within 50%.
Gottlieb, Steven Arthur; DeTar, Carleton; Tousaint, Doug
2014-07-24
This is the closeout report for the Indiana University portion of the National Computational Infrastructure for Lattice Gauge Theory project supported by the United States Department of Energy under the SciDAC program. It includes information about activities at Indian University, the University of Arizona, and the University of Utah, as those three universities coordinated their activities.
Hamiltonian Dyson-Schwinger and FRG Flow Equations of Yang-Mills Theory in Coulomb Gauge
Reinhardt, Hugo; Leder, Markus; Pawlowski, Jan M.; Weber, Axel
2011-05-23
A new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge is presented and solved for the static gluon and ghost propagators under the assumption of ghost dominance. The results are compared to those obtained in the variational approach.
Atoms and molecules in intense laser fields: gauge invariance of theory and models
NASA Astrophysics Data System (ADS)
Bandrauk, A. D.; Fillion-Gourdeau, F.; Lorin, E.
2013-08-01
Gauge invariance was discovered in the development of classical electromagnetism and was required when the latter was formulated in terms of the scalar and vector potentials. It is now considered to be a fundamental principle of nature, stating that different forms of these potentials yield the same physical description: they describe the same electromagnetic field as long as they are related to each other by gauge transformations. Gauge invariance can also be included into the quantum description of matter interacting with an electromagnetic field by assuming that the wavefunction transforms under a given local unitary transformation. The result of this procedure is a quantum theory describing the coupling of electrons, nuclei and photons. Therefore, it is a very important concept: it is used in almost every field of physics and it has been generalized to describe electroweak and strong interactions in the standard model of particles. A review of quantum mechanical gauge invariance and general unitary transformations is presented for atoms and molecules in interaction with intense short laser pulses, spanning the perturbative to highly nonlinear non-perturbative interaction regimes. Various unitary transformations for a single spinless particle time-dependent Schrödinger equation (TDSE) are shown to correspond to different time-dependent Hamiltonians and wavefunctions. Accuracy of approximation methods involved in solutions of TDSEs such as perturbation theory and popular numerical methods depend on gauge or representation choices which can be more convenient due to faster convergence criteria. We focus on three main representations: length and velocity gauges, in addition to the acceleration form which is not a gauge, to describe perturbative and non-perturbative radiative interactions. Numerical schemes for solving TDSEs in different representations are also discussed. A final brief discussion of these issues for the relativistic time-dependent Dirac equation
Gauge theory generalization of the fermion doubling theorem.
Kravec, S M; McGreevy, John
2013-10-18
It is possible to characterize certain states of matter by properties of their edge states. This implies a notion of "surface-only models": models which can only be regularized at the edge of a higher-dimensional system. After incorporating the fermion-doubling results of Nielsen and Ninomiya into this framework, we employ this idea to identify new obstructions to symmetry-preserving regulators of quantum field theory. We focus on an example which forbids regulated models of Maxwell theory with manifest electromagnetic duality symmetry.
Cheng, Lan; Xiao, Yunlong; Liu, Wenjian
2009-12-28
It is recognized only recently that the incorporation of the magnetic balance condition is absolutely essential for four-component relativistic theories of magnetic properties. Another important issue to be handled is the so-called gauge problem in calculations of, e.g., molecular magnetic shielding tensors with finite bases. It is shown here that the magnetic balance can be adapted to distributed gauge origins, leading to, e.g., magnetically balanced gauge-including atomic orbitals (MB-GIAOs) in which each magnetically balanced atomic orbital has its own local gauge origin placed on its center. Such a MB-GIAO scheme can be combined with any level of theory for electron correlation. The first implementation is done here at the coupled-perturbed Dirac-Kohn-Sham level. The calculated molecular magnetic shielding tensors are not only independent of the choice of gauge origin but also converge rapidly to the basis set limit. Close inspections reveal that (zeroth order) negative energy states are only important for the expansion of first order electronic core orbitals. Their contributions to the paramagnetism are therefore transferable from atoms to molecule and are essentially canceled out for chemical shifts. This allows for simplifications of the coupled-perturbed equations.
NASA Astrophysics Data System (ADS)
He, Huan; Zheng, Yunqin; von Keyserlingk, Curt
2017-01-01
Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter community, in part because they represent topological phases of matter, but also because they characterize the response theory of certain symmetry protected topological (SPT) phases. However, as yet there has not been a comprehensive treatment of the spectra of these models in the field theoretic setting even for Abelian gauge groups, the goal of this work is to fill the gap in the literature, especially for a selection of DW models with Abelian gauge groups but non-Abelian topological order. Particularly, we focus on the appearance of non-Abelian statistics in type-III twisted DW theories with Abelian gauge groups Z2⊗3. There are only 22 distinguishable line operators, and their fusion rules and correlation functions are calculated. The flux insertion operators have quantum dimension 2, which clearly demonstrates the non-Abelian topological order of type-III twisted DW theories.
Multiloop amplitudes of light-cone gauge NSR string field theory in noncritical dimensions
NASA Astrophysics Data System (ADS)
Ishibashi, Nobuyuki; Murakami, Koichi
2017-01-01
Feynman amplitudes of light-cone gauge superstring field theory are ill-defined because of various divergences. In a previous paper, one of the authors showed that taking the worldsheet theory to be the one in a linear dilaton background Φ = - iQX 1 with Feynman iɛ ( ɛ > 0) and Q 2 > 10 yields finite amplitudes. In this paper, we apply this worldsheet theory to dimensional regularization of the light-cone gauge NSR superstring field theory. We concentrate on the amplitudes for even spin structure with external lines in the (NS,NS) sector. We show that the multiloop amplitudes are indeed regularized in our scheme and that they coincide with the results in the first-quantized formalism through the analytic continuation Q → 0.
Infrared Renormalons versus Operator Product Expansions in Supersymmetric and Related Gauge Theories
NASA Astrophysics Data System (ADS)
Dunne, Gerald V.; Shifman, M.; Ünsal, Mithat
2015-05-01
We use the connection between infrared (IR) renormalons and condensates in the operator product expansion for correlation functions to make predictions concerning the structure of singularities in the Borel plane for the perturbative series in quantum field theories with different levels of supersymmetry. The same conspiracy can be used for establishing the absence of condensates or IR renormalons in gauge theories with an IR conformal regime or gauge theories in the Higgs phase. The absence of the renormalon-induced factorial divergence implies that instanton contributions (where present) must be well defined. We show that the conventional bubble-chain method for detecting renormalon-induced factorial divergences in these theories is not sufficient.
Conformal window of SU(N) gauge theories with fermions in higher dimensional representations
Dietrich, Dennis D.; Sannino, Francesco
2007-04-15
We study the phase diagram as a function of the number of colors and flavors of asymptotically free nonsupersymmetric theories with matter in higher-dimensional representations of arbitrary SU(N) gauge groups. Since matter in higher-dimensional representations screens more than in the fundamental a general feature is that a lower number of flavors is needed to achieve a near-conformal theory.
Plasma theory and simulation research
Birdsall, C.K.
1989-01-01
Our research group uses both theory and simulation as tools in order to increase the understanding of instabilities, heating, diffusion, transport and other phenomena in plasmas. We also work on the improvement of simulation, both theoretically and practically. Our focus has been more and more on the plasma edge (the sheath''), interactions with boundaries, leading to simulations of whole devices (someday a numerical tokamak).
1981-03-31
measured and appear to be comparable to those predicted by the Vlasov-fluid theory of Seylerl and the finite Larmor radius theory of Freidberg and...C.E. Seyler, "Vlasov-Fluid Stability of a Rigidly Rotating Theta Pinch," Phys. Fluids 22, 2324, (1979). 2. J.P. Freidberg , L.D. Pearlstein
N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
Bern, Z.; Boucher-Veronneau, C.; Johansson, H.; /Saclay
2011-08-19
We expose simple and practical relations between the integrated four- and five-point one-loop amplitudes of N {ge} 4 supergravity and the corresponding (super-)Yang-Mills amplitudes. The link between the amplitudes is simply understood using the recently uncovered duality between color and kinematics that leads to a double-copy structure for gravity. These examples provide additional direct confirmations of the duality and double-copy properties at loop level for a sample of different theories.
Notes on SUSY gauge theories on three-sphere
NASA Astrophysics Data System (ADS)
Hama, Naofumi; Hosomichi, Kazuo; Lee, Sungjay
2011-03-01
We extend theformulaforpartitionfunctions of mathcal{N}=2 superconformalgauge theories on S 3 obtained recently by Kapustin, Willett and Yaakov, to incorporate matter fields with arbitrary R-charge assignments. We use the result to check that the self-mirror property of mathcal{N}=4 SQED with two electron hypermultiplets is preserved under a certain mass deformation which breaks the supersymmetry to mathcal{N}=2.
On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity
NASA Astrophysics Data System (ADS)
Delcamp, Clement; Dittrich, Bianca; Riello, Aldo
2016-11-01
Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, we introduce a new definition of entanglement entropy for both Abelian and non-Abelian gauge theories. Being based on the notion of excitations, it provides a completely relational way of defining regions. Therefore, it naturally applies to background independent theories, e.g. gravity, by circumventing the difficulty of specifying the position of the entangling surface. We relate our construction to earlier proposals and argue that it brings these closer to each other. In particular, it yields the non-Abelian analogue of the `magnetic centre choice', as obtained through an extended-Hilbert-space method, but applied to the recently introduced fusion basis for 3D lattice gauge theories. We point out that the different definitions of entanglement entropy can be related to a choice of (squeezed) vacuum state.
Gauge equivalence of Tachyon solutions in the cubic Neveu—Schwarz string field theory
NASA Astrophysics Data System (ADS)
Aref'eva, I. Ya.; Gorbachev, R. V.
2010-11-01
We construct a simple analytic solution of the cubic Neveu—Schwarz (NS) string field theory including the GSO(-) sector. This solution is analogous to the Erler—Schnabl solution in the bosonic case and to the solution in the pure GSO(+) case previously proposed by one of us. We construct exact gauge transformations of the new solution to other known solutions for the NS string tachyon condensation. This gauge equivalence manifestly supports the previous observation that the Erler solution for the pure GSO(+) sector and our solution containing both the GSO(+) and the GSO(-) sectors have the same value of the action density.
NASA Astrophysics Data System (ADS)
Carlisle, James E.; Johnson, Clifford V.
2003-07-01
We report on our results of D3-brane probing a large class of generalised type~IIB supergravity solutions presented very recently in the literature. The structure of the solutions is controlled by a single non-linear differential equation. These solutions correspond to renormalisation group flows from pure supersymmetric gauge theory to an gauge theory with a massive adjoint scalar. The gauge group is with large. After presenting the general result, we focus on one of the new solutions, solving for the specific coordinates needed to display the explicit metric on the moduli space. We obtain an appropriately holomorphic result for the coupling. We look for the singular locus, and interestingly, the final result again manifests itself in terms of a square root branch cut on the complex plane, as previously found for a set of solutions for which the details are very different. This, together with the existence of the single simple non-linear differential equation, is further evidence in support of an earlier suggestion that there is a very simple model --- perhaps a matrix model with relation to the Calogero-Moser integrable system --- underlying this gauge theory physics.
Near the sill of the conformal window: Gauge theories with fermions in two-index representations
DeGrand, Thomas; Shamir, Yigal; Svetitsky, Benjamin
2013-09-16
We apply Schroedinger functional methods to two gauge theories with fermions in two-index representations: the SU(3) theory with Nf=2 adjoint fermions, and the SU(4) theory with Nf=6 fermions in the two-index antisymmetric representation. Each theory is believed to lie near the bottom of the conformal window for its respective representation. In the SU(3) theory we find a small beta function in strong coupling but we cannot confirm or rule out an infrared fixed point. In the SU(4) theory we find a hint of walking - a beta function that approaches the axis and then turns away from it. In both theories the mass anomalous dimension remains small even at the strongest couplings, much like the theories with fermions in the two-index symmetric representation investigated earlier.
Monopole operators and mirror symmetry in three-dimensional gauge theories
NASA Astrophysics Data System (ADS)
Borokhov, Vadim A.
Many gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories that are not polynomial in the fundamental fields and create topological disorder. They can be regarded as higher-dimensional analogs of twist and winding-state operators in free 2-D CFTs. We call them monopole operators for reasons explained in the text. The importance of monopole operators is that in the Higgs phase, they create Abrikosov-Nielsen-Olesen vortices. We study properties of these operators in three-dimensional gauge theories using large Nf expansion. For non-supersymmetric gauge theories we show that monopole operators belong to representations of the conformal group whose primaries have dimension of order N f. We demonstrate that these monopole operators transform non-trivially under the flavor symmetry group. We also consider topology-changing operators in the infrared limits of N = 2 and N = 4 supersymmetric QED as well as N = 4 SU(2) gauge theory in three dimensions. Using large N f expansion and operator-state isomorphism of the resulting superconformal field theories, we construct monopole operators that are primaries of short representation of the superconformal algebra and compute their charges under the global symmetries. Predictions of three-dimensional mirror symmetry for the quantum numbers of these monopole operators are verified. Furthermore, we argue that some of our large-Nf results are exact. This implies, in particular, that certain monopole operators in N = 4 d = 3 SQED with Nf = 1 are free fields. This amounts to a proof of 3-D mirror symmetry in these special cases.
NASA Astrophysics Data System (ADS)
Aidas, Kestutis; Kongsted, Jacob; Nielsen, Christian B.; Mikkelsen, Kurt V.; Christiansen, Ove; Ruud, Kenneth
2007-07-01
The theory of a hybrid quantum mechanics/molecular mechanics (QM/MM) approach for gauge-origin independent calculations of the molecular magnetizability using Hartree-Fock or Density Functional Theory is presented. The method is applied to liquid water using configurations generated from classical Molecular Dynamics simulation to calculate the statistical averaged magnetizability. Based on a comparison with experimental data, treating only one water molecule quantum mechanically appears to be insufficient, while a quantum mechanical treatment of also the first solvation shell leads to good agreement between theory and experiment. This indicates that the gas-to-liquid phase shift for the molecular magnetizability is to a large extent of non-electrostatic nature.
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
NASA Astrophysics Data System (ADS)
Pereira, A. D.; Sobreiro, R. F.; Sorella, S. P.
2016-10-01
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi: 10.1103/PhysRevD.92.045039 arXiv:1506.06995 [hep-th], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions.
NASA Astrophysics Data System (ADS)
Gan, W. S.
2008-12-01
This paper is to be dedicated to Prof C N Yang's 85th birthday celebration because the idea here was inspired by Prof Yang's public lecture in Singapore in 2006. There are many similarities between electromagnetic waves and acoustic waves. Maxwell's equations for em waves is the oldest gauge theory. We discover symmetries in the pair of wave equations in the acoustic stress field and the velocity field. We also derive a new equation in terms of the stress field for sound propagation in solids. This is different from the Christoffel's equation which is in term of the velocity field. We feel that stress field can better characterize the elastic properties of the sound waves. We also derive the acoustic gauge field condition and gauge invariance and symmetries for the acoustic fields. We also apply symmetries to study negative refraction. Note from Publisher: This article contains the abstract only.
General quantum-mechanical setting for field-antifield formalism as a hyper-gauge theory
NASA Astrophysics Data System (ADS)
Batalin, Igor A.; Lavrov, Peter M.
2016-09-01
A general quantum-mechanical setting is proposed for the field-antifield formalism as a unique hyper-gauge theory in the field-antifield space. We formulate a Schr\\"odinger-type equation to describe the quantum evolution in a "current time" purely formal in its nature. The corresponding Hamiltonian is defined in the form of a supercommutator of the delta-operator with a hyper-gauge Fermion. The initial wave function is restricted to be annihilated with the delta-operator. The Schr\\"odinger's equation is resolved in a closed form of the path integral, whose action contains the symmetric Weyl's symbol of the Hamiltonian. We take the path integral explicitly in the case of being a hyper-gauge Fermion an arbitrary function rather than an operator.
Phase Transition in Gauge Theories, Monopoles and the Multiple Point Principle
NASA Astrophysics Data System (ADS)
Das, C. R.; Laperashvili, L. V.
This review is devoted to the Multiple Point Principle (MPP), according to which several vacuum states with the same energy density exist in Nature. The MPP is implemented to the Standard Model (SM), Family replicated gauge group model (FRGGM) and phase transitions in gauge theories with/without monopoles. Using renormalization group equations for the SM, the effective potential in the two-loop approximation is investigated, and the existence of its postulated second minimum at the fundamental scale is confirmed. Phase transitions in the lattice gauge theories are reviewed. The lattice results for critical coupling constants are compared with those of the Higgs monopole model, in which the lattice artifact monopoles are replaced by the point-like Higgs scalar particles with magnetic charge. Considering our (3+1)-dimensional space-time as, in some way, discrete or imagining it as a lattice with a parameter a = λP, where λP is the Planck length, we have investigated the additional contributions of monopoles to the β-functions of renormalization group equations for running fine structure constants αi(μ) (i = 1, 2, 3 correspond to the U(1), SU(2) and SU(3) gauge groups of the SM) in the FRGGM extended beyond the SM at high energies. It is shown that monopoles have Nfam times smaller magnetic charge in the FRGGM than in the SM (Nfam is a number of families in the FRGGM). We have estimated also the enlargement of a number of fermions in the FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. We have reviewed that, in contrast to the case of the Anti-grand-unified-theory (AGUT), there exists a possibility of unification of all gauge interactions (including gravity) near the Planck scale due to monopoles. The possibility of the [SU(5)]3 or [SO(10)]3 unification at the GUT-scale ~1018 GeV is briefly considered.
Radiation-like scalar field and gauge fields in cosmology for a theory with dynamical time
NASA Astrophysics Data System (ADS)
Benisty, David; Guendelman, E. I.
2016-09-01
Cosmological solutions with a scalar field behaving as radiation are obtained, in the context of gravitational theory with dynamical time. The solution requires the spacial curvature of the universe k, to be zero, unlike the standard radiation solutions, which do not impose any constraint on the spatial curvature of the universe. This is because only such k = 0 radiation solutions pose a homothetic Killing vector. This kind of theory can be used to generalize electromagnetism and other gauge theories, in curved spacetime, and there are no deviations from standard gauge field equation (like Maxwell equations) in the case there exist a conformal Killing vector. But there could be departures from Maxwell and Yang-Mills equations, for more general spacetimes.
J. J. Sakurai Prize: Harmony of Scattering Amplitudes: From Gauge Theory to Supergravity
NASA Astrophysics Data System (ADS)
Bern, Zvi
2014-03-01
As explained in the two previous talks by Lance Dixon and David Kosower, on-shell methods have had an important impact on our understanding of scattering amplitudes and their application to collider physics. In this talk I will describe examples where these ideas have also had impacts in more theoretical areas. The first example shows how these methods have led to the construction of all quantum corrections to specific scattering amplitudes in maximally supersymmetric gauge theory with a large number of color charges. An active area of current research is to do the same for more intricate generic amplitudes of the theory. A second example shows how on-shell methods have uncovered new algebraic structures in gauge-theory amplitudes that have applications to quantum gravity. The advances make it possible to carry out computations in quantum gravity that would have been hopeless with more traditional Feynman diagram methods and to elucidate a remarkable connection between gauge and gravity theories. The results from these investigations have renewed hope that highly supersymmetric gravity theories may be ultraviolet finite, contrary to the prevailing wisdom.
Research in Lattice Gauge Theory and in the Phenomenology of Neutrinos and Dark Matter
Meurice, Yannick L; Reno, Mary Hall
2016-06-23
Research in theoretical elementary particle physics was performed by the PI Yannick Meurice and co-PI Mary Hall Reno. New techniques designed for precision calculations of strong interaction physics were developed using the tensor renormalization group method. Large-scale Monte Carlo simulations with dynamical quarks were performed for candidate models for Higgs compositeness. Ab-initio lattice gauge theory calculations of semileptonic decays of B-mesons observed in collider experiments and relevant to test the validity of the standard model were performed with the Fermilab/MILC collaboration. The phenomenology of strong interaction physics was applied to new predictions for physics processes in accelerator physics experiments and to cosmic ray production and interactions. A research focus has been on heavy quark production and their decays to neutrinos. The heavy quark contributions to atmospheric neutrino and muon fluxes have been evaluated, as have the neutrino fluxes from accelerator beams incident on heavy targets. Results are applicable to current and future particle physics experiments and to astrophysical neutrino detectors such as the IceCube Neutrino Observatory.
Metric Projective Geometry, BGG Detour Complexes and Partially Massless Gauge Theories
NASA Astrophysics Data System (ADS)
Gover, A. Rod; Latini, Emanuele; Waldron, Andrew
2015-11-01
A projective geometry is an equivalence class of torsion free connections sharing the same unparametrised geodesics; this is a basic structure for understanding physical systems. Metric projective geometry is concerned with the interaction of projective and pseudo-Riemannian geometry. We show that the BGG machinery of projective geometry combines with structures known as Yang-Mills detour complexes to produce a general tool for generating invariant pseudo-Riemannian gauge theories. This produces (detour) complexes of differential operators corresponding to gauge invariances and dynamics. We show, as an application, that curved versions of these sequences give geometric characterizations of the obstructions to propagation of higher spins in Einstein spaces. Further, we show that projective BGG detour complexes generate both gauge invariances and gauge invariant constraint systems for partially massless models: the input for this machinery is a projectively invariant gauge operator corresponding to the first operator of a certain BGG sequence. We also connect this technology to the log-radial reduction method and extend the latter to Einstein backgrounds.
Weak and strong coupling equilibration in nonabelian gauge theories
NASA Astrophysics Data System (ADS)
Keegan, Liam; Kurkela, Aleksi; Romatschke, Paul; van der Schee, Wilke; Zhu, Yan
2016-04-01
We present a direct comparison studying equilibration through kinetic theory at weak coupling and through holography at strong coupling in the same set-up. The set-up starts with a homogeneous thermal state, which then smoothly transitions through an out-of-equilibrium phase to an expanding system undergoing boost-invariant flow. This first apples-to-apples comparison of equilibration provides a benchmark for similar equilibration processes in heavy-ion collisions, where the equilibration mechanism is still under debate. We find that results at weak and strong coupling can be smoothly connected by simple, empirical power-laws for the viscosity, equilibration time and entropy production of the system.
Weak and strong coupling equilibration in nonabelian gauge theories
Keegan, Liam; Kurkela, Aleksi; Romatschke, Paul; ...
2016-04-06
In this study, we present a direct comparison studying equilibration through kinetic theory at weak coupling and through holography at strong coupling in the same set-up. The set-up starts with a homogeneous thermal state, which then smoothly transitions through an out-of-equilibrium phase to an expanding system undergoing boost-invariant flow. This first apples-to-apples comparison of equilibration provides a benchmark for similar equilibration processes in heavy-ion collisions, where the equilibration mechanism is still under debate. We find that results at weak and strong coupling can be smoothly connected by simple, empirical power-laws for the viscosity, equilibration time and entropy production of themore » system.« less
Weak and strong coupling equilibration in nonabelian gauge theories
Keegan, Liam; Kurkela, Aleksi; Romatschke, Paul; van der Schee, Wilke; Zhu, Yan
2016-04-06
In this study, we present a direct comparison studying equilibration through kinetic theory at weak coupling and through holography at strong coupling in the same set-up. The set-up starts with a homogeneous thermal state, which then smoothly transitions through an out-of-equilibrium phase to an expanding system undergoing boost-invariant flow. This first apples-to-apples comparison of equilibration provides a benchmark for similar equilibration processes in heavy-ion collisions, where the equilibration mechanism is still under debate. We find that results at weak and strong coupling can be smoothly connected by simple, empirical power-laws for the viscosity, equilibration time and entropy production of the system.
QCD and strongly coupled gauge theories: Challenges and perspectives
Brambilla, N.; Eidelman, S.; Foka, P.; Gardner, S.; Kronfeld, A. S.; Alford, M. G.; Alkofer, R.; Butenschoen, M.; Cohen, T. D.; Erdmenger, J.; Fabbietti, L.; Faber, M.; Goity, J. L.; Ketzer, B.; Lin, H. W.; Llanes-Estrada, F. J.; Meyer, H. B.; Pakhlov, P.; Pallante, E.; Polikarpov, M. I.; Sazdjian, H.; Schmitt, A.; Snow, W. M.; Vairo, A.; Vogt, R.; Vuorinen, A.; Wittig, H.; Arnold, P.; Christakoglou, P.; Di Nezza, P.; Fodor, Z.; Garcia i Tormo, X.; Höllwieser, R.; Janik, M. A.; Kalweit, A.; Keane, D.; Kiritsis, E.; Mischke, A.; Mizuk, R.; Odyniec, G.; Papadodimas, K.; Pich, A.; Pittau, R.; Qiu, J. -W.; Ricciardi, G.; Salgado, C. A.; Schwenzer, K.; Stefanis, N. G.; von Hippel, G. M.; Zakharov, V. I.
2014-10-21
We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to stongly-coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.
QCD and strongly coupled gauge theories: Challenges and perspectives
Brambilla, N.; Eidelman, S.; Foka, P.; ...
2014-10-21
We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to stongly-coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many researchmore » streams which flow into and out of QCD, as well as a vision for future developments.« less
QCD and strongly coupled gauge theories: challenges and perspectives.
Brambilla, N; Eidelman, S; Foka, P; Gardner, S; Kronfeld, A S; Alford, M G; Alkofer, R; Butenschoen, M; Cohen, T D; Erdmenger, J; Fabbietti, L; Faber, M; Goity, J L; Ketzer, B; Lin, H W; Llanes-Estrada, F J; Meyer, H B; Pakhlov, P; Pallante, E; Polikarpov, M I; Sazdjian, H; Schmitt, A; Snow, W M; Vairo, A; Vogt, R; Vuorinen, A; Wittig, H; Arnold, P; Christakoglou, P; Di Nezza, P; Fodor, Z; Garcia I Tormo, X; Höllwieser, R; Janik, M A; Kalweit, A; Keane, D; Kiritsis, E; Mischke, A; Mizuk, R; Odyniec, G; Papadodimas, K; Pich, A; Pittau, R; Qiu, J-W; Ricciardi, G; Salgado, C A; Schwenzer, K; Stefanis, N G; von Hippel, G M; Zakharov, V I
We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.
1982-06-30
potential (smooth curve ) and the potential from the field solve (rough curve ).There are 2048 simulation cells and 100,000 particle$. The magnetic field... curve is that obtained from the simulation test particles. An average over :was made of 100 grid cells about the given position. -6- r’ B. Alfvin Ion...AND SIMULATION - i - I January I to Jun~e 30, 1982 .. -.. :.- DOE. Contract DE,--TO3-76ET53064 -I,’,_ ONR Contract NOO014-).C-0578 =" "{DTIC ~ JUL 7
Doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group
NASA Astrophysics Data System (ADS)
Caspar, S.; Mesterházy, D.; Olesen, T. Z.; Vlasii, N. D.; Wiese, U.-J.
2016-11-01
We construct doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group G in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov-Bohm phase, which is manifested in the doubled theory in terms of a nontrivial ground-state degeneracy on a single cross. We discuss several examples of these doubled theories with different gauge groups including the cyclic group Z(k) ⊂ U(1) , the symmetric group S3 ⊂ O(2) , the binary dihedral (or quaternion) group D¯2 ⊂ SU(2) , and the finite group Δ(27) ⊂ SU(3) . In each case the spectrum of the single-cross electric Hamiltonian is determined exactly. We examine the nature of the low-lying excited states in the full Hilbert space, and emphasize the role of the center symmetry for the confinement of charges. Whether the investigated doubled models admit a non-Abelian topological state which allows for fault-tolerant quantum computation will be addressed in a future publication.
Black hole perturbation theory in a light cone gauge
NASA Astrophysics Data System (ADS)
Preston, Brent
The metric of a Schwarzschild black hole immersed in a uniform magnetic field is studied using black hole perturbation theory in a light crone coordinate system that penetrates the event horizon and possesses a clear geometrical meaning. The magnetic field, which is distorted due to the presence of the black hole, has strength B which is assumed to be small compared to the curvature of the spacetime which allows the perturbed metric to be calculated to order B 2 only. The coordinates allow for an easy identification of the event horizon and the properties of the perturbed black hole are studied. To interpret this perturbed metric, the advanced coordinates are decomposed into irreducible parts which yields the metric of a perturbed black hole in the limit r >> 2 M . Finally we compare our perturbed solution to an exact solution. We show that our perturbed solution is able to match the exact solution but has the freedom to describe a larger class of physically relevant solutions.
One-loop gap equations for the magnetic mass in d=3 gauge theory
NASA Astrophysics Data System (ADS)
Cornwall, John M.
1998-03-01
Recently several workers have attempted determinations of the so-called magnetic mass of d=3 non-Abelian gauge theories through a one-loop gap equation, using a free massive propagator as input. Self-consistency is attained only on-shell, because the usual Feynman-graph construction is gauge-dependent off-shell. We examine two previous studies of the pinch technique proper self-energy, which is gauge-invariant at all momenta, using a free propagator as input, and show that it leads to inconsistent and unphysical results. In one case the residue of the pole has the wrong sign (necessarily implying the presence of a tachyonic pole); in the second case the residue is positive, but two orders of magnitude larger than the input residue, which shows that the residue is on the verge of becoming ghost-like. This happens because of the infrared instability of d=3 gauge theory. A possible alternative one-loop determination via the effective action also fails. The lesson is that gap equations must be considered at least at the two-loop level.
1981-12-31
Bill Nevins, LLNL Use of the ZED postprocessor. Oct 9 Tom Crystal Kinetic simulations of Tokamak TEM Oct 23 Niels Otani The AIC instability...Ion test oarticles advanced in the equilibrium fields do maintain their initial distri- bution function, as desired. The next step is to be wholly
Twenty-first Century Lattice Gauge Theory: Results from the QCD Lagrangian
Kronfeld, Andreas S.; /Fermilab
2012-03-01
Quantum chromodynamics (QCD) reduces the strong interactions, in all their variety, to an elegant nonabelian gauge theory. It clearly and elegantly explains hadrons at short distances, which has led to its universal acceptance. Since its advent, however, many of its long-distance, emergent properties have been believed to be true, without having been demonstrated to be true. This paper reviews a variety of results in this regime that have been established with lattice gauge theory, directly from the QCD Lagrangian. This body of work sheds light on the origin of hadron masses, its interplay with dynamical symmetry breaking, as well as on other intriguing features such as the phase structure of QCD. In addition, nonperturbative QCD is quantitatively important to many aspects of particle physics (especially the quark flavor sector), nuclear physics, and astrophysics. This review also surveys some of the most interesting connections to those subjects.
Gauge and supersymmetry invariance of N = 2 boundary Chern-Simons theory
NASA Astrophysics Data System (ADS)
Faizal, Mir; Luo, Yuan; Smith, Douglas J.; Tan, Meng-Chwan; Zhao, Qin
2017-01-01
In this paper, we study the restoration of gauge symmetry and up to half the supersymmetry (N = (2 , 0) or N = (1 , 1) in two dimensions) for N = 2 non-Abelian Chern-Simons theories in the presence of a boundary. We describe the boundary action which is a supersymmetric WZW model coupled to the bulk Chern-Simons theory. Unlike the N = 1 case, higher supersymmetry (N = (2 , 0)) will endow the group manifold of the WZW model with a complex structure. Therefore, the N = (2 , 0) WZW model in our paper is constructed via a coset space Gc / G, where G is the same as the gauge group in the Chern-Simons action.
Gravity in the presence of fermions as an SU(2) gauge theory
NASA Astrophysics Data System (ADS)
Cianfrani, Francesco; Montani, Giovanni
2010-02-01
The Hamiltonian formulation of the Holst action in the presence of a massless fermion field with a nonminimal Lagrangian is performed without any restriction on the local Lorentz frame. It is outlined that the phase-space structure does not resemble that of a background-independent Lorentz gauge theory, as some additional constraints are present. Proper phase-space coordinates are introduced, such that SU(2) connections can be defined, and the vanishing of conjugate momenta to boost variables is predicted. Finally, it is demonstrated that for a particular value of the nonminimal parameter, the kinematics coincides with that of a background-independent SU(2) gauge theory, and the Immirzi parameter becomes the coupling constant of such an interaction between fermions and the gravitational field.
SU( N ) gauge theories in 2+1 dimensions: glueball spectra and k-string tensions
NASA Astrophysics Data System (ADS)
Athenodorou, Andreas; Teper, Michael
2017-02-01
We calculate the low-lying glueball spectrum and various string tensions in SU( N ) lattice gauge theories in 2 + 1 dimensions, and extrapolate the results to the continuum limit. We do so for for the range N ∈ [2 , 16] so as to control the N -dependence with a useful precision. We observe a number of striking near-degeneracies in the various J PC sectors of the glueball spectrum, in particular between C = + and C = - states. We calculate the string tensions of flux tubes in a number of representations, and provide evidence that the leading correction to the N -dependence of the k-string tensions is ∝ 1 /N rather than ∝ 1 /N 2, and that the dominant binding of k fundamental flux tubes into a k-string is via pairwise interactions. We comment on the possible implications of our results for the dynamics of these gauge theories.
Zucchini, R.
1988-01-01
We show that the analysis of the quantum effects in gauge theories yields several constraints which may be used to test their internal consistency and physical viability. We have studied, in particular, the Higgs sector of the minimal standard model and tested the universality of the weak interactions and the conserved-vector-current hypothesis. Finally, we have analyzed modular invariance in the closed bosonic string.
A vector supersymmetry killing IR divergences in non-commutative gauge theories
NASA Astrophysics Data System (ADS)
Blaschke, D. N.
2008-02-01
This is a report on the joint work with François Gieres, Stefan Hohenegger, Olivier Piguet and Manfred Schweda. We consider a non-commutative U(1) gauge theory with an extension which was originally proposed by A. A. Slavnov [3, 4] in order to get rid of UV/IR mixing problems. Here we show, that the improved IR behaviour of this model is mainly due to the appearence of a linear vector supersymmetry.
Toward a gauge theory for evolution equations on vector-valued spaces
Cardanobile, Stefano; Mugnolo, Delio
2009-10-15
We investigate symmetry properties of vector-valued diffusion and Schroedinger equations. For a separable Hilbert space H we characterize the subspaces of L{sup 2}(R{sup 3};H) that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge symmetries in mathematical physics is explored.
Mechanisms of CP violation in gauge theory and the recent developments
Chang, D. . Dept. of Physics and Astronomy)
1990-12-20
Various mechanisms of CP violation in gauge theory are reviewed. We discuss the impact of recent developments associated with electric dipole moment(EDM) of neutron (D{sub n}), EDM of quarks(D{sub q}), chromo-EDM of quarks(D{sub q}{sup c}), chromo-EDM of gluon(D{sub G}{sup c}), EDM of electron(D{sub e}), and EDM of W boson(D{sub W}). 89 refs., 31 figs.
Global asymmetry of many-qubit correlations: A lattice-gauge-theory approach
Williamson, Mark S.; Ericsson, Marie; Johansson, Markus; Sjoeqvist, Erik; Sudbery, Anthony; Vedral, Vlatko
2011-09-15
We introduce a bridge between the familiar gauge field theory approaches used in many areas of modern physics such as quantum field theory and the stochastic local operations and classical communication protocols familiar in quantum information. Although the mathematical methods are the same, the meaning of the gauge group is different. The measure we introduce, ''twist,'' is constructed as a Wilson loop from a correlation-induced holonomy. The measure can be understood as the global asymmetry of the bipartite correlations in a loop of three or more qubits; if the holonomy is trivial (the identity matrix), the bipartite correlations can be globally untwisted using general local qubit operations, the gauge group of our theory, which turns out to be the group of Lorentz transformations familiar from special relativity. If it is not possible to globally untwist the bipartite correlations in a state using local operations, the twistedness is given by a nontrivial element of the Lorentz group, the correlation-induced holonomy. We provide several analytical examples of twisted and untwisted states for three qubits, the most elementary nontrivial loop one can imagine.
Nilpotent Symmetries for Matter Fields in Non-Abelian Gauge Theory:
NASA Astrophysics Data System (ADS)
Malik, R. P.
In the framework of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, the derivation of the BRST and anti-BRST nilpotent symmetry transformations for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem. In our present investigation, the local, covariant, continuous and off-shell nilpotent (anti-)BRST symmetry transformations for the Dirac fields (ψ ,bar ψ ) are derived in the framework of the augmented superfield formulation where the four (3 + 1)-dimensional (4D) interacting non-Abelian gauge theory is considered on the six (4 + 2)-dimensional supermanifold parametrized by the four even space-time coordinates xμ and a couple of odd elements (θ and bar θ ) of the Grassmann algebra. The requirement of the invariance of the matter (super)currents and the horizontality condition on the (super)manifolds leads to the derivation of the nilpotent symmetries for the matter fields as well as the gauge and the (anti)ghost fields of the theory in the general scheme of augmented superfield formalism.
Hyperbolic deformation of a gauge field theory and the hierarchy problem
NASA Astrophysics Data System (ADS)
Cartas-Fuentevilla, R.; Escalante-Hernandez, A.; Herrera-Aguilar, A.
2016-11-01
The problem of the gauge hierarchy is brought up in a hypercomplex scheme for a U(1) field theory; in such a scheme, a compact gauge group is deformed through a γ-parameter that varies along a noncompact internal direction, transverse to the U(1) compact one, and thus an additional SO(1, 1) gauge symmetry is incorporated. This transverse direction can be understood as an extra internal dimension, which will control the spontaneous symmetry breakdown, and will allow us to establish a mass hierarchy. In this mechanism, there is no brane separation to be estabilized as in the braneworld paradigm, however, a different kind of fine-tuning is needed in order to generate the wished electroweak/Planck hierarchy. By analyzing the effective self-interactions and mass terms of the theory, an interesting duality is revealed between the real and hybrid parts of the effective potential. This duality relates the weak and strong self-interaction regimes of the theory, due to the fact that both mass terms and self-coupling constants appear as one-parameter flows in γ. Additionally, the γ-deformation will establish a flow for the electromagnetic coupling that mimics the renormalization group flow for the charge in QED.
Canonical transformations and loop formulation of SU(N) lattice gauge theories
NASA Astrophysics Data System (ADS)
Mathur, Manu; Sreeraj, T. P.
2015-12-01
We construct canonical transformations to reformulate SU(N) Kogut-Susskind lattice gauge theory in terms of a set of fundamental loop and string flux operators along with their canonically conjugate loop and string electric fields. The canonical relations between the initial SU(N) link operators and the final SU(N) loop and string operators, consistent with SU(N) gauge transformations, are explicitly constructed over the entire lattice. We show that as a consequence of SU(N) Gauss laws all SU(N) string degrees of freedom become cyclic and decouple from the physical Hilbert space Hp. The Kogut-Susskind Hamiltonian rewritten in terms of the fundamental physical loop operators has global SU(N) invariance. There are no gauge fields. We further show that the (1 /g2 ) magnetic field terms on plaquettes create and annihilate the fundamental plaquette loop fluxes while the (g2 ) electric field terms describe all their interactions. In the weak coupling (g2→0 ) continuum limit the SU(N) loop dynamics is described by SU(N) spin Hamiltonian with nearest neighbor interactions. In the simplest SU(2) case, where the canonical transformations map the SU(2) loop Hilbert space into the Hilbert spaces of hydrogen atoms, we analyze the special role of the hydrogen atom dynamical symmetry group S O (4 ,2 ) in the loop dynamics and the spectrum. A simple tensor network ansatz in the SU(2) gauge invariant hydrogen atom loop basis is discussed.
NASA Astrophysics Data System (ADS)
Ögetbil, O.
2007-03-01
After reviewing the existing results we give an extensive analysis of the critical points of the potentials of the gauged N=2 Yang-Mills/Einstein supergravity theories coupled to tensor multiplets and hypermultiplets. Our analysis includes all the possible gaugings of all N=2 Maxwell-Einstein supergravity theories whose scalar manifolds are symmetric spaces. In general, the scalar potential gets contributions from R-symmetry gauging, tensor couplings, and hypercouplings. We show that the coupling of a hypermultiplet into a theory whose potential has a nonzero value at its critical point, and gauging a compact subgroup of the hyperscalar isometry group will only rescale the value of the potential at the critical point by a positive factor, and therefore will not change the nature of an existing critical point. However this is not the case for noncompact SO(1,1) gaugings. An SO(1,1) gauging of the hyperisometry will generally lead to de Sitter vacua, which is analogous to the ground states found by simultaneously gauging SO(1,1) symmetry of the real scalar manifold with U(1)R in earlier literature. SO(m,1) gaugings with m>1, which give contributions to the scalar potential only in the magical Jordan family theories, on the other hand, do not lead to de Sitter vacua. Anti-de Sitter vacua are generically obtained when the U(1)R symmetry is gauged. We also show that it is possible to embed certain generic Jordan family theories into the magical Jordan family preserving the nature of the ground states. However the magical Jordan family theories have additional ground states which are not found in the generic Jordan family theories.
New torsion black hole solutions in Poincaré gauge theory
NASA Astrophysics Data System (ADS)
Cembranos, Jose A. R.; Gigante Valcarcel, Jorge
2017-01-01
We derive a new exact static and spherically symmetric vacuum solution in the framework of the Poincaré gauge field theory with dynamical massless torsion. This theory is built in such a form that allows to recover General Relativity when the first Bianchi identity of the model is fulfilled by the total curvature. The solution shows a Reissner-Nordström type geometry with a Coulomb-like curvature provided by the torsion field. It is also shown the existence of a generalized Reissner-Nordström-de Sitter solution when additional electromagnetic fields and/or a cosmological constant are coupled to gravity.
Calculation of the Mass Spectrum and Deconfining Temperature in Non-Abelian Gauge Theory.
NASA Astrophysics Data System (ADS)
Vohwinkel, Claus
1989-03-01
Using a small volume expansion the mass spectrum and deconfining temperature of SU(2) and SU(3) gauge theory are evaluated. Including non-perturbative features by restoring symmetries which were broken in perturbation theory we obtain results which are valid up to intermediate volumes. The mass spectrum obtained is in good agreement with Luscher's small volume expansion in the small-volume limit and with Monte Carlo Data in medium sized volumes. Using asymmetric volumes we are able to derive the deconfining temperature and find a reasonable agreement with Monte Carlo calculations.
Redesigning rain gauges network in Johor using geostatistics and simulated annealing
Aziz, Mohd Khairul Bazli Mohd; Yusof, Fadhilah; Daud, Zalina Mohd; Yusop, Zulkifli; Kasno, Mohammad Afif
2015-02-03
Recently, many rainfall network design techniques have been developed, discussed and compared by many researchers. Present day hydrological studies require higher levels of accuracy from collected data. In numerous basins, the rain gauge stations are located without clear scientific understanding. In this study, an attempt is made to redesign rain gauge network for Johor, Malaysia in order to meet the required level of accuracy preset by rainfall data users. The existing network of 84 rain gauges in Johor is optimized and redesigned into a new locations by using rainfall, humidity, solar radiation, temperature and wind speed data collected during the monsoon season (November - February) of 1975 until 2008. This study used the combination of geostatistics method (variance-reduction method) and simulated annealing as the algorithm of optimization during the redesigned proses. The result shows that the new rain gauge location provides minimum value of estimated variance. This shows that the combination of geostatistics method (variance-reduction method) and simulated annealing is successful in the development of the new optimum rain gauge system.
1979-09-30
mode In all of Davidson’s equations, there is a factor of /2- difference in vti due 2 to his definition of T.i =m v ti12. -3- -1 10-2- 1 0- 10-51 0.3...v E.6 max N~ -10- 0.6 v x 0.4 -0.2 a -0.4 0 1.0 2.0 3.0 4.0 5.0 6.0 16 12 8 4 (b) -0.4 -0.2 Vph -0. -. 2 0.0 0.2 0.4 A vx FIG. 5 Simulation (many mode...Drift Instability", Phys. Fluids 21, 1017 (1978). l mj 12 0.6 . . . . . . vx A 0.4. -0.2 (a) -0.4x 0 10 2.0 3.0 4.0 5.0 6.0 16 12 8 4 (b) Vph -0.4 -0.2
Not Available
1993-01-01
The major theme of the theoretical physics research conducted under DOE support over the past several years has been within the rubric of the standard model, and concerned the interplay between symmetries and dynamics. The research was thus carried out mostly in the context of gauge field theories, and usually in the presence of chiral fermions. Dynamical symmetry breaking was examined both from the point of view of perturbation theory, as well as from non-perturbative techniques associated with certain characteristic features of specific theories. Among the topics of research were: the implications of abelian and non-abelian anomalies on the spectrum and possible dynamical symmetry breaking in any theory, topological and conformal properties of quantum fields in two and higher dimensions, the breaking of global chiral symmetries by vector-like gauge theories such as QCD, the phenomenological implications of a strongly interacting Higgs sector in the standard model, and the application of soliton ideas to the physics to be explored at the SSC.
Dual-BRST symmetry: 6D Abelian 3-form gauge theory
NASA Astrophysics Data System (ADS)
Kumar, R.; Krishna, S.; Shukla, A.; Malik, R. P.
2012-04-01
Within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, we demonstrate the existence of the novel off-shell nilpotent (anti-)dual-BRST symmetries in the context of a six (5+1)-dimensional (6D) free Abelian 3-form gauge theory. Under these local and continuous symmetry transformations, the total gauge-fixing term of the Lagrangian density remains invariant. This observation should be contrasted with the off-shell nilpotent (anti-)BRST symmetry transformations, under which, the total kinetic term of the theory remains invariant. The anticommutator of the above nilpotent (anti-)BRST and (anti-)dual-BRST transformations leads to the derivation of a bosonic symmetry in the theory. There exists a discrete symmetry transformation in the theory which provides a thread of connection between the nilpotent (anti-)BRST and (anti-)dual-BRST transformations. This theory is endowed with a ghost-scale symmetry, too. We discuss the algebra of these symmetry transformations and show that the structure of the algebra is reminiscent of the algebra of de Rham cohomological operators of differential geometry.
A Deconstruction Lattice Description of the D1/D5 Brane World-Volume Gauge Theory
Giedt, Joel
2011-01-01
I genermore » alize the deconstruction lattice formulation of Endres and Kaplan to two-dimensional super-QCD with eight supercharges, denoted by (4,4), and bifundamental matter. I specialize to a particularly interesting (4,4) gauge theory, with gauge group U ( N c ) × U ( N f ) , and U ( N f ) being weakly gauged. It describes the infrared limit of the D1/D5 brane system, which has been studied extensively as an example of the AdS 3 /CFT 2 correspondence. The construction here preserves two supercharges exactly and has a lattice structure quite similar to that which has previously appeared in the deconstruction approach, that is, site, link, and diagonal fields with both the Bose and Fermi statistics. I remark on possible applications of the lattice theory that would test the AdS 3 /CFT 2 correspondence, particularly one that would exploit the recent worldsheet instanton analysis of Chen and Tong.« less
Consistency of Equations in the Second-Order Gauge-Invariant Cosmological Perturbation Theory
NASA Astrophysics Data System (ADS)
Nakamura, K.
2009-06-01
Along the general framework of the gauge-invariant perturbation theory developed in the papers [K.~Nakamura, Prog.~Theor.~Phys. 110 (2003), 723; Prog.~Theor.~Phys. 113 (2005), 481], we rederive the second-order Einstein equation on four-dimensional homogeneous isotropic background universe in a gauge-invariant manner without ignoring any mode of perturbations. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We also confirmed the consistency of all the equations of the second-order Einstein equation and the equations of motion for matter fields, which are derived in the paper [K.~Nakamura, arXiv:0804.3840]. This confirmation implies that all the derived equations of the second order are self-consistent and these equations are correct in this sense.
Nonequilibrium Spin Dynamics: from Protons in Water to a Gauge Theory of Spin-Orbit Coupling
NASA Astrophysics Data System (ADS)
Tokatly, I. V.; Sherman, E. Ya.
Nonequilibrium dynamics of spin degrees of freedom in condensed matter, ranging from classical liquids to solids and ultracold atomic gases, is one of the focus topics in physics. Here we present a gauge theory of spin dynamics in spinorbit coupled gases for a "pure" gauge realization of the spin-orbit coupling field. This approach allows one to describe the spin dynamics in fermionic systems in terms of exact general response functions and to map it on the density dynamics in a dual system without spin-orbit coupling. We apply this approach to electrons in disordered two-dimensional structures and to cold atomic gases of interacting fermions with synthetic spin-orbit coupling at very low temperatures.
Cost of seven-brane gauge symmetry in a quadrillion F-theory compactifications
NASA Astrophysics Data System (ADS)
Halverson, James; Tian, Jiahua
2017-01-01
We study seven-branes in O (1 015) four-dimensional F-theory compactifications where seven-brane moduli must be tuned in order to achieve non-Abelian gauge symmetry. The associated compact spaces B are the set of all smooth weak Fano toric threefolds. By a study of fine-star-regular triangulations of three-dimensional reflexive polytopes, the number of such spaces is estimated to be 5.8 ×1 014≲Nbases≲1.8 ×1 017 . Typically hundreds or thousands of moduli must be tuned to achieve symmetry for h11(B )<10 , but the average number drops sharply into the range O (25 )- O (200 ) as h11(B ) increases. For some low-rank groups, such as S U (2 ) and S U (3 ), there exist examples where only a few moduli must be tuned in order to achieve seven-brane gauge symmetry.
NASA Astrophysics Data System (ADS)
Chiodaroli, M.; Günaydin, M.; Johansson, H.; Roiban, R.
2016-07-01
We show that scattering amplitudes in magical, symmetric or homogeneous N =2 Maxwell-Einstein supergravities can be obtained as double copies of two gauge theories, using the framework of color-kinematics duality. The left-hand copy is N =2 super-Yang-Mills theory coupled to a hypermultiplet, whereas the right-hand copy is a nonsupersymmetric theory that can be identified as the dimensional reduction of a D -dimensional Yang-Mills theory coupled to P fermions. For generic D and P , the double copy gives homogeneous supergravities. For P =1 and D =7 , 8, 10, 14, it gives the magical supergravities. We compute explicit amplitudes, discuss their soft limits, and study the UV behavior at one loop.
Low energy gauge couplings in grand unified theories and high precision physics
Lynn, B.W. |
1993-09-01
I generalize the leading log relations between low energy SU(3){sub QCD}, SU(2){sub {rvec I}} and U(l){sub Y} effective gauge couplings to include all one-loop threshold effects of matter fields in oblique vector self energy quantum corrections for both supersymmetric and non-supersymmetric SU(5) grand unified theories. These always involve an exactly conserved current from the unbroken SU(3){sub QCD} {times} U(L){sub QED} subgroup; this fact strongly constrains any non-decoupling of heavy states as well as the generic character of threshold effects. Relations between low energy gauge couplings depend on the details of the spectra of both the superheavy and low mass sectors; I display the common origin of the logs appropriate to superheavy matter states, which can be found with well known renormalization group techniques, and the combination of logs and polynomials appropriate for light matter states, which cannot. Relations between any two or all three low energy effective gauge couplings do not depend on the top quark or standard model Higgs` masses. Neither do they depend on neutral color singlet states such as other neutral color singlet Higgs` or higgsinos, neutrinos, zinos or photinos. Further, they do not depend on degenerate SU(5) matter representations, of either spin 0 or spin 1/2 of any mass; matter representations of SU(5) can affect such relations only if there is mass splitting within them. The b quark splitting from the {tau} and {nu}{sub {tau}} can affect the relation between gauge couplings for {vert_bar}q{sub 2}{vert_bar} {yields} m{sub b}{sup 2} as can hadronic resonances and multi-hadron states for lower {vert_bar}q{sub 2}{vert_bar}. New mass-split representations of light states, such as occur in supersymmetric theories, can also affect such relations.
Generalizing twisted gauge invariance
Duenas-Vidal, Alvaro; Vazquez-Mozo, Miguel A.
2009-05-01
We discuss the twisting of gauge symmetry in noncommutative gauge theories and show how this can be generalized to a whole continuous family of twisted gauge invariances. The physical relevance of these twisted invariances is discussed.
Boundaries, mirror symmetry, and symplectic duality in 3d N=4 gauge theory
NASA Astrophysics Data System (ADS)
Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; Hilburn, Justin
2016-10-01
We introduce several families of N=(2, 2) UV boundary conditions in 3d N=4 gaugetheoriesandstudytheirIRimagesinsigma-modelstotheHiggsandCoulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respec-tively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studying two-dimensional compactifications of 3d N=4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality — an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.
Experimentally verifiable Yang-Mills spin 2 gauge theory of gravity with group U(1) x SU(2)
NASA Astrophysics Data System (ADS)
Peng, Huei
1988-06-01
A Yang-Mills spin 2 gauge theory of gravity is proposed. Based on both the verification of the helicity 2 property of the SU(2) gauge bosons of the theory and the agreement of the theory with most observational and experimental evidence, it is argued that the theory is truly a gravitational theory. Generation by the 4-momentum P sup mu of a fermion of U(1) x SU(2) internal symmetry group for gravity, but not the transformation group T sup 4 is demonstrated. It is shown that the U(1) x SU(2) group represents the time displacement and rotation in ordinary space. Thereby internal space associated with gravity is identical with Minkowski spacetime, so a gauge potential of gravity carries two spacetime indices. Then it is verified that the SU(2) gravitational boson has helicity 2. This theory predicts experimentally verifiable gravitomagnetic fields 4 times smaller than that of general relativity.
Infrared suppression of the Coulomb gauge gluon propagator in SU(3) Yang-Mills theory
NASA Astrophysics Data System (ADS)
Nakagawa, Y.
We calculate the equal-time transverse gluon propagator in Coulomb gauge QCD using a SU(3) quenched lattice gauge simulation on large lattices, up to 114 [fm4 ]. We find that the equal-time gluon propagator shows scaling violation; namely, the data for different lattice spacings do not fall on top of one curve. This problem is cured by discarding data at large momenta, which suffer from discretization errors. In the infrared region, the transverse gluon propagator is strongly suppressed and shows a turnover at about 500 [MeV]. Fitting the power law ansatz to the data at small momenta predicts the vanishing gluon propagator at zero momentum, indicating the confinement of gluons.
Fortran code for SU(3) lattice gauge theory with and without MPI checkerboard parallelization
NASA Astrophysics Data System (ADS)
Berg, Bernd A.; Wu, Hao
2012-10-01
We document plain Fortran and Fortran MPI checkerboard code for Markov chain Monte Carlo simulations of pure SU(3) lattice gauge theory with the Wilson action in D dimensions. The Fortran code uses periodic boundary conditions and is suitable for pedagogical purposes and small scale simulations. For the Fortran MPI code two geometries are covered: the usual torus with periodic boundary conditions and the double-layered torus as defined in the paper. Parallel computing is performed on checkerboards of sublattices, which partition the full lattice in one, two, and so on, up to D directions (depending on the parameters set). For updating, the Cabibbo-Marinari heatbath algorithm is used. We present validations and test runs of the code. Performance is reported for a number of currently used Fortran compilers and, when applicable, MPI versions. For the parallelized code, performance is studied as a function of the number of processors. Program summary Program title: STMC2LSU3MPI Catalogue identifier: AEMJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 26666 No. of bytes in distributed program, including test data, etc.: 233126 Distribution format: tar.gz Programming language: Fortran 77 compatible with the use of Fortran 90/95 compilers, in part with MPI extensions. Computer: Any capable of compiling and executing Fortran 77 or Fortran 90/95, when needed with MPI extensions. Operating system: Red Hat Enterprise Linux Server 6.1 with OpenMPI + pgf77 11.8-0, Centos 5.3 with OpenMPI + gfortran 4.1.2, Cray XT4 with MPICH2 + pgf90 11.2-0. Has the code been vectorised or parallelized?: Yes, parallelized using MPI extensions. Number of processors used: 2 to 11664 RAM: 200 Mega bytes per process. Classification: 11
Gauge Theory and Calibrated Geometry for Calabi-Yau 4-folds
NASA Astrophysics Data System (ADS)
Cao, Yalong
This thesis is devoted to the study of gauge theory and calibrated geometry for Calabi-Yau 4-folds. More specifically, our study is along the following five directions. 1. We develop Donaldson-Thomas type theory on Calabi-Yau 4-folds. Let X be a compact complex Calabi-Yau 4-fold. We define Donaldson-Thomas type deformation invariants (DT4 invariants) by studying moduli spaces of solutions to the Donaldson- Thomas equations on X. We also study sheaves counting problems on local Calabi-Yau 4-folds. We relate DT4 invariants of KY to the Donaldson-Thomas invariants of the associated Fano 3-fold Y. When the Calabi-Yau 4-fold is toric, we adapt the virtual localization formula to define the corresponding equivariant DT4 invariants. We also discuss the non-commutative version of DT4 invariants for quivers with relations. Finally, we compute DT4 invariants for certain Calabi-Yau 4-folds when moduli spaces are smooth and find a DT 4/GW correspondence for X. Examples of wall-crossing phenomenon in DT4 theory are also given. 2. Given a complex 4-fold X with an (Calabi-Yau 3-fold) anti-canonical divisor Y, we study relative Donaldson-Thomas invariants for this pair, which are elements in the Donaldson-Thomas cohomologies of Y. We also discuss gluing formulas which relate relative invariants and DT4 invariants for Calabi-Yau 4-folds. 3. We study orientability issues of moduli spaces from gauge theories on Calabi-Yau manifolds. Our results generalize and strengthen those for Donaldson-Thomas theory on Calabi-Yau manifolds of dimensions 3 and 4. We also prove a corresponding result in the relative situation which is relevant to the gluing formula in DT theory. 4. Motivated by Strominger-Yau-Zaslow's mirror symmetry proposal and Kontsevich's homological mirror symmetry conjecture, we study mirror phenomena (in A-model) of certain results from Donaldson-Thomas theory for Calabi-Yau 4-folds. More precisely, we study calibrated geometry in the sense of Harvey-Lawson and Lagrangian
Cold atom simulation of interacting relativistic quantum field theories.
Cirac, J Ignacio; Maraner, Paolo; Pachos, Jiannis K
2010-11-05
We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.
Instanton effects in three-dimensional supersymmetric gauge theories with matter
NASA Astrophysics Data System (ADS)
Dorey, Nick; Tong, David; Vandoren, Stefan
1998-04-01
Using standard field theory techniques we compute perturbative and instanton contributions to the Coulomb branch of three-dimensional supersymmetric QCD with N = 2 and N = 4 supersymmetry and gauge group SU(2). For the N = 4 theory with one massless flavor, we confirm the proposal of Seiberg and Witten that the Coulomb branch is the double-cover of the centered moduli space of two BPS monopoles constructed by Atiyah and Hitchin. Introducing a hypermultiplet mass term, we show that the asymptotic metric on the Coulomb branch coincides with the metric on Dancer's deformation of the monopole moduli space. For the N = 2 theory with Nf flavors, we compute the one-loop corrections to the metric and complex structure on the Coulomb branch. We then determine the superpotential including one-loop effects around the instanton background. These calculations provide an explicit check of several results previously obtained by symmetry and holomorphy arguments.
Duality and modularity in elliptic integrable systems and vacua of gauge theories
NASA Astrophysics Data System (ADS)
Bourget, Antoine; Troost, Jan
2015-04-01
We study complexified elliptic Calogero-Moser integrable systems. We determine the value of the potential at isolated extrema, as a function of the modular parameter of the torus on which the integrable system lives. We calculate the extrema for low rank B,C,D root systems using a mix of analytical and numerical tools. For so(5) we find convincing evidence that the extrema constitute a vector valued modular form for the Γ0(4) congruence subgroup of the modular group. For so(7) and so(8), the extrema split into two sets. One set contains extrema that make up vector valued modular forms for congruence subgroups (namely Γ0(4), Γ(2) and Γ(3)), and a second set contains extrema that exhibit monodromies around points in the interior of the fundamental domain. The former set can be described analytically, while for the latter, we provide an analytic value for the point of monodromy for so(8), as well as extensive numerical predictions for the Fourier coefficients of the extrema. Our results on the extrema provide a rationale for integrality properties observed in integrable models, and embed these into the theory of vector valued modular forms. Moreover, using the data we gather on the modularity of complexified integrable system extrema, we analyse the massive vacua of mass deformed supersymmetric Yang-Mills theories with low rank gauge group of type B, C and D. We map out their transformation properties under the infrared electric-magnetic duality group as well as under triality for with gauge algebra so(8). We compare the exact massive vacua on to those found in a semi-classical analysis on . We identify several intriguing features of the quantum gauge theories.
Chiral Lagrangians from lattice gauge theories in the strong coupling limit
Nagao, Taro; Nishigaki, Shinsuke M.
2001-07-01
We derive nonlinear {sigma} models (chiral Lagrangians) over symmetric spaces U(n), U(2n)/Sp(2n), and U(2n)/O(2n) from U(N), O(N), and Sp(2N) lattice gauge theories coupled to n flavors of staggered fermions, in the large-N and g{sup 2}N limit. To this end, we employ Zirnbauer{close_quote}s color-flavor transformation. We prove the spatial homogeneity of the vacuum configurations of mesons by explicitly solving the large-N saddle point equations, and thus establish these patterns of spontaneous chiral symmetry breaking in the above limit.
Chaichian, M.; Tureanu, A.; Oksanen, M.; Zet, G.
2010-04-15
We develop an internal gauge theory using a covariant star product. The space-time is a symplectic manifold endowed only with torsion but no curvature. It is shown that, in order to assure the restrictions imposed by the associativity property of the star product, the torsion of the space-time has to be covariant constant. An illustrative example is given and it is concluded that in this case the conditions necessary to define a covariant star product on a symplectic manifold completely determine its connection.
Spectral dualities in XXZ spin chains and five dimensional gauge theories
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.; Runov, B.; Zenkevich, Y.; Zotov, A.
2013-12-01
Motivated by recent progress in the study of supersymmetric gauge theories we propose a very compact formulation of spectral duality between XXZ spin chains. The action of the quantum duality is given by the Fourier transform in the spectral parameter. We investigate the duality in various limits and, in particular, prove it for q → 1, i.e. when it reduces to the XXX/Gaudin duality. We also show that the universal difference operators are given by the normal ordering of the classical spectral curves.
Microscopic theory and quantum simulation of atomic heat transport
NASA Astrophysics Data System (ADS)
Marcolongo, Aris; Umari, Paolo; Baroni, Stefano
2016-01-01
Quantum simulation methods based on electronic-structure theory are deemed unfit to cope with atomic heat transport within the Green-Kubo formalism, because quantum-mechanical energy densities and currents are inherently ill-defined at the atomic scale. We show that, although this difficulty would also affect classical simulations, thermal conductivity is indeed insensitive to such ill-definedness by virtue of a kind of gauge invariance resulting from energy extensivity and conservation. On the basis of these findings, we derive an expression for the adiabatic energy flux from density-functional theory, which allows heat transport to be simulated using ab initio equilibrium molecular dynamics. Our methodology is demonstrated by comparing its predictions to those of classical equilibrium and ab initio non-equilibrium (Müller-Plathe) simulations for a liquid-argon model, and by applying it to heavy water at ambient conditions.
Wilson loops in N = 4 gauge theory and fundamental strings in AdS
NASA Astrophysics Data System (ADS)
Drukker, Nadav
The AdS/CFT correspondence is a duality between large N SU(N) gauge theory with N = 4 supersymmetry in 4 dimensions at strong coupling and type IIB string theory on AdS5 × S 5. According to the duality, Wilson loops are given by large fundamental strings in the AdS background. This dissertation examines various aspects of this relation. There is a distinguished class of loops, which are the natural Wilson loop observables in this theory. The magnitude of their coupling to the gauge fields and the scalars is equal. We explore some of their properties, in particular, we show that their expectation values are free from ultra-violet divergence. At strong coupling those Wilson loops can be evaluated by a saddle point expansion around classical solutions of string theory, or minimal surfaces. At the classical level we conclude that the action is not the area of the surface, which is divergent, but a Legendre transform of it. At one loop in the worldsheet expansion, we develop a systematic approach to the study of semiclassical fluctuations of strings in AdS 5 × S5 based on the Green-Schwarz formalism. We show that the string partition function is well defined and finite, and issues related to different gauge choices are clarified. We study four types of loops with different geometries. A single straight line is a BPS object and the corresponding Wilson loop is one. We show this in perturbation theory at weak coupling and to one loop order at strong coupling. A circular Wilson loop is similar to a straight line, but is not BPS, and it's expectation value is not one. A particularly interesting observable is a pair of anti parallel lines. Those give the potential between two W- bosons. Another minimal surface we can find is for loops with cusps or intersections. We also discuss the zig-zag symmetry of the loop operator. In the N = 4 gauge theory the zig-zag symmetry holds when the loop does not couple to the scalar fields. We show how this is realized by formal derivation
NASA Astrophysics Data System (ADS)
Bonelli, Giulio; Sciarappa, Antonio; Tanzini, Alessandro; Vasko, Petr
2014-07-01
We show that the exact partition function of U( N) six-dimensional gauge theory with eight supercharges on ℂ2 × S 2 provides the quantization of the integrable system of hydrodynamic type known as gl( N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S 2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl( N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl( N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W N algebrae, thus providing a gauge theoretical proof of AGT correspondence.
7D bosonic higher spin gauge theory: symmetry algebra and linearized constraints
NASA Astrophysics Data System (ADS)
Sezgin, E.; Sundell, P.
2002-07-01
We construct the minimal bosonic higher spin extension of the 7D AdS algebra SO(6,2), which we call hs(8 ∗) . The generators, which have spin s=1,3,5,… , are realized as monomials in Grassmann even spinor oscillators. Irreducibility, in the form of tracelessness, is achieved by modding out an infinite-dimensional ideal containing the traces. In this a key role is played by the tree bilinear traces which form an SU(2) K algebra. We show that gauging of hs(8 ∗) yields a spectrum of physical fields with spin s=0,2,4,… which make up a UIR of hs(8 ∗) isomorphic to the symmetric tensor product of two 6D scalar doubletons. The scalar doubleton is the unique SU(2) K invariant 6D doubleton. The spin s⩾2 sector comes from an hs(8 ∗) -valued one-form which also contains the auxiliary gauge fields required for writing the curvature constraints in covariant form. The physical spin s=0 field arises in a separate zero-form in a 'quasi-adjoint' representation of hs(8 ∗) . This zero-form also contains the spin s⩾2 Weyl tensors, i.e., the curvatures which are non-vanishing on-shell. We suggest that the hs(8 ∗) gauge theory describes the minimal bosonic, massless truncation of M-theory on AdS7× S4 in an unbroken phase where the holographic dual is given by N free (2,0) tensor multiplets for large N.
Summation of all-loop UV divergences in maximally supersymmetric gauge theories
NASA Astrophysics Data System (ADS)
Borlakov, A. T.; Kazakov, D. I.; Tolkachev, D. M.; Vlasenko, D. E.
2016-12-01
We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in D=6,8,10 supersymmetric Yang-Mills theories in the planar limit. These theories belong to the class of maximally supersymmetric gauge theories and presumably possess distinguished properties beyond perturbation theory. In the previous works, we obtained the recursive relations that allow one to get the leading and subleading divergences in all loops in a pure algebraic way. The all loop summation of the leading divergences is performed with the help of the differential equations which are the generalization of the RG equations for non-renormalizable theories. Here we mainly focus on solving and analyzing these equations. We discuss the properties of the obtained solutions and interpretation of the results. The key issue is that the summation of infinite series for the leading and the subleading divergences does improve the situation and does not allow one to remove the regularization and obtain the finite answer. This means that despite numerous cancellations of divergent diagrams these theories remain non-renormalizable.
Sasakian quiver gauge theory on the Aloff-Wallach space X1,1
NASA Astrophysics Data System (ADS)
Geipel, Jakob C.
2017-03-01
We consider the SU (3)-equivariant dimensional reduction of gauge theories on spaces of the form Md ×X1,1 with d-dimensional Riemannian manifold Md and the Aloff-Wallach space X1,1 = SU (3) / U (1) endowed with its Sasaki-Einstein structure. The condition of SU (3)-equivariance of vector bundles, which has already occurred in the studies of Spin (7)-instantons on cones over Aloff-Wallach spaces, is interpreted in terms of quiver diagrams, and we construct the corresponding quiver bundles, using (parts of) the weight diagram of SU (3). We consider three examples thereof explicitly and then compare the results with the quiver gauge theory on Q3 = SU (3) / (U (1) × U (1)), the leaf space underlying the Sasaki-Einstein manifold X1,1. Moreover, we study instanton solutions on the metric cone C (X1,1) by evaluating the Hermitian Yang-Mills equation. We briefly discuss some features of the moduli space thereof, following the main ideas of a treatment of Hermitian Yang-Mills instantons on cones over generic Sasaki-Einstein manifolds in the literature.
NASA Astrophysics Data System (ADS)
Anderson, Edward
2008-09-01
I show that there is an ambiguity in how one treats auxiliary variables in gauge theories including general relativity cast as 3 + 1 geometrodynamics. Auxiliary variables may be treated pre-variationally as multiplier coordinates or as the velocities corresponding to cyclic coordinates. The latter treatment works through the physical meaninglessness of auxiliary variables' values applying also to the end points (or end spatial hypersurfaces) of the variation, so that these are free rather than fixed. (This is also known as variation with natural boundary conditions.) Further principles of dynamics workings such as Routhian reduction and the Dirac procedure are shown to have parallel counterparts for this new formalism. One advantage of the new scheme is that the corresponding actions are more manifestly relational. While the electric potential is usually regarded as a multiplier coordinate and Arnowitt, Deser and Misner have regarded the lapse and shift likewise, this paper's scheme considers new flux, instant and grid variables whose corresponding velocities are, respectively, the above-mentioned previously used variables. This paper's way of thinking about gauge theory furthermore admits interesting generalizations as regards variational principles for the conformal form of general relativity's initial value problem.
Enhanced symmetries of gauge theory and resolving the spectrum of local operators
NASA Astrophysics Data System (ADS)
Kimura, Yusuke; Ramgoolam, Sanjaye
2008-12-01
Enhanced global non-Abelian symmetries at zero coupling in Yang Mills theory play an important role in diagonalizing the two-point functions of multimatrix operators. Generalized Casimirs constructed from the iterated commutator action of these enhanced symmetries resolve all the multiplicity labels of the bases of matrix operators which diagonalize the two-point function. For the case of U(N) gauge theory with a single complex matrix in the adjoint of the gauge group we have a U(N)×4 global symmetry of the scaling operator at zero coupling. Different choices of commuting sets of Casimirs, for the case of a complex matrix, lead to the restricted Schur basis previously studied in connection with string excitations of giant gravitons and the Brauer basis studied in connection with brane-antibrane systems. More generally these remarks can be extended to the diagonalization for any global symmetry group G. Schur-Weyl duality plays a central role in connecting the enhanced symmetries and the diagonal bases.
Magnetic-Field-Induced Insulator-Conductor Transition in SU(2) Quenched Lattice Gauge Theory
Buividovich, P.V.; Kharzeev, D.; Chernodub, M.N., Kalaydzhyan, T., Luschevskaya, E.V., and M.I. Polikarpov
2010-09-24
We study the correlator of two vector currents in quenched SU(2) lattice gauge theory with a chirally invariant lattice Dirac operator with a constant external magnetic field. It is found that in the confinement phase the correlator of the components of the current parallel to the magnetic field decays much slower than in the absence of a magnetic field, while for other components the correlation length slightly decreases. We apply the maximal entropy method to extract the corresponding spectral function. In the limit of zero frequency this spectral function yields the electric conductivity of quenched theory. We find that in the confinement phase the external magnetic field induces nonzero electric conductivity along the direction of the field, transforming the system from an insulator into an anisotropic conductor. In the deconfinement phase the conductivity does not exhibit any sizable dependence on the magnetic field.
Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.; Zenkevich, Y.
2016-05-01
We consider Dotsenko-Fateev matrix models associated with compactified Calabi-Yau threefolds. They can be constructed with the help of explicit expressions for refined topological vertex, i.e. are directly related to the corresponding topological string amplitudes. We describe a correspondence between these amplitudes, elliptic and affine type Selberg integrals and gauge theories in five and six dimensions with various matter content. We show that the theories of this type are connected by spectral dualities, which can be also seen at the level of elliptic Seiberg-Witten integrable systems. The most interesting are the spectral duality between the XYZ spin chain and the Ruijsenaars system, which is further lifted to self-duality of the double elliptic system.
On fractional quantum Hall solitons and Chern-Simons quiver gauge theories
NASA Astrophysics Data System (ADS)
Belhaj, Adil
2012-05-01
We investigate a class of hierarchical multiple layers of fractional quantum Hall soliton (FQHS) systems from Chern-Simons quivers embedded in M-theory on the cotangent on a two-dimensional complex toric variety V2, which is dual to type IIA superstring on a three-dimensional complex manifold CP1 × V2 fibered over a real line {R}. Based on M-theory/type IIA duality, FQHS systems can be derived from wrapped D4-branes on 2-cycles in CP1 × V2 type IIA geometry. In this realization, the magnetic source can be identified with gauge fields obtained from the decomposition of the R-R 3-form on a generic combination of 2-cycles. Using type IIA D-brane flux data, we compute the filling factors for models relying on CP2 and the zeroth Hirzebruch surface.
Stochastic models: theory and simulation.
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
Origin of Abelian gauge symmetries in heterotic/F-theory duality
Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; Poretschkin, Maximilian; Song, Peng
2016-04-07
Here, we study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, and also derive both the Calabi-Yau geometry and the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. And while the number of geometrically massless U(1)'s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)'s is found by taking into account a Stuckelberg mechanism in the lower-dimensional effective theory. Finally, in geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.
Origin of Abelian gauge symmetries in heterotic/F-theory duality
Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; ...
2016-04-07
Here, we study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, and also derive both the Calabi-Yau geometry and the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in theirmore » low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. And while the number of geometrically massless U(1)'s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)'s is found by taking into account a Stuckelberg mechanism in the lower-dimensional effective theory. Finally, in geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.« less
Density functional theory and simulations of colloidal triangular prisms.
Marechal, Matthieu; Dussi, Simone; Dijkstra, Marjolein
2017-03-28
Nanopolyhedra form a versatile toolbox to investigate the effect of particle shape on self-assembly. Here we consider rod-like triangular prisms to gauge the effect of the cross section of the rods on liquid crystal phase behavior. We also take this opportunity to implement and test a previously proposed version of fundamental measure density functional theory (0D-FMT). Additionally, we perform Monte Carlocomputer simulations and we employ a simpler Onsager theory with a Parsons-Lee correction. Surprisingly and disappointingly, 0D-FMT does not perform better than the Tarazona and Rosenfeld's version of fundamental measure theory (TR-FMT). Both versions of FMT perform somewhat better than the Parsons-Lee theory. In addition, we find that the stability regime of the smectic phase is larger for triangular prisms than for spherocylinders and square prisms.
Entanglement entropy in (3 + 1)-d free U(1) gauge theory
NASA Astrophysics Data System (ADS)
Soni, Ronak M.; Trivedi, Sandip P.
2017-02-01
We consider the entanglement entropy for a free U(1) theory in 3+1 dimensions in the extended Hilbert space definition. By taking the continuum limit carefully we obtain a replica trick path integral which calculates this entanglement entropy. The path integral is gauge invariant, with a gauge fixing delta function accompanied by a Faddeev -Popov determinant. For a spherical region it follows that the result for the logarithmic term in the entanglement, which is universal, is given by the a anomaly coefficient. We also consider the extractable part of the entanglement, which corresponds to the number of Bell pairs which can be obtained from entanglement distillation or dilution. For a spherical region we show that the coefficient of the logarithmic term for the extractable part is different from the extended Hilbert space result. We argue that the two results will differ in general, and this difference is accounted for by a massless scalar living on the boundary of the region of interest.
Dyons and S-duality in N = 4 supersymmetric gauge theory
NASA Astrophysics Data System (ADS)
Gauntlett, Jerome P.; Lowe, David A.
1996-02-01
We analyze the spectrum of dyons in N = 4 supersymmetric Yang-Mills theory with gauge group SU(3) spintaneously broken down to U(1) × U(1). The Higgs fields select a natural basis of simple roots. Acting with S-duality on the W-boson states corresponding to simplr roots leads to an orbit of BPS dyon states that are magnetically charged with respect to one of the U(1)'s. The corresponding monopole solutions can be obtained by embedding SU(2) monopoles into SU(3) and the S-duality predictions reduce to the SU(2) case. Acting with S-duality on the W-boson corresponding to a nonsimple root leads to an infinite set of new S-duality predictions. The simplest of these corresponds to the existence of a harmonic form on the moduli space of SU(3) monopoles that have magnetic charge (1,1) with respect to the two U(1)'s. We argue that the moduli space is given by R 3 × (R 1 x M)/ |Z, where M is Euclidean Taub-NUT space, and that the latter admits the appropriate normalizable harmonic two-form. We briefly discuss the generalizations to other gauge groups.
Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
NASA Astrophysics Data System (ADS)
Williamson, Dominic J.; Bultinck, Nick; Mariën, Michael; Şahinoǧlu, Mehmet B.; Haegeman, Jutho; Verstraete, Frank
2016-11-01
Projected entangled pair states (PEPS) provide a natural ansatz for the ground states of gapped, local Hamiltonians in which global characteristics of a quantum state are encoded in properties of local tensors. We develop a framework to describe onsite symmetries, as occurring in systems exhibiting symmetry-protected topological (SPT) quantum order, in terms of virtual symmetries of the local tensors expressed as a set of matrix product operators (MPOs) labeled by distinct group elements. These MPOs describe the possibly anomalous symmetry of the edge theory, whose local degrees of freedom are concretely identified in a PEPS. A classification of SPT phases is obtained by studying the obstructions to continuously deforming one set of MPOs into another, recovering the results derived for fixed-point models [Chen et al., Phys. Rev. B 87, 155114 (2013), 10.1103/PhysRevB.87.155114]. Our formalism accommodates perturbations away from fixed-point models, opening the possibility of studying phase transitions between different SPT phases. We also demonstrate that applying the recently developed quantum state gauging procedure to a SPT PEPS yields a PEPS with topological order determined by the initial symmetry MPOs. The MPO framework thus unifies the different approaches to classifying SPT phases, via fixed-point models, boundary anomalies, or gauging the symmetry, into the single problem of classifying inequivalent sets of matrix product operator symmetries that are defined purely in terms of a PEPS.
Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang-Mills theory
NASA Astrophysics Data System (ADS)
Nakagawa, Y.; Voigt, A.; Ilgenfritz, E.-M.; Müller-Preussker, M.; Nakamura, A.; Saito, T.; Sternbeck, A.; Toki, H.
2009-06-01
We study the momentum dependence of the ghost propagator and of the space and time components of the gluon propagator at equal time in pure SU(3) lattice Coulomb-gauge theory carrying out a joint analysis of data collected independently at the Research Center for Nuclear Physics, Osaka and Humboldt University, Berlin. We focus on the scaling behavior of these propagators at β=5.8,…,6.2 and apply a matching technique to relate the data for the different lattice cutoffs. Thereby, lattice artifacts are found to be rather strong for both instantaneous gluon propagators at a large momentum. As a byproduct we obtain the respective lattice scale dependences a(β) for the transversal gluon and the ghost propagator which indeed run faster with β than two-loop running, but slightly slower than what is known from the Necco-Sommer analysis of the heavy quark potential. The abnormal a(β) dependence as determined from the instantaneous time-time gluon propagator, D44, remains a problem, though. The role of residual gauge-fixing influencing D44 is discussed.
Simplifying Multi-loop Integrands of Gauge Theory and Gravity Amplitudes
Bern, Z.; Carrasco, J.J.M.; Dixon, L.J.; Johansson, H.; Roiban, R.
2012-02-15
We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N = 4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N = 8 supergravity integrand, whose graph numerators are double copies (squares) of the N = 4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N = 4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D = 11/2, the same dimension as for N = 4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N = 8 supergravity as the subleading-in-1/N{sub c}{sup 2} single-trace divergence in N = 4 super-Yang-Mills theory.
The Domain Geometry and the Bubbling Phenomenon of Rank Two Gauge Theory
NASA Astrophysics Data System (ADS)
Huang, Hsin-Yuan; Zhang, Lei
2017-01-01
Let {Ω} be a flat torus and {G} be the Green's function of {-Δ} on {Ω}. One intriguing mystery of {G} is how the number of its critical points is related to blowup solutions of certain PDEs. In this article we prove that for the following equation that describes a Chern-Simons model in Gauge theory: Δ u_1+1/ɛ^2e^{u_2}(1-e^{u_1})=8πδ_{p1} Δ u_2+1/ɛ^2e^{u_1}(1-e^{u_2})=8πδ_{p2} in quad Ω., quad p_1-p_2 {{ is a half period}}, if fully bubbling solutions of Liouville type exist, {G} has exactly three critical points. In addition we establish necessary conditions for the existence of fully bubbling solutions with multiple bubbles.
Study of the lepton-violating ( μ-, e +) reaction in modern gauge theories
NASA Astrophysics Data System (ADS)
Leontaris, G. K.; Vergados, J. D.
1983-08-01
The lepton-violating ( μ-, e +) reaction has been studiedin the context of modern gauge theories. Both left-handed and right-left symmetric models have been examined. Special attention has been paid to the following mechanisms: (i) those mediated by massive neutrinos (light or heavy); (ii) those accompanied by massless or light physical Higgs particles (majoron); (iii) those involving more intermediate Higgs particles, e.g. singly charged isosinglets (Zee model) and doubly charged isotriplets; (iv) right-handed currents. The formalism has been applied to the experimentally interesting process μ -+ 58Ni→ 58Fe(gs)+ e+. The branching ratio is computed using realistic nuclear wave functions. It is found to be ≲10 -27 in all models, i.e. too small to be measurable in the foreseeable future. The branching ratio for the ( μ-, e +) reaction to all nuclear states is estimated to be ≲10 -20, i.e. beyond the goals of planned experiments.
Dimension two condensates in the Gribov-Zwanziger theory in Coulomb gauge
NASA Astrophysics Data System (ADS)
Guimaraes, M. S.; Mintz, B. W.; Sorella, S. P.
2015-06-01
We investigate the dimension two condensate ⟨ϕ¯ia bϕia b-ω¯ia bωia b⟩ within the Gribov-Zwanziger approach to Euclidean Yang-Mills theories in the Coulomb gauge, in both 3 and 4 dimensions. An explicit calculation shows that, at the first order, the condensate ⟨ϕ¯i a bϕia b-ω¯i a bωia b⟩ is plagued by a nonintegrable IR divergence in 3 D , while in 4 D it exhibits a logarithmic UV divergence, being proportional to the Gribov parameter γ2. These results indicate that in 3D the transverse spatial Coulomb gluon two-point correlation function exhibits a scaling behavior, in agreement with Gribov's expression. In 4D, however, they suggest that, next to the scaling behavior, a decoupling solution might emerge too.
Finite energy monopoles in non-Abelian gauge theories on odd-dimensional spaces
Kihara, Hironobu
2009-02-15
In higher-dimensional gauge theory, we need energies with higher power terms of field strength in order to realize pointwise monopoles. We consider new models with higher power terms of field strength and extraordinary kinetic terms of the scalar field. Monopole charges are computed as integrals over spheres and they are related to mapping class degree. Hedgehog solutions are investigated in these models. Every differential equation for these solutions is Abel's differential equation. A condition for the existence of a finite energy solution is shown. The spaces of 1-jets of these equations are defined as sets of zeros of polynomials. Those spaces can be interpreted as singular quartic surfaces in three-dimensional complex projective spa0008.
High-statistics measurement of the string tension in SU(3) lattice gauge theory
Fukugita, M.; Kaneko, T.; Ukawa, A.
1983-11-15
A high-statistics measurement of the string tension sigma has been performed for SU(3) lattice gauge theory, paying particular attention to errors involved in the analysis, in the interval ..beta.. = 6/g/sub 0/ /sup 2/ = 4.8--7.0 on 6/sup 4/, 8/sup 4/, and 10/sup 4/ lattices. A marked structure has been found in the string tension at ..beta.. = 5.3--5.4. Beyond ..beta.. = 5.5, our data are consistent with scaling with the ratio ..lambda../sub L// ..sqrt..sigma = (7.9 +- 0.5) x 10/sup -3/, a value larger than those previously reported. The approach to scaling is abrupt and from above, in contrast to the SU(2) case.
NASA Astrophysics Data System (ADS)
Brown, Frank R.
Coherent state techniques have proved a useful formal tool for obtaining the N = infty limit of a variety of quantum mechanical systems, in part because they allow one to explicitly construct the classical Hamiltonian and classical phase space that define the dynamics of the large N system. This construction is sufficiently concrete that it naturally suggests methods for carrying out practical calculations. We discuss two such methods, one numerical and the other a classical strong coupling expansion, for calculating the mass spectrum of pure U (infty) Hamiltonian lattice gauge theory. Both involve calculating coherent state expectation values of the quantum Hamiltonian to obtain a classical Hamiltonian as a function on the space of coherent states, and solving for the coherent state (the point in classical configuration space) that minimizes this classical Hamiltonian. Finally the frequencies of classical small oscillations about this minimum give the large N limit of the quantum mechanical excitation spectrum.
NASA Astrophysics Data System (ADS)
Palese, Marcella; Winterroth, Ekkehart
2017-02-01
We relate the existence of Noether global conserved currents associated with locally variational field equations to the existence of global solutions for a local variational problem generating global equations. Both can be characterized as the vanishing of certain cohomology classes. In the case of a 3-dimensional Chern-Simons gauge theory, the variationally featured cohomological obstruction to the existence of global solutions is sharp and equivalent to the usual obstruction in terms of the Chern characteristic class for the flatness of a principal connection. We suggest a parallelism between the geometric interpretation of characteristic classes as obstruction to the existence of flat principal connections and the interpretation of certain de Rham cohomology classes to be the obstruction to the existence of global extremals for a local variational principle.
NASA Astrophysics Data System (ADS)
Stiffler, Kory M.
Superstring theory is one current, promising attempt at unifying gravity with the other three known forces: the electromagnetic force, and the weak and strong nuclear forces. Though this is still a work in progress, much effort has been put toward this goal. A set of specific tools which are used in this effort are gauge/gravity dualities. This thesis consists of a specific implementation of gauge/gravity dualities to describe k-strings of strongly coupled gauge theories as objects dual to Dp-branes embedded in confining supergravity backgrounds from low energy superstring field theory. Along with superstring theory, k-strings are also commonly investigated with lattice gauge theory and Hamiltonian methods. A k-string is a colorless combination of quark-antiquark source pairs, between which a color flux tube develops. The two most notable terms of the k-string energy are, for large quark anti-quark separation L, the tension term, proportional to L, and the Coulombic 1/L correction, known as the Luscher term. This thesis provides an overview of superstring theories and how gauge/gravity dualities emerge from them. It shows in detail how these dualities can be used for the specific problem of calculating the k-string energy in 2 + 1 and 3 + 1 space-time dimensions as the energy of D p-branes in the dual gravitational theory. A detailed review of k-string tension calculations is given where good agreement is found with lattice gauge theory and Hamiltonian methods. In reviewing the k-string tension, we also touch on how different representations of k-strings can be described with Dp-branes through gauge/gravity dualities. The main result of this thesis is how the Luscher term is found to emerge as the one loop quantum corrections to the Dp-brane energy. In 2+1 space-time dimensions, we have Luscher term data to compare with from lattice gauge theory, where we find good agreement.
The massive fermion phase for the U(N) Chern-Simons gauge theory in D=3 at large N
Bardeen, William A.
2014-10-07
We explore the phase structure of fermions in the U(N) Chern-Simons Gauge theory in three dimensions using the large N limit where N is the number of colors and the fermions are taken to be in the fundamental representation of the U(N) gauge group. In the large N limit, the theory retains its classical conformal behavior and considerable attention has been paid to possible AdS/CFT dualities of the theory in the conformal phase. In this paper we present a solution for the massive phase of the fermion theory that is exact to the leading order of ‘t Hooft’s large Nmore » expansion. We present evidence for the spontaneous breaking of the exact scale symmetry and analyze the properties of the dilaton that appears as the Goldstone boson of scale symmetry breaking.« less
The massive fermion phase for the U(N) Chern-Simons gauge theory in D=3 at large N
Bardeen, William A.
2014-10-07
We explore the phase structure of fermions in the U(N) Chern-Simons Gauge theory in three dimensions using the large N limit where N is the number of colors and the fermions are taken to be in the fundamental representation of the U(N) gauge group. In the large N limit, the theory retains its classical conformal behavior and considerable attention has been paid to possible AdS/CFT dualities of the theory in the conformal phase. In this paper we present a solution for the massive phase of the fermion theory that is exact to the leading order of ‘t Hooft’s large N expansion. We present evidence for the spontaneous breaking of the exact scale symmetry and analyze the properties of the dilaton that appears as the Goldstone boson of scale symmetry breaking.
PyR@TE. Renormalization group equations for general gauge theories
NASA Astrophysics Data System (ADS)
Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.
2014-03-01
Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer
Closed flux tubes in D = 2 + 1 SU( N ) gauge theories: dynamics and effective string description
NASA Astrophysics Data System (ADS)
Athenodorou, Andreas; Teper, Michael
2016-10-01
We extend our earlier calculations of the spectrum of closed flux tubes in SU( N ) gauge theories in 2 + 1 dimensions, with a focus on questions raised by recent theoretical progress on the effective string action of long flux tubes and the world-sheet action for flux tubes of moderate lengths. Our new calculations in SU(4) and SU(8) provide evidence that the leading O(1 /l γ ) non-universal correction to the flux tube ground state energy does indeed have a power γ ≥ 7. We perform a study in SU(2), where we can traverse the length at which the Nambu-Goto ground state becomes tachyonic, to obtain an all- N view of the spectrum. Our comparison of the k = 2 flux tube excitation energies in SU(4) and SU(6) suggests that the massive world sheet excitation associated with the k = 2 binding has a scale that knows about the group and hence the theory in the bulk, and we comment on the potential implications of world sheet massive modes for the bulk spectrum. We provide a quantitative analysis of the surprising (near-)orthogonality of flux tubes carrying flux in different SU( N ) representations, which implies that their screening by gluons is highly suppressed even at small N.
Gauge theories of weak interactions II (Circa 1981-1982 C.E.)
NASA Astrophysics Data System (ADS)
Bég, M. A. B.; Sirlin, A.
1982-08-01
This article is a sequel to “Gauge Theories of Weak Interactions (Circa 1973-1974)”, published in the Annual Review of Nuclear Science. Our purpose is to survey the state of the art eight years after; we have spared no effort, however, to make this article self-contained, comprehensible with only an occasional reference to the previous review. The tone of our presentation is set, and the scope of the discussion is delineated, by introductory remarks which emphasize some open questions in the field. We then proceed to examine the known structure of weak interactions in the light of the theory - now established, at least as a consistent description of electroweak effects in the low-energy domain - associated with the names of Glashow, Salam and and Weinberg and commonly referred to as Quantum Flavordynamics (QFD). Here, as well as later in the paper, we try to recapture the spirit of some of the original contributions by using judiciously-defined parameters which afford a model-independent perspective of the experimental data, particularly in situations where we suspect that theoretical fine structure may be hidden in the errors. The phenomenology provides a convenient starting point for discussing the underlying theory. We review briefly the methodology of spontaneously broken gauge theories, in the canonical framework with elementary spin-0 fields injected into the Lagrangian, and its application to the SU(3) C⊗SU(2) L⊗U(1) based standard model of quark-lepton interactions. Calculations of loop-level effects are described both in the context of the standard model and of SU(5)-based grand unification; specially emphasized is our contention that the renormalizability of the theory plays a crucial role in its ability to reproduce physical reality. At this point we deviate from the beaten path of orthodoxy to explore new directions in which weak-interaction theory might conceivably go. The principal motivation lies in our desire to avoid getting trapped in a no
Osp(1{vert_bar}2) Chern-Simons gauge theory as 2D N=1 induced supergravity
Ezawa, K.; Ishikawa, A.
1997-08-01
We demonstrate the close relationship between Chern-Simons gauge theory with the gauge group Osp(1{vert_bar}2) and N=1 induced supergravity in two dimensions. More precisely, the inner product of the physical states in the former yields the partition function of the latter evaluated in the Wess-Zumino supergauge. It is also shown that the moduli space of flat Osp(1{vert_bar}2) connections naturally includes a super Teichm{umlt u}ller space of super Riemann surfaces. {copyright} {ital 1997} {ital The American Physical Society}
Fluctuations in a cosmology with a spacelike singularity and their gauge theory dual description
NASA Astrophysics Data System (ADS)
Brandenberger, Robert H.; Ferreira, Elisa G. M.; Morrison, Ian A.; Cai, Yi-Fu; Das, Sumit R.; Wang, Yi
2016-10-01
We consider a time-dependent deformation of anti-de Sitter (AdS) space-time which contains a spacelike "singularity"—a spacelike region of high curvature. Making use of the AdS/CFT correspondence we can map the bulk dynamics onto the boundary. The boundary theory has a time dependent coupling constant which becomes small at times when the bulk space-time is highly curved. We investigate the propagation of small fluctuations of a test scalar field from early times before the bulk singularity to late times after the singularity. Under the assumption that the AdS/CFT correspondence extends to deformed AdS space-times, we can map the bulk evolution of the scalar field onto the evolution of the boundary gauge field. The time evolution of linearized fluctuations is well-defined in the boundary theory as long as the coupling remains finite, so that we can extend the boundary perturbations to late times after the singularity. Assuming that the spacetime in the future of the singularity has a weakly coupled region near the boundary, we reconstruct the bulk fluctuations after the singularity crossing making use of generic properties of boundary-to-bulk propagators. Finally, we extract the spectrum of the fluctuations at late times given some initial spectrum. We find that the spectral index is unchanged, but the amplitude increases due to the squeezing of the fluctuations during the course of the evolution. This investigation can teach us important lessons on how the spectrum of cosmological perturbations passes through a bounce which is singular from the bulk point of view but which is resolved using an ultraviolet complete theory of quantum gravity.
NASA Astrophysics Data System (ADS)
Ehlers, Lennart; Refsgaard, Jens Christian; Sonnenborg, Torben O.; He, Xin; Jensen, Karsten H.
2016-04-01
Precipitation is a key input to hydrological models. Spatially distributed rainfall used in hydrological modelling is commonly based on the interpolation of gauge rainfall using conventional geostatistical techniques such as kriging, e.g. Salamon and Feyen [2009], Stisen et al. [2011]. While being effective point interpolators [Moulin et al., 2009], these techniques are unable to reproduce the spatial variability inherent in the rainfall process at unsampled locations. Stochastic simulation approaches provide the means to better capture this variability and hence to quantify the associated spatial uncertainty [McMillan et al., 2011]. The objective of this study is to quantify uncertainties in interpolated gauge based rainfall by employing sequential Gaussian simulation (SGS) coupled with ordinary kriging (OK) to generate realizations of daily precipitation at a 2x2 km2 grid. The rainfall gauge data was collected in a 1055 km2 subcatchment within the HOBE catchment (Jutland, Denmark) [Jensen and Illangasekare, 2011]. The following uncertainties are considered: i) interpolation uncertainty ii) uncertainty on the point measurement iii) location uncertainty. Results from using different numbers of SGS realizations and different lengths of the simulated period as well as different assumptions on the underlying uncertainties will be presented and discussed with regard to mean annual catchment rainfall. Jensen, K. H., and T. H. Illangasekare (2011), HOBE: A Hydrological Observatory, Vadose Zone J, 10(1), 1-7. McMillan, H., B. Jackson, M. Clark, D. Kavetski, and R. Woods (2011), Rainfall uncertainty in hydrological modelling: An evaluation of multiplicative error models, J Hydrol, 400(1-2), 83-94. Moulin, L., E. Gaume, and C. Obled (2009), Uncertainties on mean areal precipitation: assessment and impact on streamflow simulations, Hydrol Earth Syst Sc, 13(2), 99-114. Salamon, P., and L. Feyen (2009), Assessing parameter, precipitation, and predictive uncertainty in a
Cluster algorithm for two-dimensional U(1) lattice gauge theory
NASA Astrophysics Data System (ADS)
Sinclair, R.
1992-03-01
We use gauge fixing to rewrite the two-dimensional U(1) pure gauge model with Wilson action and periodic boundary conditions as a nonfrustrated XY model on a closed chain. The Wolff single-cluster algorithm is then applied, eliminating critical slowing down of topological modes and Polyakov loops.
Anomalous triple gauge couplings in the effective field theory approach at the LHC
NASA Astrophysics Data System (ADS)
Falkowski, Adam; González-Alonso, Martín; Greljo, Admir; Marzocca, David; Son, Minho
2017-02-01
We discuss how to perform consistent extractions of anomalous triple gauge couplings (aTGC) from electroweak boson pair production at the LHC in the Standard Model Effective Field Theory (SMEFT). After recasting recent ATLAS and CMS searches in pp → W Z( W W ) → ℓ'νℓ+ℓ-(νℓ) channels, we find that: (a) working consistently at order Λ-2 in the SMEFT expansion the existing aTGC bounds from Higgs and LEP-2 data are not improved, (b) the strong limits quoted by the experimental collaborations are due to the partial Λ-4 corrections (dimension-6 squared contributions). Using helicity selection rule arguments we are able to explain the suppression in some of the interference terms, and discuss conditions on New Physics (NP) models that can benefit from such LHC analyses. Furthermore, standard analyses assume implicitly a quite large NP scale, an assumption that can be relaxed by imposing cuts on the underlying scale of the process ( √{widehat{s}} ). In practice, we find almost no correlation between √{widehat{s}} and the experimentally accessible quantities, which complicates the SMEFT interpretation. Nevertheless, we provide a method to set (conservative) aTGC bounds in this situation, and recast the present searches accordingly. Finally, we introduce a simple NP model for aTGC to compare the bounds obtained directly in the model with those from the SMEFT analysis.
Poincare gauge theory of gravity: Friedman cosmology with even and odd parity modes: Analytic part
Baekler, Peter; Hehl, Friedrich W.; Nester, James M.
2011-01-15
We propose a cosmological model in the framework of the Poincare gauge theory of gravity (PG). The gravitational Lagrangian is quadratic in both curvature and torsion. In our specific model, the Lagrangian contains (i) the curvature scalar R and the curvature pseudoscalar X linearly and quadratically (including an RX term) and (ii) pieces quadratic in the torsion vector V and the torsion axial vector A (including a VA term). We show generally that in quadratic PG models we have nearly the same number of parity conserving terms ('world') and of parity violating terms ('shadow world'). This offers new perspectives in cosmology for the coupling of gravity to matter and antimatter. Our specific model generalizes the fairly realistic ''torsion cosmologies'' of Shie-Nester-Yo (2008) and Chen et al. (2009). With a Friedman type ansatz for an orthonormal coframe and a Lorentz connection, we derive the two field equations of PG in an explicit form and discuss their general structure in detail. In particular, the second field equation can be reduced to first order ordinary differential equations for the curvature pieces R(t) and X(t). Including these along with certain relations obtained from the first field equation and curvature definitions, we present a first order system of equations suitable for numerical evaluation. This is deferred to the second, numerical part of this paper.
Metastable vacuum decay and θ dependence in gauge theory. Deformed QCD as a toy model
NASA Astrophysics Data System (ADS)
Bhoonah, Amit; Thomas, Evan; Zhitnitsky, Ariel R.
2015-01-01
We study a number of different ingredients related to the θ dependence, metastable excited vacuum states and other related subjects using a simplified version of QCD, the so-called "deformed QCD". This model is a weakly coupled gauge theory, which, however, preserves all the relevant essential elements allowing us to study hard and nontrivial features which are known to be present in real strongly coupled QCD. Our main focus in this work is to test the ideas related to the metastable vacuum states (which are known to be present in strongly coupled QCD in large N limit) in a theoretically controllable manner using the "deformed QCD" as a toy model. We explicitly show how the metastable states emerge in the system, why their lifetime is large, and why these metastable states must be present in the system for the self-consistency of the entire picture of the QCD vacuum. We also speculate on possible relevance of the metastable vacuum states in explanation of the violation of local P and CP symmetries in heavy ion collisions.
NASA Astrophysics Data System (ADS)
Cvetič, G.; Kim, C. S.
We assume that the standard model (SM) breaks down around some energy Λ and is replaced there by a new (Higgsless) flavor gauge theory (FGT) with fewer input parameters in the interactions corresponding to the Yukawa sector of SM. This would imply more symmetry for the values of the Yukawa (running) parameters of SM at E Λ, possibly by a (approximate) flavor democracy (for the quark mass sector). We investigate this possibility by studying the renormalization group equations (RGE's) for the quark Yukawa couplings of SM with one and two Higgs doublets, by running them from the known physical values at low energies (E 1 GeV) to Λ (> 1 TeV) and comparing the resulting quark masses mq (E Λ) for various mt and υU/υD. Unlike previous investigations of these RGE's, we do not implement the requirement mt(Λpole) = ∞. We found that SM with two Higgs doublets (type 2) is most likely to experience a gradual transition to FGT. Our results also shed more light on the adequacy and deficiencies of the usual RGE approaches within TMSM and related models. We also found that, independent of the assumption of a transition mechanism to FGT, mt phy< ˜ 200 GeV for Λpole≪ ΛPlanck in most cases of SM with two Higgs doublets.
NASA Astrophysics Data System (ADS)
Wang, Juven; Gu, Zheng-Cheng; Wen, Xiao-Gang
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs, recently observed by Kapustin. We find new examples of mixed gauge-gravity actions for U(1) SPTs in 3+1D and 4+1D via the Stiefel-Whitney class and the gravitational Chern-Simons term. [Work based on Phys. Rev. Lett. 114, 031601 (2015) arXiv:1405.7689
SU(2) gauge theory with two fundamental flavors: A minimal template for model building
NASA Astrophysics Data System (ADS)
Arthur, Rudy; Drach, Vincent; Hansen, Martin; Hietanen, Ari; Pica, Claudio; Sannino, Francesco
2016-11-01
We investigate the continuum spectrum of the SU(2) gauge theory with Nf=2 flavors of fermions in the fundamental representation. This model provides a minimal template which is ideal for a wide class of Standard Model extensions featuring novel strong dynamics that range from composite (Goldstone) Higgs theories to several intriguing types of dark matter candidates, such as the strongly interacting massive particles (SIMPs). We improve our previous lattice analysis [1] by adding more data at light quark masses, at two additional lattice spacings, by determining the lattice cutoff via a Wilson flow measure of the w0 parameter, and by measuring the relevant renormalization constants nonperturbatively in the regularization-invariant momentum (RI'-MOM) scheme. Our result for the lightest isovector state in the vector channel, in units of the pseudoscalar decay constant, is mV/FPS˜13.1 (2.2 ) (combining statistical and systematic errors). For the axial channel our result is mA/FPS˜14.5 (3.6 ) , which however does include a similarly sized additional systematic error due to residual excited-states contamination. In the context of the composite (Goldstone) Higgs models, our result for the spin-one resonances are mV>3.2 (5 ) TeV and mA>3.6 (9 ) TeV , which are above the current LHC constraints. In the context of dark matter models, for the SIMP case our results indicate the occurrence of a compressed spectrum at the required large dark pion mass, which implies the need to include the effects of spin-one resonances in phenomenological estimates.
Renormalization of interactions of ultracold atoms in simulated Rashba gauge fields
Ozawa, Tomoki; Baym, Gordon
2011-10-15
Interactions of ultracold atoms with Rashba spin-orbit coupling, currently being studied with simulated (artificial) gauge fields, have nontrivial ultraviolet and infrared behavior. Examining the ultrastructure of the Bethe-Salpeter equation, we show that the linear ultraviolet divergence in the bare interaction can be renormalized as usual in terms of low-energy scattering lengths, and that for both bosons and fermions ultraviolet logarithmic divergences are absent. Calculating the leading order effective interaction with full dependence on the spin-orbit coupling strength and the center-of-mass momentum of the colliding pair, we elucidate the relation between mean-field interactions and physical three-dimensional scattering lengths. As a consequence of infrared logarithmic divergences in the two-particle propagator, the effective interaction vanishes as the center-of-mass momentum approaches zero.
Gauge engineering and propagators
NASA Astrophysics Data System (ADS)
Maas, Axel
2017-03-01
Beyond perturbation theory gauge-fixing becomes more involved due to the Gribov-Singer ambiguity: The appearance of additional gauge copies requires to define a procedure how to handle them. For the case of Landau gauge the structure and properties of these additional gauge copies will be investigated. Based on these properties gauge conditions are constructed to account for these gauge copies. The dependence of the propagators on the choice of these complete gauge-fixings will then be investigated using lattice gauge theory for Yang-Mills theory. It is found that the implications for the infrared, and to some extent mid-momentum behavior, can be substantial. In going beyond the Yang-Mills case it turns out that the influence of matter can generally not be neglected. This will be briefly discussed for various types of matter.
Lattice gauge theory on a massively parallel computing facility. Final report
Sugar, R.
1998-08-07
This grant provided access to the massively parallel computing facilities at Oak Ridge National Laboratory for the study of lattice gauge theory. The major project was a calculation of the weak decay constants of pseudoscalar mesons with one light and one heavy quark. A number of these constants have not yet been measured, so the calculations constituted a set of predictions which will be tested by future experiments. More importantly, f{sub B} and f{sub B{sub s}}, the decay constants of the B and B{sub s} mesons, are crucial inputs for extracting information regarding the CKM matrix element V{sub td} from experimental measurements of B-{anti B} mixing, and future measurements of B{sub s}-{anti B}{sub s} mixing planned for the B-factory currently under construction at the Stanford Linear Accelerator Center. V{sub td} is one of the least well determined parameters of the Standard Model of High Energy Physics. It does not appear likely that F{sub B} and f{sub B{sub s}} will be measured experimentally in the near future, so lattice calculations such as this will play a crucial role in extracting information about the Standard Model from the B-factory experiments. The author has carried out the most accurate calculations of the heavy-light decay constants to date within the quenched approximation, that is ignoring the effects of sea quarks. Furthermore, his was the only group to have estimated the errors in the decay constants associated with the quenched approximation.
NASA Astrophysics Data System (ADS)
Benioff, Paul
2015-05-01
The purpose of this paper is to put the description of number scaling and its effects on physics and geometry on a firmer foundation, and to make it more understandable. A main point is that two different concepts, number and number value are combined in the usual representations of number structures. This is valid as long as just one structure of each number type is being considered. It is not valid when different structures of each number type are being considered. Elements of base sets of number structures, considered by themselves, have no meaning. They acquire meaning or value as elements of a number structure. Fiber bundles over a space or space time manifold, M, are described. The fiber consists of a collection of many real or complex number structures and vector space structures. The structures are parameterized by a real or complex scaling factor, s. A vector space at a fiber level, s, has, as scalars, real or complex number structures at the same level. Connections are described that relate scalar and vector space structures at both neighbor M locations and at neighbor scaling levels. Scalar and vector structure valued fields are described and covariant derivatives of these fields are obtained. Two complex vector fields, each with one real and one imaginary field, appear, with one complex field associated with positions in M and the other with position dependent scaling factors. A derivation of the covariant derivative for scalar and vector valued fields gives the same vector fields. The derivation shows that the complex vector field associated with scaling fiber levels is the gradient of a complex scalar field. Use of these results in gauge theory shows that the imaginary part of the vector field associated with M positions acts like the electromagnetic field. The physical relevance of the other three fields, if any, is not known.
Spontaneous Breaking of Scale Invariance in U(N) Chern-Simons Gauge Theories in Three Dimensions
Bardeen, William
2014-10-24
I explore the existence of a massive phase in a conformally invariant U(N) Chern-Simons gauge theories in D = 3 with matter fields in the fundamental representation. These models have attracted recent attention as being dual, in the conformal phase, to theories of higher spin gravity on AdS 4. Using the 1t Hooft large N expansion, exact solutions are obtained for scalar current correlators in the massive phase where the conformal symmetry is spontaneously broken. A massless dilaton appears as a composite state, and its properties are discussed. Solutions exist for matters field that are either bosons or fermions.
Spontaneous Breaking of Scale Invariance in U(N) Chern-Simons Gauge Theories in Three Dimensions
Bardeen, William A.
2015-09-24
I explore the existence of a massive phase in a conformally invariant U(N) Chern-Simons gauge theories in D = 3 with matter fields in the fundamental representation. These models have attracted recent attention as being dual, in the conformal phase, to theories of higher spin gravity on AdS 4. Using the 0t Hooft large N expansion, exact solutions are obtained for scalar current correlators in the massive phase where the conformal symmetry is spontaneously broken. A massless dilaton appears as a composite state, and its properties are discussed. Solutions exist for matters field that are either bosons or fermions.
NASA Astrophysics Data System (ADS)
Capri, M. A. L.; Dudal, D.; Pereira, A. D.; Fiorentini, D.; Guimaraes, M. S.; Mintz, B. W.; Palhares, L. F.; Sorella, S. P.
2017-02-01
In order to construct a gauge-invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge-invariant transverse configurations Ah . Such configurations can be obtained through the minimization of the functional Amin2 along the gauge orbit within the BRST-invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of nonperturbative aspects of the theory in a BRST-invariant and gauge-parameter-independent way. In particular, it turns out that the poles of ⟨Aμh(k )Aνh(-k )⟩ are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter α entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST-invariant formulation introduced before. Moreover, the correlator ⟨Aμh(k )Aνh(-k )⟩ enables us to attach a BRST-invariant meaning to the possible positivity violation of the corresponding temporal Schwinger correlator, giving thus for the first time a consistent, gauge parameter independent, setup to adopt the positivity violation of ⟨Aμh(k )Aνh(-k )⟩ as a signature for gluon confinement. Finally, in the context of gauge theories supplemented with a fundamental Higgs field, we use ⟨Aμh(k )Aνh(-k )⟩ to probe the pole structure of the massive gauge boson in a gauge-invariant fashion.
Renormalization of composite operators in Yang-Mills theories using a general covariant gauge
Collins, J.C.; Scalise, R.J. )
1994-09-15
Essential to QCD applications of the operator product expansion, etc., is a knowledge of those operators that mix with gauge-invariant operators. A standard theorem asserts that the renormalization matrix is triangular: Gauge-invariant operators have alien'' gauge-variant operators among their counterterms, but, with a suitably chosen basis, the necessary alien operators have only themselves as counterterms. Moreover, the alien operators are supposed to vanish in physical matrix elements. A recent calculation by Hamberg and van Neerven apparently contradicts these results. By explicit calculations with the energy-momentum tensor, we show that the problems arise because of subtle infrared singularities that appear when gluonic matrix elements are taken on shell at zero momentum transfer.
NASA Astrophysics Data System (ADS)
Dolan, Louise; Sun, Yang
2015-06-01
We compute the partition function of four-dimensional abelian gauge theory on a general four-torus T 4 with flat metric using Dirac quantization. In addition to an symmetry, it possesses symmetry that is electromagnetic S-duality. We show explicitly how this S-duality of the 4 d abelian gauge theory has its origin in symmetries of the 6 d (2 , 0) tensor theory, by computing the partition function of a single fivebrane compactified on T 2 times T 4, which has symmetry. If we identify the couplings of the abelian gauge theory with the complex modulus of the T 2 torus , then in the small T 2 limit, the partition function of the fivebrane tensor field can be factorized, and contains the partition function of the 4 d gauge theory. In this way the symmetry of the 6d tensor partition function is identified with the S-duality symmetry of the 4d gauge partition function. Each partition function is the product of zero mode and oscillator contributions, where the acts suitably. For the 4d gauge theory, which has a Lagrangian, this product redistributes when using path integral quantization.
Electroweak theory based on S U (4 )L⊗U (1 )X gauge group
NASA Astrophysics Data System (ADS)
Long, H. N.; Hue, L. T.; Loi, D. V.
2016-07-01
This paper includes two main parts. In the first part, we present generalized gauge models based on the S U (3 )C⊗S U (4 )L⊗U (1 )X (3-4-1) gauge group with arbitrary electric charges of exotic leptons. The mixing matrix of neutral gauge bosons is analyzed, and the eigenmasses and eigenstates are obtained. The anomaly-free as well as matching conditions are discussed precisely. In the second part, we present a new development of the original 3-4-1 model [R. Foot, H. N. Long, and T. A. Tran, Phys. Rev. D 50, R34 (1994), F. Pisano and V. Pleitez, Phys. Rev. D 51, 3865 (1995).]. Different from previous works, in this paper the neutrinos, with the help of the scalar decuplet H , get the Dirac masses at the tree level. The vacuum expectation value (VEV) of the Higgs boson field in the decuplet H acquiring the VEV responsible for neutrino Dirac mass leads to mixing in separated pairs of singly charged gauge bosons, namely the Standard Model (SM) W boson and K , the new gauge boson acting in the right-handed lepton sector, as well as the singly charged bileptons X and Y . Due to the mixing, there occurs a right-handed current carried by the W boson. From the expression of the electromagnetic coupling constant, ones get the limit of the sine-squared of the Weinberg angle, sin2θW<0.25 , and a constraint on electric charges of extra leptons. In the limit of lepton number conservation, the Higgs sector contains all massless Goldstone bosons for massive gauge bosons and the SM-like Higgs boson. Some phenomenology is discussed.
Light-induced gauge fields for ultracold atoms
NASA Astrophysics Data System (ADS)
Goldman, N.; Juzeliūnas, G.; Öhberg, P.; Spielman, I. B.
2014-12-01
Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle—the graviton—that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms ‘feeling’ laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials—both Abelian and non-Abelian—in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.
NASA Astrophysics Data System (ADS)
Grützmann, Melchior; Strobl, Thomas
2015-10-01
Starting with minimal requirements from the physical experience with higher gauge theories, i.e. gauge theories for a tower of differential forms of different form degrees, we discover that all the structural identities governing such theories can be concisely recombined into what is called a Q-structure or, equivalently, an L∞-algebroid. This has many technical and conceptual advantages: complicated higher bundles become just bundles in the category of Q-manifolds in this approach (the many structural identities being encoded in the one operator Q squaring to zero), gauge transformations are generated by internal vertical automorphisms in these bundles and even for a relatively intricate field content the gauge algebra can be determined in some lines and is given by what is called the derived bracket construction. This paper aims equally at mathematicians and theoretical physicists; each more physical section is followed by a purely mathematical one. While the considerations are valid for arbitrary highest form degree p, we pay particular attention to p = 2, i.e. 1- and 2-form gauge fields coupled nonlinearly to scalar fields (0-form fields). The structural identities of the coupled system correspond to a Lie 2-algebroid in this case and we provide different axiomatic descriptions of those, inspired by the application, including e.g. one as a particular kind of a vector-bundle twisted Courant algebroid.
Diffusion Processes: Experiment, Theory, Simulations
NASA Astrophysics Data System (ADS)
Pekalski, Andrzej
The articles in this book reflect the omnipresence of diffusion processes in the natural sciences. They describe experimental results as well as theoretical models and computer simulations, and address a wide readership including graduate students. The problems treated stem from physics, astronomy, physical chemistry, biology, and medicine. The papers are presented in a tutorial style and reflect the present-day trends in the field.
NASA Astrophysics Data System (ADS)
Uranga, A. M.
2009-11-01
This special section is devoted to the proceedings of the conference `Winter School on Strings, Supergravity and Gauge Theories', which took place at CERN, the European Centre for Nuclear Research, in Geneva, Switzerland 9-13 February 2009. This event is part of a yearly series of scientific schools, which represents a well established tradition. Previous events have been held at SISSA, in Trieste, Italy, in February 2005 and at CERN in January 2006, January 2007 and January 2008, and were funded by the European Mobility Research and Training Network `Constituents, Fundamental Forces and Symmetries of the Universe'. The next event will take place again at CERN, in January 2010. The school was primarily meant for young doctoral students and postdoctoral researchers working in the area of string theory. It consisted of several general lectures of four hours each, whose notes are published in this special section, and six working group discussion sessions, focused on specific topics of the network research program. It was well attended by over 200 participants. The topics of the lectures were chosen to provide an introduction to some of the areas of recent progress, and to the open problems, in string theory. One of the most active areas in string theory in recent years has been the AdS/CFT or gauge/gravity correspondence, which proposes the complete equivalence of string theory on (asymptotically) anti de Sitter spacetimes with certain quantum (gauge) field theories. The duality has recently been applied to understanding the hydrodynamical properties of a hot plasma in gauge theories (like the quark-gluon plasma created in heavy ion collisions at the RHIC experiment at Brookhaven, and soon at the LHC at CERN) in terms of a dual gravitational AdS theory in the presence of a black hole. These developments were reviewed in the lecture notes by M Rangamani. In addition, the AdS/CFT duality has been proposed as a tool to study interesting physical properties in other
Filtration theory using computer simulations
Bergman, W.; Corey, I.
1997-08-01
We have used commercially available fluid dynamics codes based on Navier-Stokes theory and the Langevin particle equation of motion to compute the particle capture efficiency and pressure drop through selected two- and three-dimensional fiber arrays. The approach we used was to first compute the air velocity vector field throughout a defined region containing the fiber matrix. The particle capture in the fiber matrix is then computed by superimposing the Langevin particle equation of motion over the flow velocity field. Using the Langevin equation combines the particle Brownian motion, inertia and interception mechanisms in a single equation. In contrast, most previous investigations treat the different capture mechanisms separately. We have computed the particle capture efficiency and the pressure drop through one, 2-D and two, 3-D fiber matrix elements. 5 refs., 11 figs.
Conformal window of gauge theories with four-fermion interactions and ideal walking technicolor
NASA Astrophysics Data System (ADS)
Fukano, Hidenori S.; Sannino, Francesco
2010-08-01
We investigate the effects of four-fermion interactions on the phase diagram of strongly interacting theories for any representation as function of the number of colors and flavors. We show that the conformal window, for any representation, shrinks with respect to the case in which the four-fermion interactions are neglected. The anomalous dimension of the mass increases beyond the unity value at the lower boundary of the new conformal window. We plot the new phase diagram which can be used, together with the information about the anomalous dimension, to propose ideal models of walking technicolor. We discover that when the extended technicolor sector, responsible for giving masses to the standard model fermions, is sufficiently strongly coupled the technicolor theory, in isolation, must have an infrared fixed point for the full model to be phenomenologically viable. Using the new phase diagram we show that the simplest one family and minimal walking technicolor models are the archetypes of models of dynamical electroweak symmetry breaking. Our predictions can be verified via first principle lattice simulations.
Theory, Modeling, and Simulation of Semiconductor Lasers
NASA Technical Reports Server (NTRS)
Ning, Cun-Zheng; Saini, Subbash (Technical Monitor)
1998-01-01
Semiconductor lasers play very important roles in many areas of information technology. In this talk, I will first give an overview of semiconductor laser theory. This will be followed by a description of different models and their shortcomings in modeling and simulation. Our recent efforts in constructing a fully space and time resolved simulation model will then be described. Simulation results based on our model will be presented. Finally the effort towards a self-consistent and comprehensive simulation capability for the opto-electronics integrated circuits (OEICs) will be briefly reviewed.
Kanazawa, Takuya
2009-08-15
We extend the inequality of Tomboulis and Yaffe in SU(2) lattice gauge theory (LGT) to SU(N) LGT and to general classical spin systems, by use of reflection positivity. Basically the inequalities guarantee that a system in a box that is sufficiently insensitive to boundary conditions has a non-zero mass gap. We explicitly illustrate the theorem in some solvable models. Strong-coupling expansion is then utilized to discuss some aspects of the theorem. Finally, a conjecture for exact expression to the off-axis mass gap of the triangular Ising model is presented. The validity of the conjecture is tested in multiple ways.
FTEs: Theory, Simulation, and Observations
NASA Technical Reports Server (NTRS)
Siebeck, David G.; Zhang, H.
2011-01-01
Flux transfer events (FTEs) are ropes of interconnected magnetosheath and magnetospheric magnetic field lines generated by bursty reconnection at the dayside magnetopause. Theory predicts that the combined pressure gradient and magnetic curvature forces should determine the speed at which the events move and the locations where they can be observed. We present results indicating that events form on the dayside magnetopause for both northward and southward IMF orientations, but that the events for northward IMF orientations exhibit far weaker signatures until they reach the magnetospheric flanks and argue that this is consistent with observations indicating that events on the dayside tend to occur for southward IMF orientations, but those on the flank do not. We show that the component and antiparallel reconnection models predict events in strikingly different quadrants outside the flanks of the magnetotail.Observations of events in all four quadrants indicate that both models are required. The motion of events inferred from multispacecraft timing during periods of northward IMF orientation is generally consistent with the component reconnection model.
Remarks on a Lorentz-breaking 4D chiral gauge theory
NASA Astrophysics Data System (ADS)
Scarpelli, A. P. Baêta; Gomes, M.; Petrov, A. Yu.; da Silva, A. J.
2016-01-01
We investigate a Lorentz-violating chiral model composed of two fermions, a complex scalar field, and a gauge field. We show that, by conveniently adjusting the parameters of the model, it is possible to generate an unambiguous Carroll-Field-Jackiw term and, at the same time, provide the cancellation of the chiral anomaly. The renormalizability of the model is investigated, and it is shown that the same counterterms needed in the symmetric phase also renormalize the model with broken symmetry.
Quantum Theory of Antisymmetric Higher Rank Tensor Gauge Field in Higher Dimensional Space-Time
NASA Astrophysics Data System (ADS)
Kimura, T.
1981-01-01
In a higher dimensional space-time, the Lagrangian formalism and the canonical operator formalism of covariant quantization of the antisymmetric tensor gauge field of higher rank are formulated consistently by introducing BRS transformation and Lagrangian multiplier fields From the effective Lagrangian, the numbers of the physical components and the effective ghosts are counted correctly without referring to a special reference frame. The confinement of unphysical components is assured from the viewpoint of the ``quartet mechanism'' of Kugo and Ojima.
Gauge symmetry from decoupling
NASA Astrophysics Data System (ADS)
Wetterich, C.
2017-02-01
Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang-Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.
NASA Astrophysics Data System (ADS)
Derendinger, J.-P.; Orlando, D.; Uranga, A.
2008-11-01
This special issue is devoted to the proceedings of the conference 'RTN Winter School on Strings, Supergravity and Gauge Theories', which took place at CERN, the European Centre for Nuclear Research, in Geneva, Switzerland, on the 21 25 January 2008. This event was organized in the framework of the European Mobility Research and Training Network entitled 'Constituents, Fundamental Forces and Symmetries of the Universe'. It is part of a yearly series of scientific schools, which represents what is by now a well established tradition. The previous ones have been held at SISSA, in Trieste, Italy, in February 2005 and at CERN in January 2006. The next one will again take place at CERN, in February 2009. The school was primarily meant for young doctoral students and postdoctoral researchers working in the area of string theory. It consisted of several general lectures of four hours each, whose notes are published in the present proceedings, and five working group discussion sessions, focused on specific topics of the network research program. It was attended by approximatively 250 participants. The topics of the lectures were chosen to provide an introduction to some of the areas of recent progress, and to the open problems, in string theory. One of the most active areas in string theory in recent years is the AdS/CFT or gauge/gravity correspondence, which proposes the complete equivalence of string theory on (asymptotically) anti-de Sitter spacetimes with gauge theories. The duality relates the weak coupling regime of one system to the strongly coupled regime of the other, and is therefore very non-trivial to test beyond the supersymmetry-protected BPS sector. One of the key ideas to quantitatively match several quantities on both sides is the use of integrability, both in the gauge theory and the string side. The lecture notes by Nick Dorey provide a pedagogical introduction to the fascinating topic of integrability in AdS/CFT. On the string theory side, progress has
NASA Astrophysics Data System (ADS)
Dütsch, Michael
2015-12-01
The usual derivation of the Lagrangian of a model for massive vector bosons, by spontaneous symmetry breaking of a gauge theory, implies that the prefactors of the various interaction terms are uniquely determined functions of the coupling constant(s) and the masses. Since, under the renormalization group (RG) flow, different interaction terms get different loop-corrections, it is uncertain whether these functions remain fixed under this flow. We investigate this question for the U(1)-Higgs-model to 1-loop order in the framework of Epstein-Glaser renormalization. Our main result reads: choosing the renormalization mass scale(s) in a way corresponding to the minimal subtraction scheme, the geometrical interpretation as a spontaneously broken gauge theory gets lost under the RG-flow. This holds also for the clearly stronger property of BRST-invariance of the Lagrangian. On the other hand, we prove that physical consistency, which is a weak form of BRST-invariance of the time-ordered products, is maintained under the RG-flow.
Scheme-independent calculation of γψ ¯ ψ ,I R for an SU(3) gauge theory
NASA Astrophysics Data System (ADS)
Ryttov, Thomas A.; Shrock, Robert
2016-11-01
We present a scheme-independent calculation of the infrared value of the anomalous dimension of the fermion bilinear, γψ ¯ψ ,I R in an SU(3) gauge theory as a function of the number of fermions, Nf, via a series expansion in powers of Δf, where Δf=(16.5 -Nf), to order Δf4. We perform an extrapolation to obtain the first determination of the exact γψ ¯ψ ,I R from continuum field theory. The results are compared with calculations of the n -loop values of this anomalous dimension from series in powers of the coupling and from lattice measurements.
NASA Astrophysics Data System (ADS)
Heffner, J.; Reinhardt, H.
2015-04-01
Yang-Mills theory is studied at finite temperature within the Hamiltonian approach in Coulomb gauge by means of the variational principle using a Gaussian-type Ansatz for the vacuum wave functional. Temperature is introduced by compactifying one spatial dimension. As a consequence the finite-temperature behavior is encoded in the vacuum wave functional calculated on the spatial manifold R2×S1(L ) where L-1 is the temperature. The finite-temperature equations of motion are obtained by minimizing the vacuum energy density to two-loop order. We show analytically that these equations yield the correct zero-temperature limit while at infinite temperature they reduce to the equations of the 2 +1 -dimensional theory in accordance with dimensional reduction. The resulting propagators are compared to those obtained from the grand canonical ensemble where an additional Ansatz for the density matrix is required.
NASA Astrophysics Data System (ADS)
Capri, M. A. L.; Lemes, V. E. R.; Sobreiro, R. F.; Sorella, S. P.; Thibes, R.
2006-11-01
We pursue the study of SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge by taking into account the effects of the Gribov horizon. The Gribov approximation, previously introduced in [M. A. L. Capri, V. E. R. Lemes, R. F. Sobreiro, S. P. Sorella, and R. Thibes, Phys. Rev. D 72, 085021 (2005).], is improved through the introduction of the horizon function, which is constructed under the requirements of localizability and renormalizability. By following Zwanziger’s treatment of the horizon function in the Landau gauge, we prove that, when cast in local form, the horizon term of the maximal Abelian gauge leads to a quantized theory which enjoys multiplicative renormalizability, a feature which is established to all orders by means of the algebraic renormalization. Furthermore, it turns out that the horizon term is compatible with the local residual U(1) Ward identity, typical of the maximal Abelian gauge, which is easily derived. As a consequence, the nonrenormalization theorem, ZgZA1/2=1, relating the renormalization factors of the gauge coupling constant Zg and of the diagonal gluon field ZA, still holds in the presence of the Gribov horizon. Finally, we notice that a generalized dimension two gluon operator can be also introduced. It is BRST invariant on-shell, a property which ensures its multiplicative renormalizability. Its anomalous dimension is not an independent parameter of the theory, being obtained from the renormalization factors of the gauge coupling constant and of the diagonal antighost field.
Study of baryon and lepton violating two-proton annihilation in gauge theories
NASA Astrophysics Data System (ADS)
Vergados, J. D.
1982-12-01
The baryon and lepton violation process (A,Z) --> (A - 2,Z - 2) + e+ + e+ is investigated within the framework of two gauge models recently proposed. One is an SUL(2) × U(1) × SUC(3) model extended to include two isospin triplets which couple to quarks and leptons. The second is an extension of the minimal GUT SU(5) model to include a 45-plet and a 50-plet of Higgs scalars. With a reasonable choice of the parameters of these models and a proper treatment of nuclear physics, mean lifetimes of 1033 yr may be expected.
NASA Astrophysics Data System (ADS)
Colli, Matteo; Lanza, Luca; Rasmussen, Roy; Thériault, Julie
2016-04-01
Despite its importance, accurate measurements of precipitation remains a challenge. Measurement errors for solid precipitation, which are often ignored for automated systems, frequently range from 20% to 70% due to undercatch in windy conditions. While solid precipitation measurements have been the subject of many studies, there have been only a limited number of numerical modeling efforts to estimate the collection efficiency of solid precipitation gauges when exposed to the wind, in both shielded and unshielded configurations. The available models use CFD simulations of the airflow pattern generated by the aerodynamic response of the gauge/shield geometry to perform the Lagrangian tracking of solid precipitation particles (Thériault et al., 2012; Colli et al. 2016a and 2016b). Validation of the results against field observations yields similarities in the overall behavior, but the model output only approximately reproduces the dependence of the experimental collection efficiency on wind speed. We present recent developments of such a modelling approach including various gauge/shield configurations, the influence of the drag coefficient calculation on the model performance, and the role of the particle size distribution in explaining the scatter of the collection efficiency observed at any particular wind speed (Colli et al. 2015). Comparison with observations at the Marshall (CO) field test site is used to validate results of the various modelling schemes and to support the analysis of the microphysical characteristics of ice crystals. References: Colli, M., Rasmussen, R.M., Thèriault, J.M., Lanza, L.G., Baker, B.C. and J. Kochendorfer (2015). An improved trajectory model to evaluate the collection performance of snow gauges. J.Appl.Meteor.Climatol., 54(8), pages 1826-1836. Colli, M., Lanza, L.G., Rasmussen, R.M. and J.M. Thèriault (2016a). The collection efficiency of shielded and unshielded precipitation gauges. Part I: CFD airflow modelling. J. of
Capri, M.A.L.; Dudal, D.; Guimaraes, M.S.; Justo, I.F.; Sorella, S.P.; and others
2014-04-15
It is well accepted that dealing with the Gribov ambiguity has a major impact on correlation functions in gauge-fixed Yang–Mills theories, in particular in the low momentum regime where standard perturbation theory based on the Faddeev–Popov approach fails. Recent results, derived from functional tools (Dyson–Schwinger equations or exact RG) or the effective Gribov–Zwanziger action method, pointed towards e.g. gauge boson correlation functions that are not compatible with the properties of observable degrees of freedom. Although such an observation is a welcome feature for gauge theories exhibiting confinement, it would be a discomfort for gauge theories supplemented with Higgs fields, cf. the experimental success of the electroweak model based on a SU(2)×U(1) gauge group. The purpose of this short note is to assure that the effective action resolution to the Gribov ambiguity reduces to the standard Faddeev–Popov method in the perturbative regime of sufficiently small coupling/large Higgs condensate, thereby not compromising the physical particle spectrum of massive gauge bosons and a massless photon for the SU(2)×U(1) gauge–Higgs model. The closer the theory gets to the limit of vanishing Higgs condensate, the more the Gribov problem resurfaces with all its consequences. We give some speculations w.r.t. the Fradkin–Shenker insights about the phase diagram. -- Highlights: •Gribov horizon influences gauge propagators in a strong-coupling regime. •No influence of Gribov horizon in weak-coupling. •Inclusion of U(1) factor leads to very rich behavior of propagators.
Boson stars in a theory of complex scalar fields coupled to the U(1) gauge field and gravity
NASA Astrophysics Data System (ADS)
Kumar, Sanjeev; Kulshreshtha, Usha; Shankar Kulshreshtha, Daya
2014-08-01
We study boson shells and boson stars in a theory of a complex scalar field coupled to the U(1) gauge field {{A}_{\\mu }} and Einstein gravity with the potential V(|\\Phi |)\\;:=\\frac{1}{2}{{m}^{2}}{{\\left( |\\Phi |+a \\right)}^{2}}. This could be considered either as a theory of a massive complex scalar field coupled to an electromagnetic field and gravity in a conical potential, or as a theory in the presence of a potential that is an overlap of a parabolic and conical potential. Our theory has a positive cosmological constant (\\Lambda :=4\\pi G{{m}^{2}}{{a}^{2}}). Boson stars are found to come in two types, having either ball-like or shell-like charge density. We studied the properties of these solutions and also determined their domains of existence for some specific values of the parameters of the theory. Similar solutions have also been obtained by Kleihaus, Kunz, Laemmerzahl and List, in a V-shaped scalar potential.
a -function for N =2 supersymmetric gauge theories in three dimensions
NASA Astrophysics Data System (ADS)
Gracey, J. A.; Jack, I.; Poole, C.; Schröder, Y.
2017-01-01
Recently, the existence of a candidate a -function for renormalizable theories in three dimensions was demonstrated for a general theory at leading order and for a scalar-fermion theory at next-to-leading order. Here we extend this work by constructing the a -function at next-to-leading order for an N =2 supersymmetric Chern-Simons theory. This increase in precision for the a -function necessitated the evaluation of the underlying renormalization-group functions at four loops.
NASA Astrophysics Data System (ADS)
Iliaš, Miroslav; Jensen, Hans Jørgen Aa.; Bast, Radovan; Saue, Trond
2013-07-01
The use of magnetic-field dependent London atomic orbitals, also called gauge including atomic orbitals, is known to be an efficient choice for accurate non-relativistic calculations of magnetisabilities. In this work, the appropriate formulas were extended and implemented in the framework of the four-component relativistic linear response method at the self-consistent field single reference level. Benefits of employing the London atomic orbitals in relativistic calculations are illustrated with Hartree-Fock wave functions on the XF3 (X = N, P, As, Sb, Bi) series of molecules. Significantly better convergence of magnetisabilities with respect to the basis set size is observed compared to calculations employing a common gauge origin. In fact, it is mandatory to use London atomic orbitals unless you want to use ridiculously large basis sets. Relativistic effects on magnetisabilities are found to be quite small (<5%) for this particular set of molecules, but should be investigated on a larger set of molecules. We emphasise the breakdown of the connection between the paramagnetic contribution to magnetisabilities and rotational g tensors in the relativistic domain and discuss its origin. Finally, we visualise the magnetisability density which shows markedly atomic features evocative of Pascal's rules.
Simulation Methodology in Nursing Education and Adult Learning Theory
ERIC Educational Resources Information Center
Rutherford-Hemming, Tonya
2012-01-01
Simulation is often used in nursing education as a teaching methodology. Simulation is rooted in adult learning theory. Three learning theories, cognitive, social, and constructivist, explain how learners gain knowledge with simulation experiences. This article takes an in-depth look at each of these three theories as each relates to simulation.…
Higher-Loop Amplitude Monodromy Relations in String and Gauge Theory.
Tourkine, Piotr; Vanhove, Pierre
2016-11-18
The monodromy relations in string theory provide a powerful and elegant formalism to understand some of the deepest properties of tree-level field theory amplitudes, like the color-kinematics duality. This duality has been instrumental in tremendous progress on the computations of loop amplitudes in quantum field theory, but a higher-loop generalization of the monodromy construction was lacking. In this Letter, we extend the monodromy relations to higher loops in open string theory. Our construction, based on a contour deformation argument of the open string diagram integrands, leads to new identities that relate planar and nonplanar topologies in string theory. We write one and two-loop monodromy formulas explicitly at any multiplicity. In the field theory limit, at one-loop we obtain identities that reproduce known results. At two loops, we check our formulas by unitarity in the case of the four-point N=4 super-Yang-Mills amplitude.
Scattering process in the Scalar Duffin-Kemmer-Petiau gauge theory
NASA Astrophysics Data System (ADS)
Beltran, J.; Pimentel, B. M.; Soto, D. E.
2016-04-01
In this work we calculate the cross section of the scattering process of the Duffin-Kemmer-Petiau theory coupling with the Maxwell’s electromagnetic field. Specifically, we find the propagator of the free theory, the scattering amplitudes and cross sections at Born level for the Moeller and Compton scattering process of this model. For this purpose we use the analytic representation for free propagators and take account the framework of the Causal Perturbation Theory of Epstein and Glaser.
Theory, Modeling and Simulation Annual Report 2000
Dixon, David A.; Garrett, Bruce C.; Straatsma, Tp; Jones, Donald R.; Studham, Ronald S.; Harrison, Robert J.; Nichols, Jeffrey A.
2001-11-01
This annual report describes the 2000 research accomplishments for the Theory, Modeling, and Simulation (TM&S) directorate, one of the six research organizations in the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL) at Pacific Northwest National Laboratory (PNNL). EMSL is a U.S. Department of Energy (DOE) national scientific user facility and is the centerpiece of the DOE commitment to providing world-class experimental, theoretical, and computational capabilities for solving the nation's environmental problems.
Theory, Modeling and Simulation Annual Report 2000
Dixon, David A; Garrett, Bruce C; Straatsma, TP; Jones, Donald R; Studham, Scott; Harrison, Robert J; Nichols, Jeffrey A
2001-11-01
This annual report describes the 2000 research accomplishments for the Theory, Modeling, and Simulation (TM and S) directorate, one of the six research organizations in the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL) at Pacific Northwest National Laboratory (PNNL). EMSL is a U.S. Department of Energy (DOE) national scientific user facility and is the centerpiece of the DOE commitment to providing world-class experimental, theoretical, and computational capabilities for solving the nation's environmental problems.
Theory and simulations of rotating convection
Barker, Adrian J.; Dempsey, Adam M.; Lithwick, Yoram
2014-08-10
We study thermal convection in a rotating fluid in order to better understand the properties of convection zones in rotating stars and planets. We first derive a mixing-length theory for rapidly rotating convection, arriving at the results of Stevenson via simple physical arguments. The theory predicts the properties of convection as a function of the imposed heat flux and rotation rate, independent of microscopic diffusivities. In particular, it predicts the mean temperature gradient, the rms velocity and temperature fluctuations, and the size of the eddies that dominate heat transport. We test all of these predictions with high resolution three-dimensional hydrodynamical simulations of Boussinesq convection in a Cartesian box. The results agree remarkably well with the theory across more than two orders of magnitude in rotation rate. For example, the temperature gradient is predicted to scale as the rotation rate to the four-fifths power at fixed flux, and the simulations yield 0.75 ± 0.06. We conclude that the mixing-length theory is a solid foundation for understanding the properties of convection zones in rotating stars and planets.
Theory and Simulations of Rotating Convection
NASA Astrophysics Data System (ADS)
Barker, Adrian J.; Dempsey, Adam M.; Lithwick, Yoram
2014-08-01
We study thermal convection in a rotating fluid in order to better understand the properties of convection zones in rotating stars and planets. We first derive a mixing-length theory for rapidly rotating convection, arriving at the results of Stevenson via simple physical arguments. The theory predicts the properties of convection as a function of the imposed heat flux and rotation rate, independent of microscopic diffusivities. In particular, it predicts the mean temperature gradient, the rms velocity and temperature fluctuations, and the size of the eddies that dominate heat transport. We test all of these predictions with high resolution three-dimensional hydrodynamical simulations of Boussinesq convection in a Cartesian box. The results agree remarkably well with the theory across more than two orders of magnitude in rotation rate. For example, the temperature gradient is predicted to scale as the rotation rate to the four-fifths power at fixed flux, and the simulations yield 0.75 ± 0.06. We conclude that the mixing-length theory is a solid foundation for understanding the properties of convection zones in rotating stars and planets.
NASA Astrophysics Data System (ADS)
Degrand, Thomas
2011-12-01
I carry out a finite-size scaling study of the correlation length in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions, using recent data published by Fodor, Holland, Kuti, Nógradi and Schroeder [Z. Fodor, K. Holland, J. Kuti, D. Nogradi, and C. Schroeder, Phys. Lett. B 703, 348 (2011).PYLBAJ0370-269310.1016/j.physletb.2011.07.037]. I make the assumption that the system is conformal in the zero-mass, infinite volume limit, that scaling is violated by both nonzero fermion mass and by finite volume, and that the scaling function in each channel is determined self-consistently by the data. From several different observables I extract a common exponent for the scaling of the correlation length ξ with the fermion mass mq, ξ˜mq-1/ym with ym˜1.35. Shortcomings of the analysis are discussed.
Equation of state for SU(3) gauge theory via the energy-momentum tensor under gradient flow
NASA Astrophysics Data System (ADS)
Kitazawa, Masakiyo; Iritani, Takumi; Asakawa, Masayuki; Hatsuda, Tetsuo; Suzuki, Hiroshi
2016-12-01
The energy density and the pressure of SU(3) gauge theory at finite temperature are studied by direct lattice measurements of the renormalized energy-momentum tensor obtained by the gradient flow. Numerical analyses are carried out with β =6.287 - 7.500 corresponding to the lattice spacing a =0.013 - 0.061 fm . The spatial (temporal) sizes are chosen to be Ns=64 , 96, 128 (Nτ=12 , 16, 20, 22, 24) with the aspect ratio, 5.33 ≤Ns/Nτ≤8 . Double extrapolation, a →0 (the continuum limit) followed by t →0 (the zero flow-time limit), is taken using the numerical data. Above the critical temperature, the thermodynamic quantities are obtained with a few percent precision including statistical and systematic errors. The results are in good agreement with previous high-precision data obtained by using the integral method.
NASA Astrophysics Data System (ADS)
Vergados, J. D.
1983-05-01
The lepton violating processes β-β-, β+β+, (e -, e +) and double electron capture have been investigated in the context of modern gauge theories. Mechanisms involving light or heavy intermediate Majorana neutrinos, with or without right-handed currents, as well as Higgs particles, have been studied. The lepton-violating emission of light bosons, recently proposed by Georgi, Glashow and Nussinov, has also been analyzed. From the analysis of the 48Ca → 48Ti data the following limits emerge: ∣ < m v > ∣ < 80 eV, m N > (2-20) × 10 3GeV, m W R > 400 GeVand g v eoverlinevex 0 < 5 × 10 -3. The above limits are then used to predict the lifetimes for β+β+, (e -, e +) and double electron capture in the A = 58, 92 and 96 systems employing realistic nuclear models.
Theory and Simulations of Solar System Plasmas
NASA Technical Reports Server (NTRS)
Goldstein, Melvyn L.
2011-01-01
"Theory and simulations of solar system plasmas" aims to highlight results from microscopic to global scales, achieved by theoretical investigations and numerical simulations of the plasma dynamics in the solar system. The theoretical approach must allow evidencing the universality of the phenomena being considered, whatever the region is where their role is studied; at the Sun, in the solar corona, in the interplanetary space or in planetary magnetospheres. All possible theoretical issues concerning plasma dynamics are welcome, especially those using numerical models and simulations, since these tools are mandatory whenever analytical treatments fail, in particular when complex nonlinear phenomena are at work. Comparative studies for ongoing missions like Cassini, Cluster, Demeter, Stereo, Wind, SDO, Hinode, as well as those preparing future missions and proposals, like, e.g., MMS and Solar Orbiter, are especially encouraged.
Ma, Qintian; Yang, Qingyuan; Zhong, Chongli; Mi, Jianguo; Liu, Dahuan
2010-04-06
Capillary phase transitions of CH(4) confined in a series of metal-organic frameworks (MOFs) were investigated in this work using gauge cell Monte Carlo simulations. The results show that capillary phase transitions can occur in MOFs, and the effects of temperature, pore size, and adsorption energy are very significant. Furthermore, this work shows the confinement can induce a shift in critical point for fluids confined in MOFs, leading to a decrease in critical temperature and an increase in critical density. The critical point shift is more obvious for MOFs with small pore size and large adsorption energy.
NASA Astrophysics Data System (ADS)
Hidajatullah-Maksoed, Widastra
2015-04-01
Arthur Cayley at least investigate by creating the theory of permutation group[F:∖∖Group_theory.htm] where in cell elements addressing of the lattice Qmf used a Cayley tree, the self-afine object Qmf is described by the combination of the finite groups of rotation & inversion and the infinite groups of translation & dilation[G Corso & LS Lacena: ``Multifractal lattice and group theory'', Physica A: Statistical Mechanics &Its Applications, 2005, v 357, issue I, h 64-70; http://www.sciencedirect.com/science/articel/pii/S0378437105005005 ] hence multifractal can be related to group theory. Many grateful Thanks to HE. Mr. Drs. P. SWANTORO & HE. Mr. Ir. SARWONO KUSUMAATMADJA.
Some global problems in gauge theories (Variations on a theme of Aharonov and Bohm)
Wilczek, F.
1989-12-01
Several situations are discussed, in which the sort of global considerations made famous by Aharonov and Bohm in their discussion of the interaction of charged particles with magnetic flux tubes have important physical implications. It is argued that discrete gauge symmetries in the continuum make sense, and manifest themselves most clearly in Aharonov-Bohm type scattering of charged particles off string singularities. The existence of such discrete symmetries has important implications for the quantum mechanics of topologically non-trivial space-times in general and black holes in particular. It is argued that in the non-abelian case essentially new features arise, most notably that the symmetry group of the homogeneous ground state generally ceases to be globally defined in the presence of a string. When continuous rather than discrete symmetries are involved, a variety of fascinating and as yet poorly understood dynamical effects occur. Perhaps the most striking is a new form of string superconductivity, that exists for purely topological reasons, and is not well modeled by regarding the string as a superconducting wire. 8 refs., 2 figs.
Theory, modeling and simulation: Annual report 1993
Dunning, T.H. Jr.; Garrett, B.C.
1994-07-01
Developing the knowledge base needed to address the environmental restoration issues of the US Department of Energy requires a fundamental understanding of molecules and their interactions in insolation and in liquids, on surfaces, and at interfaces. To meet these needs, the PNL has established the Environmental and Molecular Sciences Laboratory (EMSL) and will soon begin construction of a new, collaborative research facility devoted to advancing the understanding of environmental molecular science. Research in the Theory, Modeling, and Simulation program (TMS), which is one of seven research directorates in the EMSL, will play a critical role in understanding molecular processes important in restoring DOE`s research, development and production sites, including understanding the migration and reactions of contaminants in soils and groundwater, the development of separation process for isolation of pollutants, the development of improved materials for waste storage, understanding the enzymatic reactions involved in the biodegradation of contaminants, and understanding the interaction of hazardous chemicals with living organisms. The research objectives of the TMS program are to apply available techniques to study fundamental molecular processes involved in natural and contaminated systems; to extend current techniques to treat molecular systems of future importance and to develop techniques for addressing problems that are computationally intractable at present; to apply molecular modeling techniques to simulate molecular processes occurring in the multispecies, multiphase systems characteristic of natural and polluted environments; and to extend current molecular modeling techniques to treat complex molecular systems and to improve the reliability and accuracy of such simulations. The program contains three research activities: Molecular Theory/Modeling, Solid State Theory, and Biomolecular Modeling/Simulation. Extended abstracts are presented for 89 studies.
Entanglement monotonicity and the stability of gauge theories in three spacetime dimensions.
Grover, Tarun
2014-04-18
We employ the recent results on the generalization of the central charge theorem to three spacetime dimensions to derive nonperturbative results for several strongly interacting quantum field theories, including quantum electrodynamics (QED-3), and the theory corresponding to certain quantum phase transitions in condensed matter systems. In particular, by demanding that the universal constant part of the entanglement entropy decreases along the renormalization group flow (F theorem), we find sufficient conditions for the stability of QED-3 against chiral symmetry breaking and confinement. Using similar ideas, we derive strong constraints on the nature of quantum critical points in condensed matter systems with topological order.
Generalized Lorentz-Dirac equation for a strongly coupled gauge theory.
Chernicoff, Mariano; García, J Antonio; Güijosa, Alberto
2009-06-19
We derive a semiclassical equation of motion for a "composite" quark in strongly coupled large-N_{c} N = 4 super Yang-Mills theory, making use of the anti-de Sitter space/conformal field theory correspondence. The resulting nonlinear equation incorporates radiation damping, and reduces to the standard Lorentz-Dirac equation for external forces that are small on the scale of the quark Compton wavelength, but has no self-accelerating or preaccelerating solutions. From this equation one can read off a nonstandard dispersion relation for the quark, as well as a Lorentz-covariant formula for its radiation rate.
Theory and simulation of chemically reacting elastomers
NASA Astrophysics Data System (ADS)
Rottach, Dana R.
The field of rubber elasticity has advanced significantly in the past several decades. New models of rubber elasticity have been proposed and adjusted to better match the behavior of elastomeric networks. The manner in which these properties change with age has, however, been relatively neglected. Theories developed for classical models of rubber elasticity have been largely forgotten. This work aims to incorporate an especially elegant treatment of the aging of rubbers brought forth for early classical models into modern theories of the behavior of rubbery polymeric networks. Tobolsky's independent network hypothesis was developed during the early days of polymer physics to describe the aging of elastomers. It was shown rigorous for the classical descriptions of rubber elasticity, the affine and phantom models but has been neglected by more modern, more accurate models of rubber. This research has three main aspects. First, to corroborate the independent network hypothesis using simulations. Second, to incorporate the independent network concept into modern theories of rubber elasticity. Finally, to apply the effective crosslink density concept, developed for the classical models to account for crosslink decay, to the modern theories considered previously. Constituitive models incorporating the independent network hypothesis and the stress transfer effect is made possible by this research.
A new algorithm of Langevin simulation and its application to the SU(2) and SU(3) lattice gauge
NASA Astrophysics Data System (ADS)
Nakajima, Hideo; Furui, Sadataka
1998-04-01
The 2nd order Runge-Kutta scheme Langevin simulation of unquenched QCD in pseudofermion method derived from our general theory shows a behaviour as a function of the Langevin step t better than the Fukugita, Oyanagi, Ukawa's scheme.
Unsal, Mithat
2007-03-06
We study the phase diagrams of N = {infinity} vector-like, asymptotically free gauge theories as a function of volume, on S{sup 3} x S{sup 1}. The theories of interest are the ones with fermions in two index representations [adjoint, (anti)symmetric, and bifundamental abbreviated as QCD(adj), QCD(AS/S) and QCD(BF)], and are interrelated via orbifold or orientifold projections. The phase diagrams reveal interesting phenomena such as disentangled realizations of chiral and center symmetry, confinement without chiral symmetry breaking, zero temperature chiral transitions, and in some cases, exotic phases which spontaneously break the discrete symmetries such as C, P, T as well as CPT. In a regime where the theories are perturbative, the deconfinement temperature in SYM, and QCD(AS/S/BF) coincide. The thermal phase diagrams of thermal orbifold QCD(BF), orientifold QCD(AS/S), and N = 1 SYM coincide, provided charge conjugation symmetry for QCD(AS/S) and Z{sub 2} interchange symmetry of the QCD(BF) are not broken in the phase continuously connected to R{sup 4} limit. When the S{sup 1} circle is endowed with periodic boundary conditions, the (nonthermal) phase diagrams of orbifold and orientifold QCD are still the same, however, both theories possess chirally symmetric phases which are absent in N=1 SYM. The match and mismatch of the phase diagrams depending on the spin structure of fermions along the S{sup 1} circle is naturally explained in terms of the necessary and sufficient symmetry realization conditions which determine the validity of the nonperturbative orbifold orientifold equivalence.
Physics of collisionless shocks: theory and simulation
NASA Astrophysics Data System (ADS)
Stockem Novo, A.; Bret, A.; Fonseca, R. A.; Silva, L. O.
2016-01-01
Collisionless shocks occur in various fields of physics. In the context of space and astrophysics they have been investigated for many decades. However, a thorough understanding of shock formation and particle acceleration is still missing. Collisionless shocks can be distinguished into electromagnetic and electrostatic shocks. Electromagnetic shocks are of importance mainly in astrophysical environments and they are mediated by the Weibel or filamentation instability. In such shocks, charged particles gain energy by diffusive shock acceleration. Electrostatic shocks are characterized by a strong electrostatic field, which leads to electron trapping. Ions are accelerated by reflection from the electrostatic potential. Shock formation and particle acceleration will be discussed in theory and simulations.
SIMP from a strong U(1) gauge theory with a monopole condensation
NASA Astrophysics Data System (ADS)
Kamada, Ayuki; Yamada, Masaki; Yanagida, Tsutomu T.; Yonekura, Kazuya
2016-09-01
We provide a variant model of a strongly interacting massive particle (SIMP), where composite dark matter (DM) comes from a strongly interacting U(1) theory. We first explain a non-Abelian version of the model with an additional singlet field, which is mixed with the Higgs field to maintain kinetic equilibrium between the hidden and Standard Model (SM) sectors. The mixing leads to signals that would be detected by future collider experiments, direct DM detection experiments, and beam-dump experiments. Then we investigate a U(1) theory with a scalar monopole, where U(1) charged particles are confined by a monopole condensation. In this model, the radial component of the monopole can mix with the Higgs field, so that we do not need to introduce the additional singlet field.
NASA Astrophysics Data System (ADS)
Schieb, Daniel J.; Haberbusch, Mark S.; Yeckley, Alexander J.
2006-05-01
Sierra Lobo tested its patented Cryo-Tracker(R) probe and Mass Gauging System in a large scale Expendable Launch Vehicle (ELV) liquid oxygen tank simulation for NASA. Typical Liquid Oxygen (LOX) tank operations were simulated at Lockheed Martin's Engineering Propulsion Laboratory in Denver, Colorado. The Cryo-Tracker(R) probe is 33 feet long, the longest built to date. It was mounted in the tank at only two locations, separated by 26 feet. Each test simulated typical Lockheed Martin booster pre-launch tanking operations, including filling the tank with LOX at fill rates typically used at the launch pad, and maintaining the fill level for a period representative of a typical pad hold. The Cryo-Tracker(R) Mass Gauging System was the primary instrument used for monitoring the fill and controlling the topping operations. Each test also simulated a typical flight profile, expelling the LOX at representative pressures and expulsion flow rates. During expulsion, the Cryo-Tracker(R) System served to generate an Engine Cut-Off (ECO) signal. Test objectives were as follows: Cryo-Tracker(R) data will be validated by flight-like propellant instruments currently used in launch vehicles; the probe will survive the harsh environment (which will be documented by a digital video camera) with no loss of signal or structural integrity; the system will successfully measure liquid levels and temperatures under all conditions and calculate propellant mass in real-time; the system will successfully demonstrate its feasibility as a control sensor for LOX filling and topping operations, as well as for engine cut-off. All objectives were met and the test results are presented.
Derivation of Calabi-Yau Crystals from Chern-Simons Gauge Theory
NASA Astrophysics Data System (ADS)
Okuda, Takuya
2005-03-01
We derive new crystal melting models from Chern-Simons theory on the three-sphere. Via large N duality, these models compute amplitudes for A-model on the resolved conifold. The crystal is bounded by two walls whose distance corresponds to the Kähler modulus of the geometry. An interesting phenomenon is found where the Kahler modulus is shifted by the presence of non-compact D-branes. We also discuss the idea of using the crystal models as means of proving more general large N dualities to all order in gs.
Minimally extended elctroweak gauge theories in SO(10) and E/sub 6/
Robinett, R.W.; Rosner, J.L.
1982-11-01
The possibility of minimally extending the standard SU(2)/sub L/xU(1) electroweak theory within the context of SO(10) and E/sub 6/ grand unification by adding U(1) factors is explored. The neutrino neutral-current interactions in these schemes are arranged to coincide with the standard-model predictions. Limits on the masses of the extra Z's generated by these U(1) factors are obtained by considering other parity-violating effects. Additional Z's as light as 2.5 to 3.0 times the standard model Z/sup 0/ mass are allowed.
Order of the deconfining phase transition in SU(3) lattice gauge theory
Fukugita, M. ); Okawa, M. ); Ukawa, A. )
1989-10-23
The nature of the finite-temperature deconfining phase transition is studied by Monte Carlo simulation on lattices ranging over 8{sup 3}{times}4 to 36{sup 3}{times}4. The spatial-volume dependence of the susceptibility and the mass gap strongly support a first-order transition. This is corroborated by an explicit construction of the effective {ital Z}(3) spin system whose dominant two-spin couplings are found to be all positive.
NASA Astrophysics Data System (ADS)
Derendinger, J.-P.; Scrucca, C. A.; Uranga, A. M.
2006-11-01
This special issue is devoted to the proceedings of the conference 'Winter School on Strings, Supergravity and Gauge Theories', which took place at CERN, the European Centre for Nuclear Research, in Geneva, Switzerland, from the 16 to the 20 of January 2006. This event was organized in the framework of the European Mobility Research and Training Network entitled 'Constituents, Fundamental Forces and Symmetries of the Universe'. It is part of a yearly series of scientific schools which have become a traditional rendezvous for young researchers of the community. The previous one was held at SISSA, in Trieste, Italy, in February 2005, and the next one will take place again at CERN, in January 2007. The school was primarily meant for young doctoral students and postdoctoral researchers working in the area of string theory. It consisted of five general lectures of four hours each, whose notes are published in the present proceedings, and five working group discussion sessions, focused on specific topics of the network research program. It was attended by approximately 250 participants. The topics of the lectures were chosen to provide an introduction to some of the areas of recent progress and to the open problems in string theory. String theory is expected to provide insights into the description of systems where the role of gravity is crucial. One prominent example of such systems are time-dependent backgrounds with big bang singularities, whose status in string theory is reviewed in the lecture notes by Ben Craps. In another main problem in quantum gravity, string theory gives a fascinating microscopic description of black holes and their properties. The lectures by Shiraz Minwalla review the thermal properties of black holes from their microscopic description in terms of a holographically dual large N field theory. Progress in the description of black hole microstates, and its interplay with the macroscopic description in terms of supergravity solutions via the
The Secret Life of Quarks: National Computational Infrastructure for Lattice Gauge Theory
Sugar, Robert L.
2013-05-13
The objective of this grant was to develop algorithms and software for the numerical study of quantum chromodynamics (QCD) and of quantum field theories of interest for the understanding of physical phenomena that go beyond the standard model of high energy physics. Thirteen institutions were involved in this effort. The roles of the University of California, Santa Barbara in the project were to supply overall leadership and coordination, and to administer travel funds for participants at institutions that did not receive direct funding from the DOE. The purposes of these trips were to enable collaborative research on algorithms and software, and to report on algorithm and software development, and on scientific results obtained from it, at scientific meetings. These funds were also used to support travel by the Santa Barbara Principal Investigator in support of the project, and by co-Principal Investigators at institutions not receiving DOE funding. A total of 126 trips were supported.
Modeling active memory: Experiment, theory and simulation
NASA Astrophysics Data System (ADS)
Amit, Daniel J.
2001-06-01
Neuro-physiological experiments on cognitively performing primates are described to argue that strong evidence exists for localized, non-ergodic (stimulus specific) attractor dynamics in the cortex. The specific phenomena are delay activity distributions-enhanced spike-rate distributions resulting from training, which we associate with working memory. The anatomy of the relevant cortex region and the physiological characteristics of the participating elements (neural cells) are reviewed to provide a substrate for modeling the observed phenomena. Modeling is based on the properties of the integrate-and-fire neural element in presence of an input current of Gaussian distribution. Theory of stochastic processes provides an expression for the spike emission rate as a function of the mean and the variance of the current distribution. Mean-field theory is then based on the assumption that spike emission processes in different neurons in the network are independent, and hence the input current to a neuron is Gaussian. Consequently, the dynamics of the interacting network is reduced to the computation of the mean and the variance of the current received by a cell of a given population in terms of the constitutive parameters of the network and the emission rates of the neurons in the different populations. Within this logic we analyze the stationary states of an unstructured network, corresponding to spontaneous activity, and show that it can be stable only if locally the net input current of a neuron is inhibitory. This is then tested against simulations and it is found that agreement is excellent down to great detail. A confirmation of the independence hypothesis. On top of stable spontaneous activity, keeping all parameters fixed, training is described by (Hebbian) modification of synapses between neurons responsive to a stimulus and other neurons in the module-synapses are potentiated between two excited neurons and depressed between an excited and a quiescent neuron
NASA Astrophysics Data System (ADS)
Furuuchi, Kazuyuki; Koyama, Yoji
2016-06-01
We continue our investigation of large field inflation models obtained from higher-dimensional gauge theories, initiated in our previous study [1]. We focus on Dante's Inferno model which was the most preferred model in our previous analysis. We point out the relevance of the IR obstruction to UV completion, which constrains the form of the potential of the massive vector field, under the current observational upper bound on the tensor to scalar ratio. We also show that in simple examples of the potential arising from DBI action of a D5-brane and that of an NS5-brane that the inflation takes place in the field range which is within the convergence radius of the Taylor expansion. This is in contrast to the well known examples of axion monodromy inflation where inflaton takes place outside the convergence radius of the Taylor expansion. This difference arises from the very essence of Dante's Inferno model that the effective inflaton potential is stretched in the inflaton field direction compared with the potential for the original field.
NASA Astrophysics Data System (ADS)
Baer, Howard; Barger, Vernon; Savoy, Mike
2015-06-01
More than 30 years ago, Arnowitt-Chamseddine-Nath and others established the compelling framework of supergravity gauge theories (SUGRA) as a picture for the next step in beyond the standard model physics. We review the current SUGRA scenario in light of recent data from LHC8 collider searches and the Higgs boson discovery. While many SUSY and non-SUSY scenarios are highly disfavored or even excluded by LHC, the essential SUGRA scenario remains intact and as compelling as ever. For naturalness, some non-universality between matter and Higgs sector soft terms is required along with substantial trilinear soft terms. SUSY models with radiatively-driven naturalness are found with high scale fine-tuning at a modest ˜ 10%. In this case, natural SUSY might be discovered at LHC13 but could also easily elude sparticle search endeavors. A linear {{e}+}{{e}-} collider with \\sqrt{s}\\gt 2m(higgsino) is needed to provide the definitive search for the required light higgsino states which are the hallmark of natural SUSY. In the most conservative scenario, we advocate inclusion of a Peccei-Quinn sector so that dark matter is composed of a WIMP/axion admixture i.e. two dark matter particles.
Furuuchi, Kazuyuki; Koyama, Yoji
2016-06-21
We continue our investigation of large field inflation models obtained from higher-dimensional gauge theories, initiated in our previous study http://dx.doi.org/10.1088/1475-7516/2015/02/031. We focus on Dante’s Inferno model which was the most preferred model in our previous analysis. We point out the relevance of the IR obstruction to UV completion, which constrains the form of the potential of the massive vector field, under the current observational upper bound on the tensor to scalar ratio. We also show that in simple examples of the potential arising from DBI action of a D5-brane and that of an NS5-brane that the inflation takes place in the field range which is within the convergence radius of the Taylor expansion. This is in contrast to the well known examples of axion monodromy inflation where inflaton takes place outside the convergence radius of the Taylor expansion. This difference arises from the very essence of Dante’s Inferno model that the effective inflaton potential is stretched in the inflaton field direction compared with the potential for the original field.
Skachkov, Dmitry; Krykunov, Mykhaylo; Kadantsev, Eugene; Ziegler, Tom
2010-05-11
We present here a method that can calculate NMR shielding tensors from first principles for systems with translational invariance. Our approach is based on Kohn-Sham density functional theory and gauge-including atomic orbitals. Our scheme determines the shielding tensor as the second derivative of the total electronic energy with respect to an external magnetic field and a nuclear magnetic moment. The induced current density due to a periodic perturbation from nuclear magnetic moments is obtained through numerical differentiation, whereas the influence of the responding perturbation in terms of the external magnetic field is evaluated analytically. The method is implemented into the periodic program BAND. It employs a Bloch basis set made up of Slater-type or numeric atomic orbitals and represents the Kohn-Sham potential fully without the use of effective core potentials. Results from calculations of NMR shielding constants based on the present approach are presented for isolated molecules as well as systems with one-, two- and three-dimensional periodicity. The reported values are compared to experiment and results from calculations on cluster models.
Calculation of masses of charge leptons of different generations in gauge field theory
Kushnirenko, A.N.
1986-11-01
In this study the authors calculate the masses of the charge leptons of different generations (the electron, muon, and tau-lepton) with the framework of the unified theory of weak and electromagnetic interactions. They assume that the bare masses of the charge leptons are nonzero and the bare masses of the neutral leptons (i.e., the neutrinos) are equal to zero. The total (experimental) mass of a charge lepton is due to its interaction with the vacua of the electromagnetic, W-boson, and Z-boson fields. The contribution of these vacua to the mass of the charged lepton is equivalent to the contribution from the vacuum of a certain equivalent fictitious field, whose quanta they will call fictitions. The fictition is as an auxiliary fictitious particle, which is introduced to realize the calculational apparatus that they introduce. They assume that the fictition is a pseudoscalar particle with a mass M/sub p/ = ..mu..hc and with a zero spin and a zero electric charge
Holomorphic field realization of SH c and quantum geometry of quiver gauge theories
NASA Astrophysics Data System (ADS)
Bourgine, Jean-Emile; Matsuo, Yutaka; Zhang, Hong
2016-04-01
In the context of 4D/2D dualities, SH c algebra, introduced by Schiffmann and Vasserot, provides a systematic method to analyse the instanton partition functions of N=2 supersymmetricgaugetheories. Inthispaper,werewritetheSH c algebrainterms of three holomorphic fields D 0( z), D ±1( z) with which the algebra and its representations are simplified. The instanton partition functions for arbitrary N=2 super Yang-Mills theories with A n and A n (1) type quiver diagrams are compactly expressed as a product of four building blocks, Gaiotto state, dilatation, flavor vertex operator and intertwiner which are written in terms of SH c and the orthogonal basis introduced by Alba, Fateev, Litvinov and Tarnopolskiy. These building blocks are characterized by new conditions which generalize the known ones on the Gaiotto state and the Carlsson-Okounkov vertex. Consistency conditions of the inner product give algebraic relations for the chiral ring generating functions defined by Nekrasov, Pestun and Shatashvili. In particular we show the polynomiality of the qq-characters which have been introduced as a deformation of the Yangian characters. These relations define a second quantization of the Seiberg-Witten geometry, and, accordingly, reduce to a Baxter TQ-equation in the Nekrasov-Shatashvili limit of the Omega-background.
Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
NASA Astrophysics Data System (ADS)
Spill, Fabian
In the following paper, which is based on the author's PhD thesis submitted to Imperial College London, we explore the applicability of Yangian symmetry to various integrable models, in particular, in relation with S-matrices. One of the main themes in this work is that, after a careful study of the mathematics of the symmetry algebras one finds that in an integrable model, one can directly reconstruct S-matrices just from the algebra. It has been known for a long time that S-matrices in integrable models are fixed by symmetry. However, Lie algebra symmetry, the Yang-Baxter equation, crossing and unitarity, which constrain the S-matrix in integrable models, are often taken to be separate, independent properties of the S-matrix. Here, we construct scattering matrices purely from the Yangian, showing that the Yangian is the right algebraic object to unify all required symmetries of many integrable models. In particular, we reconstruct the S-matrix of the principal chiral field, and, up to a CDD factor, of other integrable field theories with 𝔰𝔲(n) symmetry. Furthermore, we study the AdS/CFT correspondence, which is also believed to be integrable in the planar limit. We reconstruct the S-matrices at weak and at strong coupling from the Yangian or its classical limit. We give a pedagogical introduction into the subject, presenting a unified perspective of Yangians and their applications in physics. This paper should hence be accessible to mathematicians who would like to explore the application of algebraic objects to physics as well as to physicists interested in a deeper understanding of the mathematical origin of physical quantities.
A proposal of the gauge theory description of the small Schwarzschild black hole in AdS5 × S5
NASA Astrophysics Data System (ADS)
Hanada, Masanori; Maltz, Jonathan
2017-02-01
Based on 4d N = 4 SYM on {R}^1× {S}^3 , a gauge theory description of a small black hole in AdS5×S5 is proposed. The change of the number of dynamical degrees of freedom associated with the emission of the scalar fields' eigenvalues plays a crucial role in this description. By analyzing the microcanonical ensemble, the Hagedorn behavior of long strings at low energy is obtained. Modulo an assumption based on the AdS/CFT duality for a large black hole, the energy of the small ten-dimensional Schwarzschild black hole E ˜ 1 /( G 10,N T 7) is derived. A heuristic gauge theory argument supporting this assumption is also given. The same argument applied to the ABJM theory correctly reproduces the relation for the eleven-dimensional Schwarzschild black hole. One of the consequences of our proposal is that the small and large black holes are very similar when seen from the gauge theory point of view.
Theory and Simulations of Tapered Diblock Polymers
NASA Astrophysics Data System (ADS)
Hall, Lisa M.; Seo, Youngmi; Brown, Jonathan R.
We study tapered block polymers, AB diblock polymers with a gradient region inserted between the pure A and B blocks such that composition smoothly transitions from A to B (or B to A in the case of inverse tapers). Phase diagrams were created using self consistent field theory (SCFT), and coarse-grained molecular dynamics (MD) simulations were used to study polymer conformations and diffusion, including diffusion of monomer-sized penetrants preferentially dissolved in one of the phases. As has been observed experimentally, we find that tapering makes the A and B blocks more miscible, decreasing domain spacing and shifting the order to disorder transition to lower temperatures. We predict a widening of the bicontinuous double gyroid region of the phase diagram for moderate length normal tapers versus diblocks, suggesting taper length can be used as a control parameter to obtain network phases even at high molecular weight, as may be desirable in transport applications. Additionally, in some inverse tapered systems, SCFT predicts phases not present in the standard AB diblock phase diagram, and MD simulations show how the chains fold back and forth across the interface. In these inverse tapered polymers, as segregation strength is increased, the competing effects of folding and stretching produces lamellae that have domain spacing nearly independent of temperature. We also find that diffusion of penetrants in normal tapers is significantly faster than that in inverse tapers, which is likely related to their unusual conformations. This material is based upon work supported by DOE Grant SC0014209.
ERIC Educational Resources Information Center
Kapralos, Bill; Hogan, Michelle; Pribetic, Antonin I.; Dubrowski, Adam
2011-01-01
Purpose: Gaming and interactive virtual simulation environments support a learner-centered educational model allowing learners to work through problems acquiring knowledge through an active, experiential learning approach. To develop effective virtual simulations and serious games, the views and perceptions of learners and educators must be…
Some comments on unitarity gauge
NASA Astrophysics Data System (ADS)
Lopez-Osorio, M. A.; Martinez-Pascual, E.; Toscano, J. J.
2004-04-01
A pedagogical discussion on the unitarity gauge within the context of Hamiltonian path integral formalism is presented. A model based on the group O(N), spontaneously broken down to the subgroup O(N - 1), is used to illustrate the main aspects of this gauge-fixing procedure. Among the issues, discussed with some extent, are: (1) the structure of model's constraints following the Dirac's method, (2) the gauge-fixing procedure, using the unitarity gauge for the massive gauge fields and the Coulomb one for the massless gauge fields, (3) the absence of BRST symmetry in this gauge-fixing procedure and its implications on the renormalizability of the theory, and (4) the static role of the ghost and anti-ghost fields associated with the massive gauge fields and how their contributions can be eliminated by using the dimensional regularization scheme.
Aldrovandi, R.; Pereira, J.G.
1986-05-15
Because it acts on space-time and is not semisimple, the Poincare group cannot lead to a gauge theory of the usual kind. A candidate model is discussed which keeps itself as close as possible to the typical gauge scheme. Its field equations are the Yang-Mills equations for the Poincare group. It is shown that there exists no Lagrangian for these equations.
Coherent Synchrotron Radiation: Theory and Simulations.
Novokhatski, Alexander; /SLAC
2012-03-29
The physics of coherent synchrotron radiation (CSR) emitted by ultra-relativistic electron bunches, known since the last century, has become increasingly important with the development of high peak current free electron lasers and shorter bunch lengths in storage rings. Coherent radiation can be described as a low frequency part of the familiar synchrotron radiation in bending magnets. As this part is independent of the electron energy, the fields of different electrons of a short bunch can be in phase and the total power of the radiation will be quadratic with the number of electrons. Naturally the frequency spectrum of the longitudinal electron distribution in a bunch is of the same importance as the overall electron bunch length. The interest in the utilization of high power radiation from the terahertz and far infrared region in the field of chemical, physical and biological processes has led synchrotron radiation facilities to pay more attention to the production of coherent radiation. Several laboratories have proposed the construction of a facility wholly dedicated to terahertz production using the coherent radiation in bending magnets initiated by the longitudinal instabilities in the ring. Existing synchrotron radiation facilities also consider such a possibility among their future plans. There is a beautiful introduction to CSR in the 'ICFA Beam Dynamics Newsletter' N 35 (Editor C. Biscari). In this paper we recall the basic properties of CSR from the theory and what new effects, we can get from the precise simulations of the coherent radiation using numerical solutions of Maxwell's equations. In particular, transverse variation of the particle energy loss in a bunch, discovered in these simulations, explains the slice emittance growth in bending magnets of the bunch compressors and transverse de-coherence in undulators. CSR may play same the role as the effect of quantum fluctuations of synchrotron radiation in damping rings. It can limit the minimum
Mehran, Ali; AghaKouchak, Amir; Phillips, Thomas J.
2014-02-25
Numerous studies have emphasized that climate simulations are subject to various biases and uncertainties. The objective of this study is to cross-validate 34 Coupled Model Intercomparison Project Phase 5 (CMIP5) historical simulations of precipitation against the Global Precipitation Climatology Project (GPCP) data, quantifying model pattern discrepancies and biases for both entire data distributions and their upper tails. The results of the Volumetric Hit Index (VHI) analysis of the total monthly precipitation amounts show that most CMIP5 simulations are in good agreement with GPCP patterns in many areas, but that their replication of observed precipitation over arid regions and certain sub-continental regions (e.g., northern Eurasia, eastern Russia, central Australia) is problematical. Overall, the VHI of the multi-model ensemble mean and median also are superior to that of the individual CMIP5 models. However, at high quantiles of reference data (e.g., the 75th and 90th percentiles), all climate models display low skill in simulating precipitation, except over North America, the Amazon, and central Africa. Analyses of total bias (B) in CMIP5 simulations reveal that most models overestimate precipitation over regions of complex topography (e.g. western North and South America and southern Africa and Asia), while underestimating it over arid regions. Also, while most climate model simulations show low biases over Europe, inter-model variations in bias over Australia and Amazonia are considerable. The Quantile Bias (QB) analyses indicate that CMIP5 simulations are even more biased at high quantiles of precipitation. Lastly, we found that a simple mean-field bias removal improves the overall B and VHI values, but does not make a significant improvement in these model performance metrics at high quantiles of precipitation.
Mehran, Ali; AghaKouchak, Amir; Phillips, Thomas J.
2014-02-25
Numerous studies have emphasized that climate simulations are subject to various biases and uncertainties. The objective of this study is to cross-validate 34 Coupled Model Intercomparison Project Phase 5 (CMIP5) historical simulations of precipitation against the Global Precipitation Climatology Project (GPCP) data, quantifying model pattern discrepancies and biases for both entire data distributions and their upper tails. The results of the Volumetric Hit Index (VHI) analysis of the total monthly precipitation amounts show that most CMIP5 simulations are in good agreement with GPCP patterns in many areas, but that their replication of observed precipitation over arid regions and certain sub-continentalmore » regions (e.g., northern Eurasia, eastern Russia, central Australia) is problematical. Overall, the VHI of the multi-model ensemble mean and median also are superior to that of the individual CMIP5 models. However, at high quantiles of reference data (e.g., the 75th and 90th percentiles), all climate models display low skill in simulating precipitation, except over North America, the Amazon, and central Africa. Analyses of total bias (B) in CMIP5 simulations reveal that most models overestimate precipitation over regions of complex topography (e.g. western North and South America and southern Africa and Asia), while underestimating it over arid regions. Also, while most climate model simulations show low biases over Europe, inter-model variations in bias over Australia and Amazonia are considerable. The Quantile Bias (QB) analyses indicate that CMIP5 simulations are even more biased at high quantiles of precipitation. Lastly, we found that a simple mean-field bias removal improves the overall B and VHI values, but does not make a significant improvement in these model performance metrics at high quantiles of precipitation.« less
NASA Astrophysics Data System (ADS)
Mehran, A.; AghaKouchak, A.; Phillips, T. J.
2014-02-01
The objective of this study is to cross-validate 34 Coupled Model Intercomparison Project Phase 5 (CMIP5) historical simulations of precipitation against the Global Precipitation Climatology Project (GPCP) data, quantifying model pattern discrepancies, and biases for both entire distributions and their upper tails. The results of the volumetric hit index (VHI) analysis of the total monthly precipitation amounts show that most CMIP5 simulations are in good agreement with GPCP patterns in many areas but that their replication of observed precipitation over arid regions and certain subcontinental regions (e.g., northern Eurasia, eastern Russia, and central Australia) is problematical. Overall, the VHI of the multimodel ensemble mean and median also are superior to that of the individual CMIP5 models. However, at high quantiles of reference data (75th and 90th percentiles), all climate models display low skill in simulating precipitation, except over North America, the Amazon, and Central Africa. Analyses of total bias (B) in CMIP5 simulations reveal that most models overestimate precipitation over regions of complex topography (e.g., western North and South America and southern Africa and Asia), while underestimating it over arid regions. Also, while most climate model simulations show low biases over Europe, intermodel variations in bias over Australia and Amazonia are considerable. The quantile bias analyses indicate that CMIP5 simulations are even more biased at high quantiles of precipitation. It is found that a simple mean field bias removal improves the overall B and VHI values but does not make a significant improvement at high quantiles of precipitation.
NASA Astrophysics Data System (ADS)
Baulieu, Laurent
1996-02-01
We construct a framework which unifies in pairs the fields and anti-fields of the Batalin and Vilkovisky quantization method. We consider gauge theories of p-forms coupled to Yang-Mills fields. Our algorithm generates many topological models of the Chern-Simons type or of the Donaldson-Witten type. Some of these models can undergo a partial breaking of their topological symmetries. We investigate the properties of 2D gravity in the Batalin and Vilkovisky quantization scheme. We find a structure which satisfies the holomorphic factorization and also properties analogous to those existing in the topological theories of forms. New conformal fields are introduced with their invariant action.
Application of control theory to dynamic systems simulation
NASA Technical Reports Server (NTRS)
Auslander, D. M.; Spear, R. C.; Young, G. E.
1982-01-01
The application of control theory is applied to dynamic systems simulation. Theory and methodology applicable to controlled ecological life support systems are considered. Spatial effects on system stability, design of control systems with uncertain parameters, and an interactive computing language (PARASOL-II) designed for dynamic system simulation, report quality graphics, data acquisition, and simple real time control are discussed.
NASA Astrophysics Data System (ADS)
Teyssandier, Pierre; Tucker, Robin W.
1996-01-01
We discuss the definitions of standard clocks in theories of gravitation. These definitions are motivated by the invariance of actions under different gauge symmetries. We contrast the definition of a standard Weyl clock with that of a clock in general relativity and argue that the historical criticisms of theories based on non-metric compatible connections by Einstein, Pauli and others must be considered in the context of Weyl's original gauge symmetry. We argue that standard Einsteinian clocks can be defined in non-Riemannian theories of gravitation by adopting the Weyl group as a local gauge symmetry that preserves the metric and discuss the hypothesis that atomic clocks may be adopted to measure proper time in the presence of non-Riemannian gravitational fields. These ideas are illustrated in terms of a recently developed model of gravitation based on a non-Riemannian spacetime geometry.
NASA Astrophysics Data System (ADS)
Kato, Seikou; Kondo, Kei-Ichi; Shibata, Akihiro
2015-02-01
In the S U (2 ) Yang-Mills theory on the four-dimensional Euclidean lattice, we confirm the gauge-independent "Abelian" dominance (or the restricted field dominance) and gauge-independent magnetic-monopole dominance in the string tension of the linear potential extracted from the Wilson loop in the fundamental representation. The dual Meissner effect is observed by demonstrating the squeezing of the chromoelectric field flux connecting a pair of a quark and an antiquark. In addition, the circular magnetic-monopole current is induced around the chromoelectric flux. The type of the dual superconductivity is also determined by fitting the result with the dual Ginzburg-Landau model. Thus, the dual superconductor picture for quark confinement is supported in a gauge-independent manner. These results are obtained based on a reformulation of the lattice Yang-Mills theory based on the change of variables à la Cho-Duan-Ge-Faddeev-Niemi combined with a non-Abelian Stokes theorem for the Wilson loop operator. We give a new procedure (called the reduction) for obtaining the color direction field that plays the central role in this reformulation.
Gauged twistor spinors and symmetry operators
NASA Astrophysics Data System (ADS)
Ertem, Ümit
2017-03-01
We consider gauged twistor spinors which are supersymmetry generators of supersymmetric and superconformal field theories in curved backgrounds. We show that the spinor bilinears of gauged twistor spinors satisfy the gauged conformal Killing-Yano equation. We prove that the symmetry operators of the gauged twistor spinor equation can be constructed from ordinary conformal Killing-Yano forms in constant curvature backgrounds. This provides a way to obtain gauged twistor spinors from ordinary twistor spinors.
NASA Astrophysics Data System (ADS)
Baxter, J. Erik
2016-10-01
We investigate the existence of black hole and soliton solutions to four dimensional, anti-de Sitter (adS), Einstein-Yang-Mills theories with general semisimple connected and simply connected gauge groups, concentrating on the so-called regular case. We here generalise results for the asymptotically flat case, and compare our system with similar results from the well-researched adS {mathfrak {su}}(N) system. We find the analysis differs from the asymptotically flat case in some important ways: the biggest difference is that for Λ <0, solutions are much less constrained as r→ infty , making it possible to prove the existence of global solutions to the field equations in some neighbourhood of existing trivial solutions, and in the limit of |Λ |→ infty . In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the {mathfrak {su}}(N) case proved important to stability.
NASA Technical Reports Server (NTRS)
Lee, Kimyeong; Stein-Schabes, Jaime A.; Watkins, Richard; Widrow, Lawrence M.
1988-01-01
Classical non-topological soliton configurations are considered within the theory of a complex scalar field with a gauged U symmetry. Their existence and stability against dispersion are demonstrated and some of their properties are investigated analytically and numerically. The soliton configuration is such that inside the soliton the local U symmetry is broken, the gauge field becomes massive and for a range of values of the coupling constants the soliton becomes a superconductor pushing the charge to the surface. Furthermore, because of the repulsive Coulomb force, there is a maximum size for these objects, making impossible the existence of Q-matter in bulk form. Also briefly discussed are solitons with fermions in a U gauge theory.
Kurachi, Masafumi; Shrock, Robert
2006-09-01
We consider a vectorial, confining SU(N) gauge theory with a variable number, N{sub f}, of massless fermions transforming according to the fundamental representation. Using the Schwinger-Dyson and Bethe-Salpeter equations, we calculate the S parameter in terms of the current-current correlation functions. We focus on values of N{sub f} such that the theory is in the crossover region between the regimes of walking behavior and QCD-like (nonwalking) behavior. Our calculations indicate that the contribution to S from a given fermion decreases as one moves from the QCD-like to the walking regimes. The implications of this result for technicolor theories are discussed.
NASA Astrophysics Data System (ADS)
Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus
2013-07-01
-orbit coupling (Rashba and Dresselhaus couplings), familiar from AMO and condensed matter physics. They lead to yet another variety of fascinating phenomena such as the quantum spin Hall effect, three-dimensional topological insulators, topological superconductors and superfluids of various kinds. One also expects here the appearance of excitations in a form of topological edge states that can support robust transport, or entangled Majorana fermions in the case of topological superconductors or superfluids. Again, while many kinds of topological insulators have been realized in condensed matter systems, a controlled way of creating them in AMO systems and studying quantum phase transitions between various kinds of them is obviously very appealing and challenging. The various systems listed so far correspond to static gauge fields, which are externally imposed by the experimentalists. Even more fascinating is the possibility of generating synthetically dynamical gauge fields, i.e. gauge fields that evolve in time according to an interacting gauge theory, e.g., a full lattice gauge theory (LGT). These dynamical gauge fields can also couple to matter fields, allowing the quantum simulation of such complex systems (notoriously hard to simulate using 'traditional' computers), which are particularly relevant for modern high-energy physics. So far, most of the theoretical proposals concern the simulation of Abelian gauge theories, however, several groups have recently proposed extensions to the non-Abelian scenarios. The scope of the present focused issue of Journal of Physics B is to cover all of these developments, with particular emphasis on the non-Abelian gauge fields. The 14 papers in this issue include contributions from the leading theory groups working in this field; we believe that this collection will provide the reference set for quantum simulations of gauge fields. Although the special issue contains exclusively theoretical proposals and studies, it should be stressed that
Reinforce Networking Theory with OPNET Simulation
ERIC Educational Resources Information Center
Guo, Jinhua; Xiang, Weidong; Wang, Shengquan
2007-01-01
As networking systems have become more complex and expensive, hands-on experiments based on networking simulation have become essential for teaching the key computer networking topics to students. The simulation approach is the most cost effective and highly useful because it provides a virtual environment for an assortment of desirable features…
ERIC Educational Resources Information Center
Apperly, Ian A.
2008-01-01
The debate between Simulation-Theory (ST) and Theory-Theory (TT) provides the dominant theoretical framework for research on "theory of mind" (ToM). Behavioural research has failed to provide clear methods for discriminating between these theories, but a number of recent studies have claimed that neuroimaging methods do allow key predictions of ST…
Mars Tumbleweed Simulation Using Singular Perturbation Theory
NASA Technical Reports Server (NTRS)
Raiszadeh, Behzad; Calhoun, Phillip
2005-01-01
The Mars Tumbleweed is a new surface rover concept that utilizes Martian winds as the primary source of mobility. Several designs have been proposed for the Mars Tumbleweed, all using aerodynamic drag to generate force for traveling about the surface. The Mars Tumbleweed, in its deployed configuration, must be large and lightweight to provide the ratio of drag force to rolling resistance necessary to initiate motion from the Martian surface. This paper discusses the dynamic simulation details of a candidate Tumbleweed design. The dynamic simulation model must properly evaluate and characterize the motion of the tumbleweed rover to support proper selection of system design parameters. Several factors, such as model flexibility, simulation run times, and model accuracy needed to be considered in modeling assumptions. The simulation was required to address the flexibility of the rover and its interaction with the ground, and properly evaluate its mobility. Proper assumptions needed to be made such that the simulated dynamic motion is accurate and realistic while not overly burdened by long simulation run times. This paper also shows results that provided reasonable correlation between the simulation and a drop/roll test of a tumbleweed prototype.
NASA Astrophysics Data System (ADS)
Brauer, Claudia; Overeem, Aart; Uijlenhoet, Remko
2015-04-01
Several rainfall measurement techniques are available for hydrological applications, each with its own spatial and temporal resolution. We investigated the effect of differences in rainfall estimates on discharge simulations in a lowland catchment by forcing a novel rainfall-runoff model (WALRUS) with rainfall data from gauges, radars and microwave links. The hydrological model used for this analysis is the recently developed Wageningen Lowland Runoff Simulator (WALRUS). WALRUS is a rainfall-runoff model accounting for hydrological processes relevant to areas with shallow groundwater (e.g. groundwater-surface water feedback). Here, we used WALRUS for case studies in the Hupsel Brook catchment. We used two automatic rain gauges with hourly resolution, located inside the catchment (the base run) and 30 km northeast. Operational (real-time) and climatological (gauge-adjusted) C-band radar products and country-wide rainfall maps derived from microwave link data from a cellular telecommunication network were also used. Discharges simulated with these different inputs were compared to observations. Traditionally, the precipitation research community places emphasis on quantifying spatial errors and uncertainty, but for hydrological applications, temporal errors and uncertainty should be quantified as well. Its memory makes the hydrologic system sensitive to missed or badly timed rainfall events, but also emphasizes the effect of a bias in rainfall estimates. Systematic underestimation of rainfall by the uncorrected operational radar product leads to very dry model states and an increasing underestimation of discharge. Using the rain gauge 30 km northeast of the catchment yields good results for climatological studies, but not for forecasting individual floods. Simulating discharge using the maps derived from microwave link data and the gauge-adjusted radar product yields good results for both events and climatological studies. This indicates that these products can be
Special issue on non-Abelian gauge fields Special issue on non-Abelian gauge fields
NASA Astrophysics Data System (ADS)
Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus
2012-09-01
Building a universal quantum computer is a central goal of emerging quantum technologies and it is expected to revolutionize science and technology. Unfortunately, this future does not seem very close, however, quantum computers built for a special purpose, i.e., quantum simulators, are currently being developed in many leading laboratories. Numerous schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in artificial, or synthetic, Abelian or even non-Abelian gauge fields. Abelian gauge fields are analogues to the standard magnetic field and lead to fascinating effects such as the integer or fractional quantum Hall effects (IQHE, FQHE) and vortex lattices. Non-Abelian gauge fields couple the motional states of the particles to their internal degrees of freedom (such as hyperfine states for atoms or ions, electronic spins for electrons, etc). In this sense, external non-Abelian fields extend the concept of spin-orbit coupling, which is familiar from AMO and condensed matter physics. They lead to yet another variety of fascinating novel phenomena such as the quantum spin Hall effect (QSHE), 3D topological insulators, topological superconductors and superfluids of various kinds. Even more fascinating is the possibility of generating synthetic gauge fields that are dynamical, i.e., that evolve in time according to the corresponding lattice gauge theory (LGT). These dynamical gauge fields can also couple to matter fields, allowing the quantum simulation of such complex systems (notoriously hard to simulate using 'traditional' computers), which are particularly relevant for modern high-energy physics. So far there are only theoretical
Using Historical Simulations to Teach Political Theory
ERIC Educational Resources Information Center
Gorton, William; Havercroft, Jonathan
2012-01-01
As teachers of political theory, our goal is not merely to help students understand the abstract reasoning behind key ideas and texts of our discipline. We also wish to convey the historical contexts that informed these ideas and texts, including the political aims of their authors. But the traditional lecture-and-discussion approach tends to…
Benini, Francesco; Dymarsky, Anatoly; Franco, Sebastian; Kachru, Shamit; Simic, Dusan; Verlinde, Herman; /Princeton, Inst. Advanced Study
2009-06-19
We discuss gravitational backgrounds where supersymmetry is broken at the end of a warped throat, and the SUSY-breaking is transmitted to the Standard Model via gauginos which live in (part of) the bulk of the throat geometry. We find that the leading effect arises from splittings of certain 'messenger mesons,' which are adjoint KK-modes of the D-branes supporting the Standard Model gauge group. This picture is a gravity dual of a strongly coupled field theory where SUSY is broken in a hidden sector and transmitted to the Standard Model via a relative of semi-direct gauge mediation.
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L.; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; Garcia-Ripoll, J. J.; Solano, E.
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Quantum simulation of quantum field theories in trapped ions.
Casanova, J; Lamata, L; Egusquiza, I L; Gerritsma, R; Roos, C F; García-Ripoll, J J; Solano, E
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Betts, Robert E.; Crawford, John F.
1989-01-01
An aging gauge comprising a container having a fixed or a variable sized t opening with a cap which can be opened to control the sublimation rate of a thermally sublimational material contained within the container. In use, the aging gauge is stored with an item to determine total heat the item is subjected to and also the maximum temperature to which the item has been exposed. The aging gauge container contains a thermally sublimational material such as naphthalene or similar material which has a low sublimation rate over the temperature range from about 70.degree. F. to about 160.degree. F. The aging products determined by analyses of a like item aged along with the aging gauge for which the sublimation amount is determined is employed to establish a calibration curve for future aging evaluation. The aging gauge is provided with a means for determining the maximum temperature exposure (i.e., a thermally indicating material which gives an irreversible color change, Thermocolor pigment). Because of the relationship of doubling reaction rates for increases of 10.degree. C., equivalency of item used in accelerated aging evaluation can be obtained by referring to a calibration curve depicting storage temperature on the abscissa scale and multiplier on the ordinate scale.
Betts, Robert E.; Crawford, John F.
1989-04-04
An aging gauge comprising a container having a fixed or a variable sized t opening with a cap which can be opened to control the sublimation rate of a thermally sublimational material contained within the container. In use, the aging gauge is stored with an item to determine total heat the item is subjected to and also the maximum temperature to which the item has been exposed. The aging gauge container contains a thermally sublimational material such as naphthalene or similar material which has a low sublimation rate over the temperature range from about 70.degree. F. to about 160.degree. F. The aging products determined by analyses of a like item aged along with the aging gauge for which the sublimation amount is determined is employed to establish a calibration curve for future aging evaluation. The aging gauge is provided with a means for determining the maximum temperature exposure (i.e., a thermally indicating material which gives an irreversible color change, Thermocolor pigment). Because of the relationship of doubling reaction rates for increases of 10.degree. C., equivalency of item used in accelerated aging evaluation can be obtained by referring to a calibration curve depicting storage temperature on the abscissa scale and multiplier on the ordinate scale.
Theory and simulations of quantum glass forming liquids.
Markland, Thomas E; Morrone, Joseph A; Miyazaki, Kunimasa; Berne, B J; Reichman, David R; Rabani, Eran
2012-02-21
A comprehensive microscopic dynamical theory is presented for the description of quantum fluids as they transform into glasses. The theory is based on a quantum extension of mode-coupling theory. Novel effects are predicted, such as reentrant behavior of dynamical relaxation times. These predictions are supported by path integral ring polymer molecular dynamics simulations. The simulations provide detailed insight into the factors that govern slow dynamics in glassy quantum fluids. Connection to other recent work on both quantum glasses as well as quantum optimization problems is presented.
Barrett, W.H.; Greenwoll, J.I.; Smith, C.W.; Johnson, D.E.; De La Cruz, C.F.
1995-08-01
This paper describes recent work to improve the measurement of the stress response of materials to intense, short pulses of radiation. When Saturn fires, large prompt electrical noise pulses are induced in stress measurement circuits. The conventional wisdom has been that the shorted guard ring quartz gauge was the only configuration with acceptable prompt signal-to-noise characteristics for stress measurements in this pulsed radiation environment. However, because of abnormal signal distortion, the shorted guard ring gauge is restricted to a maximum stress of about 8 kbars. Below this level, the normal, quantified signal distortion is correctable with analytical deconvolution techniques. The shunted guard ring gauge is acceptable for Egli fidelity measurements to about 25 kbars with negligible signal distortion. Experiments were conducted on the Saturn soft x-ray source which show that higher fidelity shunted guard ring gauges can successfully measure stress with acceptable induced noise. We also found that a 50-ohm impedance matching resistor at the gauge reduced the prompt noise amplitude and improved the baseline quality of the measurement prior to shock wave arrival.
Faizal, Mir; Higuchi, Atsushi
2008-09-15
The propagators of the Faddeev-Popov (FP) ghosts for Yang-Mills theories and perturbative quantum gravity in the covariant gauge are infrared (IR) divergent in de Sitter spacetime. We point out, however, that the modes responsible for these divergences will not contribute to loop diagrams in computations of time-ordered products in either Yang-Mills theories or perturbative quantum gravity. Therefore, we propose that the IR-divergent FP-ghost propagator should be regularized by a small mass term that is sent to zero in the end of any perturbative calculations. This proposal is equivalent to using the effective FP-ghost propagators, which we present in an explicit form, obtained by removing the modes responsible for the IR divergences. We also make some comments on the corresponding propagators in anti-de Sitter spacetime.
Quantum gauge freedom in very special relativity
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker; Panigrahi, Prasanta K.
2017-02-01
We demonstrate Yokoyama gaugeon formalism for the Abelian one-form gauge (Maxwell) as well as for Abelian two-form gauge theory in the very special relativity (VSR) framework. In VSR scenario, the extended action due to introduction of gaugeon fields also possesses form invariance under quantum gauge transformations. It is observed that the gaugeon field together with gauge field naturally acquire mass, which is different from the conventional Higgs mechanism. The quantum gauge transformation implements a shift in gauge parameter. Further, we analyze the BRST symmetric gaugeon formalism in VSR which embeds only one subsidiary condition rather than two.
Capri, M.A.L. . E-mail: marcio@dft.if.uerj.br; Sobreiro, R.F. . E-mail: sobreiro@uerj.br; Sorella, S.P. . E-mail: sorella@uerj.br; Thibes, R. . E-mail: thibes@dft.if.uerj.br
2007-08-15
A detailed discussion of the renormalization properties of a class of gauges which interpolates among the Landau, Coulomb and maximal Abelian gauges is provided in the framework of the algebraic renormalization in Euclidean Yang-Mills theories in four dimensions.
Dynamical Messengers for Gauge Mediation
Hook, Anson; Torroba, Gonzalo; /SLAC /Stanford U., Phys. Dept.
2011-08-17
We construct models of indirect gauge mediation where the dynamics responsible for breaking supersymmetry simultaneously generates a weakly coupled subsector of messengers. This provides a microscopic realization of messenger gauge mediation where the messenger and hidden sector fields are unified into a single sector. The UV theory is SQCD with massless and massive quarks plus singlets, and at low energies it flows to a weakly coupled quiver gauge theory. One node provides the primary source of supersymmetry breaking, which is then transmitted to the node giving rise to the messenger fields. These models break R-symmetry spontaneously, produce realistic gaugino and sfermion masses, and give a heavy gravitino.
Theory, modeling, and simulation annual report, 1992
Not Available
1993-05-01
This report briefly discusses research on the following topics: development of electronic structure methods; modeling molecular processes in clusters; modeling molecular processes in solution; modeling molecular processes in separations chemistry; modeling interfacial molecular processes; modeling molecular processes in the atmosphere; methods for periodic calculations on solids; chemistry and physics of minerals; graphical user interfaces for computational chemistry codes; visualization and analysis of molecular simulations; integrated computational chemistry environment; and benchmark computations.
MSTS - Multiphase Subsurface Transport Simulator theory manual
White, M.D.; Nichols, W.E.
1993-05-01
The US Department of Energy, through the Yucca Mountain Site Characterization Project Office, has designated the Yucca Mountain site in Nevada for detailed study as the candidate US geologic repository for spent nuclear fuel and high-level radioactive waste. Site characterization will determine the suitability of the Yucca Mountain site for the potential waste repository. If the site is determined suitable, subsequent studies and characterization will be conducted to obtain authorization from the Nuclear Regulatory Commission to construct the potential waste repository. A principal component of the characterization and licensing processes involves numerically predicting the thermal and hydrologic response of the subsurface environment of the Yucca Mountain site to the potential repository over a 10,000-year period. The thermal and hydrologic response of the subsurface environment to the repository is anticipated to include complex processes of countercurrent vapor and liquid migration, multiple-phase heat transfer, multiple-phase transport, and geochemical reactions. Numerical simulators based on mathematical descriptions of these subsurface phenomena are required to make numerical predictions of the thermal and hydrologic response of the Yucca Mountain subsurface environment The engineering simulator called the Multiphase Subsurface Transport Simulator (MSTS) was developed at the request of the Yucca Mountain Site Characterization Project Office to produce numerical predictions of subsurface flow and transport phenomena at the potential Yucca Mountain site. This document delineates the design architecture and describes the specific computational algorithms that compose MSTS. Details for using MSTS and sample problems are given in the {open_quotes}User`s Guide and Reference{close_quotes} companion document.
ERIC Educational Resources Information Center
Asal, Victor; Kratoville, Jayson
2013-01-01
Simulations are being used more and more in political science generally and in international relations specifically. While there is a growing body of literature describing different simulations and a small amount of literature that empirically tests the impact of simulations, scholars have written very little linking the pedagogic theory behind…
Breeding curvature from extended gauge covariance
NASA Astrophysics Data System (ADS)
Aldrovandi, R.
1991-05-01
Independence between spacetime and “internal” space in gauge theories is related to the adjoint-covariant behaviour of the gauge potential. The usual gauge scheme is modified to allow a coupling between both spaces. Gauging spacetime translations produce field equations similar to Einstein equations. A curvature-like quantity of mixed differential-algebraic character emerges. Enlarged conservation laws are present, pointing to the presence of an covariance.
Huang, Yu-tin; Johansson, Henrik
2013-04-26
We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or two-algebra super-Yang-Mills theory when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions, implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N = 12,10,8 supergravity theories and discuss its validity for all multiplicity.
Continuum Edge Gyrokinetic Theory and Simulations
Xu, X Q; Xiong, Z; Dorr, M R; Hittinger, J A; Bodi, K; Candy, J; Cohen, B I; Cohen, R H; Colella, P; Kerbel, G D; Krasheninnikov, S; Nevins, W M; Qin, H; Rognlien, T D; Snyder, P B; Umansky, M V
2007-01-09
The following results are presented from the development and application of TEMPEST, a fully nonlinear (full-f) five dimensional (3d2v) gyrokinetic continuum edge-plasma code. (1) As a test of the interaction of collisions and parallel streaming, TEMPEST is compared with published analytic and numerical results for endloss of particles confined by combined electrostatic and magnetic wells. Good agreement is found over a wide range of collisionality, confining potential, and mirror ratio; and the required velocity space resolution is modest. (2) In a large-aspect-ratio circular geometry, excellent agreement is found for a neoclassical equilibrium with parallel ion flow in the banana regime with zero temperature gradient and radial electric field. (3) The four-dimensional (2d2v) version of the code produces the first self-consistent simulation results of collisionless damping of geodesic acoustic modes and zonal flow (Rosenbluth-Hinton residual) with Boltzmann electrons using a full-f code. The electric field is also found to agree with the standard neoclassical expression for steep density and ion temperature gradients in the banana regime. In divertor geometry, it is found that the endloss of particles and energy induces parallel flow stronger than the core neoclassical predictions in the SOL. (5) Our 5D gyrokinetic formulation yields a set of nonlinear electrostatic gyrokinetic equations that are for both neoclassical and turbulence simulations.
Microscopic molecular superfluid response: theory and simulations
NASA Astrophysics Data System (ADS)
Zeng, Tao; Roy, Pierre-Nicholas
2014-04-01
Since its discovery in 1938, superfluidity has been the subject of much investigation because it provides a unique example of a macroscopic manifestation of quantum mechanics. About 60 years later, scientists successfully observed this phenomenon in the microscopic world though the spectroscopic Andronikashvili experiment in helium nano-droplets. This reduction of scale suggests that not only helium but also para-H2 (pH2) can be a candidate for superfluidity. This expectation is based on the fact that the smaller number of neighbours and surface effects of a finite-size cluster may hinder solidification and promote a liquid-like phase. The first prediction of superfluidity in pH2 clusters was reported in 1991 based on quantum Monte Carlo simulations. The possible superfluidity of pH2 was later indirectly observed in a spectroscopic Andronikashvili experiment in 2000. Since then, a growing number of studies have appeared, and theoretical simulations have been playing a special role because they help guide and interpret experiments. In this review, we go over the theoretical studies of pH2 superfluid clusters since the experiment of 2000. We provide a historical perspective and introduce the basic theoretical formalism along with key experimental advances. We then present illustrative results of the theoretical studies and comment on the possible future developments in the field. We include sufficient theoretical details such that the review can serve as a guide for newcomers to the field.
NASA Astrophysics Data System (ADS)
Jiang, Shanhu; Ren, Liliang; Hong, Yang; Yong, Bin; Yang, Xiaoli; Yuan, Fei; Ma, Mingwei
2012-07-01
SummaryThis study first focuses on comprehensive evaluating three widely used satellite precipitation products (TMPA 3B42V6, TMPA 3B42RT, and CMORPH) with a dense rain gauge network in the Mishui basin (9972 km2) in South China and then optimally merge their simulated hydrologic flows with the semi-distributed Xinanjiang model using the Bayesian model averaging method. The initial satellite precipitation data comparisons show that the reanalyzed 3B42V6, with a bias of -4.54%, matched best with the rain gauge observations, while the two near real-time satellite datasets (3B42RT and CMORPH) largely underestimated precipitation by 42.72% and 40.81% respectively. With the model parameters first benchmarked by the rain gauge data, the behavior of the streamflow simulation from the 3B42V6 was also the most optimal amongst the three products, while the two near real-time satellite datasets produced deteriorated biases and Nash-Sutcliffe coefficients (NSCEs). Still, when the model parameters were recalibrated by each individual satellite data, the performance of the streamflow simulations from the two near real-time satellite products were significantly improved, thus demonstrating the need for specific calibrations of the hydrological models for the near real-time satellite inputs. Moreover, when optimally merged with respect to the streamflows forced by the two near real-time satellite precipitation products and all the three satellite precipitation products using the Bayesian model averaging method, the resulted streamflow series further improved and became more robust. In summary, the three current state-of-the-art satellite precipitation products have demonstrated potential in hydrological research and applications. The benchmarking, recalibration, and optimal merging schemes for streamflow simulation at a basin scale described in the present work will hopefully be a reference for future utilizations of satellite precipitation products in global and regional
Theory, modeling and simulation of superconducting qubits
Berman, Gennady P; Kamenev, Dmitry I; Chumak, Alexander; Kinion, Carin; Tsifrinovich, Vladimir
2011-01-13
We analyze the dynamics of a qubit-resonator system coupled with a thermal bath and external electromagnetic fields. Using the evolution equations for the set of Heisenberg operators that describe the whole system, we derive an expression for the resonator field, that includes the resonator-drive, the resonator-bath, and resonator-qubit interactions. The renormalization of the resonator frequency, caused by the qubit-resonator interaction, is accounted for. Using the solutions for the resonator field, we derive the equation that describes the qubit dynamics. The dependence of the qubit evolution during the measurement time on the fidelity of a single-shot measurement is studied. The relation between the fidelity and measurement time is shown explicitly. We proposed a novel adiabatic method for the phase qubit measurement. The method utilizes a low-frequency, quasi-classical resonator inductively coupled to the qubit. The resonator modulates the qubit energy, and the back reaction of the qubit causes a shift in the phase of the resonator. The resonator phase shift can be used to determine the qubit state. We have simulated this measurement taking into the account the energy levels outside the phase qubit manifold. We have shown that, for qubit frequencies in the range of 8-12GHZ, a resonator frequency of 500 MHz and a measurement time of 100 ns, the phase difference between the two qubit states is greater than 0.2 rad. This phase difference exceeds the measurement uncertainty, and can be detected using a classical phase-meter. A fidelity of 0.9999 can be achieved for a relaxation time of 0.5 ms. We also model and simulate a microstrip-SQUID amplifier of frequency about 500 MHz, which could be used to amplify the resonator oscillations in the phase qubit adiabatic measurement. The voltage gain and the amplifier noise temperature are calculated. We simulate the preparation of a generalized Bell state and compute the relaxation times required for achieving high
Theory of compressive modeling and simulation
NASA Astrophysics Data System (ADS)
Szu, Harold; Cha, Jae; Espinola, Richard L.; Krapels, Keith
2013-05-01
Modeling and Simulation (M&S) has been evolving along two general directions: (i) data-rich approach suffering the curse of dimensionality and (ii) equation-rich approach suffering computing power and turnaround time. We suggest a third approach. We call it (iii) compressive M&S (CM&S); because the basic Minimum Free-Helmholtz Energy (MFE) facilitating CM&S can reproduce and generalize Candes, Romberg, Tao & Donoho (CRT&D) Compressive Sensing (CS) paradigm as a linear Lagrange Constraint Neural network (LCNN) algorithm. CM&S based MFE can generalize LCNN to 2nd order as Nonlinear augmented LCNN. For example, during the sunset, we can avoid a reddish bias of sunlight illumination due to a long-range Rayleigh scattering over the horizon. With CM&S we can take instead of day camera, a night vision camera. We decomposed long wave infrared (LWIR) band with filter into 2 vector components (8~10μm and 10~12μm) and used LCNN to find pixel by pixel the map of Emissive-Equivalent Planck Radiation Sources (EPRS). Then, we up-shifted consistently, according to de-mixed sources map, to the sub-micron RGB color image. Moreover, the night vision imaging can also be down-shifted at Passive Millimeter Wave (PMMW) imaging, suffering less blur owing to dusty smokes scattering and enjoying apparent smoothness of surface reflectivity of man-made objects under the Rayleigh resolution. One loses three orders of magnitudes in the spatial Rayleigh resolution; but gains two orders of magnitude in the reflectivity, and gains another two orders in the propagation without obscuring smog . Since CM&S can generate missing data and hard to get dynamic transients, CM&S can reduce unnecessary measurements and their associated cost and computing in the sense of super-saving CS: measuring one & getting one's neighborhood free .
Recent Progress in Nuclear Lattice Simulations with Effective Field Theory
NASA Astrophysics Data System (ADS)
Lee, D.
2007-10-01
This proceedings article summarizes recent work presented at Chiral Dynamics 2006 on nuclear lattice simulations with chiral effective field theory for light nuclei. This work has been done in collaboration with Bubar {gra} Borasoy , Evgeny Epelbaum, Hermann Krebs, and Ulf-G. Meißner.