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.
4d {N}=2 gauge theories and quivers: the non-simply laced case
NASA Astrophysics Data System (ADS)
Cecotti, Sergio; Del Zotto, Michele
2012-10-01
We construct the BPS quivers with superpotential for the 4d {N}=2 gauge theories with non-simply laced Lie groups ( B n , C n , F 4 and G 2). The construction is inspired by the BIKMSV geometric engineering of these gauge groups as non-split singular elliptic fibrations. From the categorical viewpoint of arXiv:1203.6734, the fibration of the light category L( {g} ) over the (degenerate) Gaiotto curve has a monodromy given by the action of the outer automorphism of the corresponding unfolded Lie algebra. In view of the Katz-Vafa `matter from geometry' mechanism, the monodromic idea may be extended to the construction of ( Q, W) for SYM coupled to higher matter representations. This is done through a construction we call specialization.
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.
NASA Astrophysics Data System (ADS)
Karndumri, Parinya
2016-08-01
We study various supersymmetric renormalization group (RG) flows of N =3 Chern-Simons-Matter theory in three dimensions by using four-dimensional N =3 gauged supergravity coupled to eight vector multiplets with S O (3 )×S U (3 ) gauge group. The AdS4 critical point preserving the full S O (3 )×S U (3 ) provides a gravity dual of N =3 superconformal field theory with flavor symmetry S U (3 ). We study the scalar potential and identify a new supersymmetric AdS4 critical point preserving the full N =3 supersymmetry and unbroken S O (3 )×U (1 ) symmetry. An analytic RG flow solution interpolating between S O (3 )×S U (3 ) and S O (3 )×U (1 ) critical points is explicitly given. We then investigate possible RG flows from these AdS4 critical points to nonconformal field theories in the IR. All of the singularities appearing in the IR turn out to be physically acceptable. Furthermore, we look for supersymmetric solutions of the form AdS2×Σ2 with Σ2 being a two-sphere or a two-dimensional hyperbolic space and find a number of AdS2 geometries preserving four supercharges with S O (2 )×S O (2 )×S O (2 ) and S O (2 )×S O (2 ) symmetries.
Notoph gauge theory: Superfield formalism
NASA Astrophysics Data System (ADS)
Malik, R. P.
2011-05-01
We derive absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the 4D free Abelian 2-form gauge theory by exploiting the superfield approach to BRST formalism. The antisymmetric tensor gauge field of the above theory was christened as the "notoph" (i.e. the opposite of "photon") gauge field by Ogievetsky and Palubarinov way back in 1966-67. We briefly outline the problems involved in obtaining the absolute anticonimutativity of the (anti-) BRST transformations and their resolution within the framework of geometrical superfield approach to BRST formalism. One of the highlights of our results is the emergence of a Curci-Ferrari type of restriction in the context of 4D Abelian 2-form (notoph) gauge theory which renders the nilpotent (anti-) BRST symmetries of the theory to be absolutely anticommutative in nature.
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.
Generalized higher gauge theory
NASA Astrophysics Data System (ADS)
Ritter, Patricia; Sämann, Christian; Schmidt, Lennart
2016-04-01
We study a generalization of higher gauge theory which makes use of generalized geometry and seems to be closely related to double field theory. The local kinematical data of this theory is captured by morphisms of graded manifolds between the canonical exact Courant Lie 2-algebroid T M ⊕ T ∗ M over some manifold M and a semistrict gauge Lie 2-algebra. We discuss generalized curvatures and infinitesimal gauge transformations. Finite gauge transformation as well as global kinematical data are then obtained from principal 2-bundles over 2-spaces. As dynamical principle, we consider first the canonical Chern-Simons action for such a gauge theory. We then show that a previously proposed 3-Lie algebra model for the six-dimensional (2,0) theory is very naturally interpreted as a generalized higher gauge theory.
NASA Astrophysics Data System (ADS)
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
2016-07-01
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
Clear evidence of a continuum theory of 4D Euclidean simplicial quantum gravity
NASA Astrophysics Data System (ADS)
Egawa, H. S.; Horata, S.; Yukawa, T.
2002-03-01
Four-dimensional (4D) simplicial quantum gravity coupled to both scalar fields ( NX) and gauge fields ( NA) has been studied using Monte-Carlo simulations. The matter dependence of the string susceptibility exponent γ (4) is estimated. Furthermore, we compare our numerical results with Background-Metric-Indepenent (BMI) formulation conjectured to describe the quantum field theory of gravity in 4D. The numerical results suggest that the 4D simplicial quantum gravity is related to the conformal gravity in 4D. Therefore, we propose a phase structure in detail with adding both scalar and gauge fields and discuss the possibility and the property of a continuum theory of 4D Euclidean simplicial quantum gravity.
Clear evidence of a continuum theory of 4D Euclidean simplicial quantum gravity
NASA Astrophysics Data System (ADS)
Egawa, H. S.; Horata, S.; Yukawa, T.
Four-dimensional (4D) simplicial quantum gravity coupled to both scalar fields (NX) and gauge fields (NA) has been studied using Monte-Carlo simulations. The matter dependence of the string susceptibility exponent γ(4) is estimated. Furthermore, we compare our numerical results with Background-Metric-Indepenent (BMI) formulation conjectured to describe the quantum field theory of gravity in 4D. The numerical results suggest that the 4D simplicial quantum gravity is related to the conformal gravity in 4D. Therefore, we propose a phase structure in detail with adding both scalar and gauge fields and discuss the possibility and the property of a continuum theory of 4D Euclidean simplicial quantum gravity.
NASA Astrophysics Data System (ADS)
Mojaza, Matin; Pica, Claudio; Sannino, Francesco
2010-12-01
We compute the nonzero temperature free energy up to the order g6ln(1/g) in the coupling constant for vectorlike SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged in such a way that the theory develops a perturbative stable infrared fixed point at zero temperature. Because of large distance conformality we trade the coupling constant with its fixed point value and define a reduced free energy which depends only on the number of flavors, colors, and matter representation. We show that the reduced free energy changes sign, at the second, fifth, and sixth order in the coupling, when decreasing the number of flavors from the upper end of the conformal window. If the change in sign is interpreted as a signal of an instability of the system then we infer a critical number of flavors. Surprisingly this number, if computed to the order g2, agrees with previous predictions for the lower boundary of the conformal window for nonsupersymmetric gauge theories. The higher order results tend to predict a higher number of critical flavors. These are universal properties, i.e. they are independent of the specific matter representation.
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.
Geometry and dynamics of a coupled 4 D-2 D quantum field theory
NASA Astrophysics Data System (ADS)
Bolognesi, Stefano; Chatterjee, Chandrasekhar; Evslin, Jarah; Konishi, Kenichi; Ohashi, Keisuke; Seveso, Luigi
2016-01-01
Geometric and dynamical aspects of a coupled 4 D-2 D interacting quantum field theory — the gauged nonAbelian vortex — are investigated. The fluctuations of the internal 2 D nonAbelian vortex zeromodes excite the massless 4 D Yang-Mills modes and in general give rise to divergent energies. This means that the well-known 2 D C{P}^{N-1} zeromodes associated with a nonAbelian vortex become nonnormalizable.
NASA Astrophysics Data System (ADS)
Correa, Diego H.; Silva, Guillermo A.
2008-07-01
We discuss how geometrical and topological aspects of certain 1/2-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.
Correa, Diego H.; Silva, Guillermo A.
2008-07-28
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.
Methods of Contemporary Gauge Theory
NASA Astrophysics Data System (ADS)
Makeenko, Yuri
2002-08-01
Preface; Part I. Path Integrals: 1. Operator calculus; 2. Second quantization; 3. Quantum anomalies from path integral; 4. Instantons in quantum mechanics; Part II. Lattice Gauge Theories: 5. Observables in gauge theories; 6. Gauge fields on a lattice; 7. Lattice methods; 8. Fermions on a lattice; 9. Finite temperatures; Part III. 1/N Expansion: 10. O(N) vector models; 11. Multicolor QCD; 12. QCD in loop space; 13. Matrix models; Part IV. Reduced Models: 14. Eguchi-Kawai model; 15. Twisted reduced models; 16. Non-commutative gauge theories.
Methods of Contemporary Gauge Theory
NASA Astrophysics Data System (ADS)
Makeenko, Yuri
2005-11-01
Preface; Part I. Path Integrals: 1. Operator calculus; 2. Second quantization; 3. Quantum anomalies from path integral; 4. Instantons in quantum mechanics; Part II. Lattice Gauge Theories: 5. Observables in gauge theories; 6. Gauge fields on a lattice; 7. Lattice methods; 8. Fermions on a lattice; 9. Finite temperatures; Part III. 1/N Expansion: 10. O(N) vector models; 11. Multicolor QCD; 12. QCD in loop space; 13. Matrix models; Part IV. Reduced Models: 14. Eguchi-Kawai model; 15. Twisted reduced models; 16. Non-commutative gauge theories.
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.
Progress in lattice gauge theory
Creutz, M.
1983-01-01
These lectures first provide an overview of the current status of lattice gauge theory calculations. They then review some technical points on group integration, gauge fixing, and order parameters. Various Monte Carlo algorithms are discussed. Finally, alternatives to the Wilson action are considered in the context of universality for the continuum limit. 41 references.
Quiver gauge theories and integrable lattice models
NASA Astrophysics Data System (ADS)
Yagi, Junya
2015-10-01
We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d N=1 theories known as brane box and brane tilling models, 3d N=2 and 2d N=(2,2) theories obtained from them by compactification, and 2d N=(0,2) theories closely related to these theories. We argue that their supersymmetric indices carry structures of TQFTs equipped with line operators, and as a consequence, are equal to the partition functions of lattice models. The integrability of these models follows from the existence of extra dimension in the TQFTs, which emerges after the theories are embedded in M-theory. The Yang-Baxter equation expresses the invariance of supersymmetric indices under Seiberg duality and its lower-dimensional analogs.
Higher derivative corrections to BPS black hole attractors in 4d gauged supergravity
NASA Astrophysics Data System (ADS)
Hristov, Kiril; Katmadas, Stefanos; Lodato, Ivano
2016-05-01
We analyze BPS black hole attractors in 4d gauged supergravity in the presence of higher derivative supersymmetric terms, including a Weyl-squared-type action, and determine the resulting corrections to the Bekenstein-Hawking entropy. The near-horizon geometry AdS2×S2 (or other Riemann surface) preserves half of the supercharges in N = 2 supergravity with Fayet-Iliopoulos gauging. We derive a relation between the entropy and the black hole charges that suggests via AdS/CFT how subleading corrections contribute to the supersymmetric index in the dual microscopic picture.
Deconfinement Transition and High Temperature Phase in Lattice Gauge Theories
NASA Astrophysics Data System (ADS)
Papa, Alessandro
2002-09-01
This paper is organized in two parts. In the first one, I present a recent determination of the critical exponent ν of the correlation length in 3D SU(3) and in 4D SU(2) pure gauge theories at finite temperature, by a new approach inspired by-universality and based on finite size scaling. Moreover, I discuss possible implications of universality on the spectrum of screening masses in 4D SU(2) just above the critical temperature. In the second part, I propose two topics, well known in the literature, to be investigated by numerical simulations on the lattice, namely the Polyakov loop model by Pisarski for the high temperature phase of 4D SU(N) pure gauge theories and the Roberge-Weiss formulation of 4D SU(N) gauge theories with fermions and with imaginary chemical potential.
Gauge theory and chemical structure.
Mattingly, James
2003-05-01
The possibility of chemical structure in the context of quantized matter is examined by way of Richard Bader's Atoms in Molecules. I critically examine his notion of "electronic charge density"-showing that he cannot really mean "density of charge"-and I argue that the appropriate concept is expectation value of charge. This still allows him to define chemical structure, but it makes problematic his appeals to the explanatory power of structure. This is because, as Rosenfeld and Bohr showed, the expectation value of charge cannot be taken as the electronic field experienced by other charges. I suggest that we can recover the efficacy of structure by thinking of chemistry as a gauge theory. Current consensus in the study of gauge theories indicates that gauge potentials represent a new type of property; while no member of the family of functions comprising the gauge potential is real, the potential itself is causally potent. I illustrate this in the case of electrodynamics, where the vector potential can causally influence charges in the absence of electric or magnetic fields. I show how chemical structure can be considered to be a gauge field. Following Bader, I take it to be a family of geometric configurations, no one of which is possessed by a given molecule. I claim that current research in gauge theory licenses the attribution of causal potency to this notion of structure, despite its lack of reality. I thus begin the process of freeing the explanatory resources of gauge theory from physics alone. PMID:12796102
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.
Machines for lattice gauge theory
Mackenzie, P.B.
1989-05-01
The most promising approach to the solution of the theory of strong interactions is large scale numerical simulation using the techniques of lattice gauge theory. At the present time, computing requirements for convincing calculations of the properties of hadrons exceed the capabilities of even the most powerful commercial supercomputers. This has led to the development of massively parallel computers dedicated to lattice gauge theory. This talk will discuss the computing requirements behind these machines, and general features of the components and architectures of the half dozen major projects now in existence. 20 refs., 1 fig.
Massive supersymmetric quantum gauge theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Gut, M.; Scharf, G.
2005-08-01
We continue the study of the supersymmetric vector multiplet in a purely quantum framework. We obtain some new results which make the connection with the standard literature. First we construct the one-particle physical Hilbert space taking into account the (quantum) gauge structure of the model. Then we impose the condition of positivity for the scalar product only on the physical Hilbert space. Finally we obtain a full supersymmetric coupling which is gauge invariant in the supersymmetric sense in the first order of perturbation theory. By integrating out the Grassmann variables we get an interacting Lagrangian for a massive Yang-Mills theory related to ordinary gauge theory; however the number of ghost fields is doubled so we do not obtain the same ghost couplings as in the standard model Lagrangian.
Positive Energy Conditions in 4D Conformal Field Theory
NASA Astrophysics Data System (ADS)
Farnsworth, Kara; Luty, Markus; Prilepina, Valentina
2016-03-01
We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality avgT00 >= - C /L4 , where L is the size of the smearing region, and C is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the ``conformal collider'' constraints of Hofman and Maldacena. We speculate that there may be theories that violate the Hofman-Maldacena bounds, but satisfy our bounds. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarkably simple functions of momenta, and may be of interest in their own right.
Advances in lattice gauge theory
Duke, D.W.; Owens, J.F.
1985-01-01
This book presents papers on advances in lattice gauge theory. Topics covered include fermion Monte Carlo algorithms, portrait of a proton, critical behavior in QCD, the standard Higgs-model on the lattice, analytic calculation of mass gaps, and simulation of discrete Euclidean quantum gravity.
Kreimer, Dirk . E-mail: kreimer@ihes.fr
2006-12-15
We exhibit the role of Hochschild cohomology in quantum field theory with particular emphasis on gauge theory and Dyson-Schwinger equations, the quantum equations of motion. These equations emerge from Hopf- and Lie algebra theory and free quantum field theory only. In the course of our analysis, we exhibit an intimate relation between the Slavnov-Taylor identities for the couplings and the existence of Hopf sub-algebras defined on the sum of all graphs at a given loop order, surpassing the need to work on single diagrams.
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.
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.
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
2016-03-01
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
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
Ward identities and gauge independence in general chiral gauge theories
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2015-07-01
Using the Batalin-Vilkovisky formalism, we study the Ward identities and the equations of gauge dependence in potentially anomalous general gauge theories, renormalizable or not. A crucial new term, absent in manifestly nonanomalous theories, is responsible for interesting effects. We prove that gauge invariance always implies gauge independence, which in turn ensures perturbative unitarity. Precisely, we consider potentially anomalous theories that are actually free of gauge anomalies thanks to the Adler-Bardeen theorem. We show that when we make a canonical transformation on the tree-level action, it is always possible to re-renormalize the divergences and re-fine-tune the finite local counterterms, so that the renormalized Γ functional of the transformed theory is also free of gauge anomalies, and is related to the renormalized Γ functional of the starting theory by a canonical transformation. An unexpected consequence of our results is that the beta functions of the couplings may depend on the gauge-fixing parameters, although the physical quantities remain gauge independent. We discuss nontrivial checks of high-order calculations based on gauge independence and determine how powerful they are.
Gauge anomalies in an effective field theory
Preskill, J. )
1991-09-01
A four-dimensional gauge theory with anomalous fermion content can be consistently quantized, provided that at least some gauge fields are permitted to have nonvanishing masses. Such a theory is nonrenormalizable; there is a maximal value of the ultraviolet cutoff {Lambda}, beyond which the locality of the theory breaks down. The maximal {Lambda} can be estimated in perturbation theory and has a qualitatively different character in Abelian and non-Abelian anomalous gauge theories.
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 theory of glass transition
NASA Astrophysics Data System (ADS)
Vasin, Mikhail
2011-05-01
A new analytical approach for the description of the glass transition in a frustrated system is suggested. The theory is based on the non-equilibrium dynamics technique, and takes into account the interaction of the local order field with the massive gauge field, which describes frustration-induced plastic deformation. The glass transition is regarded as a phase transition interrupted because of the premature critical slowing-down of one of the degrees of freedom caused by the frustrations. It is shown that freezing of the system appears when the correlation length and relaxation time of the gauge field diverge. The Vogel-Fulcher-Tammann relation for the transition kinetics and the critical exponent for the nonlinear susceptibility, 2.5\\lesssim \\gamma \\leq 3 , are derived in the framework of the suggested approach. An expression for the temperature dependence of the heat capacity near to the glass transition is derived. This dependence is qualitatively in good agreement with experimental data. The presented theory reproduces the characteristic form of the langphiphirangt correlation function dependence on time, and explains the boson peak appearance on this curve. In addition, the function of the glass transition temperature value with cooling rate is derived; this dependence fully conforms with known experimental data.
Cosmology and unified gauge theory
NASA Astrophysics Data System (ADS)
Oraifeartaigh, L.
1981-09-01
Theoretical points in common between cosmology and unified gauge theory (UGT) are reviewed, with attention given to areas of one which have proven useful for the other. The underlying principles for both theoretical frameworks are described, noting the differences in scale, i.e., 10 to the 25th cm in cosmology and 10 to the -15th cm for UGT. Cosmology has produced bounds on the number of existing neutrino species, and also on the mass of neutrinos, two factors of interest in particle physics. Electrons, protons, and neutrinos, having been spawned from the same massive leptons, each composed of three quarks, have been predicted to be present in equal numbers in the Universe by UGT, in line with necessities of cosmology. The Grand UGT also suggests specific time scales for proton decay, thus accounting for the observed baryon assymmetry.
Gauge Coupling Unification in F-Theory Grand Unified Theories
Blumenhagen, Ralph
2009-02-20
We investigate gauge coupling unification for F-theory type IIB orientifold constructions of SU(5) grand unified theories (GUT) with gauge symmetry breaking via nontrivial hypercharge flux. This flux has the nontrivial effect that it splits the values of the three minimal supersymmetric standard model gauge couplings at the string scale, thus potentially spoiling the celebrated one-loop gauge coupling unification. It is shown how F-theory can evade this problem in a natural way.
Gauge coupling unification in F-theory grand unified theories.
Blumenhagen, Ralph
2009-02-20
We investigate gauge coupling unification for F-theory type IIB orientifold constructions of SU(5) grand unified theories (GUT) with gauge symmetry breaking via nontrivial hypercharge flux. This flux has the nontrivial effect that it splits the values of the three minimal supersymmetric standard model gauge couplings at the string scale, thus potentially spoiling the celebrated one-loop gauge coupling unification. It is shown how F-theory can evade this problem in a natural way. PMID:19257658
Abelian p-form (p = 1, 2, 3) gauge theories as the field theoretic models for the Hodge theory
NASA Astrophysics Data System (ADS)
Kumar, R.; Krishna, S.; Shukla, A.; Malik, R. P.
2014-09-01
Taking the simple examples of an Abelian 1-form gauge theory in two (1+1)-dimensions, a 2-form gauge theory in four (3+1)-dimensions and a 3-form gauge theory in six (5+1)-dimensions of space-time, we establish that such gauge theories respect, in addition to the gauge symmetry transformations that are generated by the first-class constraints of the theory, additional continuous symmetry transformations. We christen the latter symmetry transformations as the dual-gauge transformations. We generalize the above gauge and dual-gauge transformations to obtain the proper (anti-)BRST and (anti-)dual-BRST transformations for the Abelian 3-form gauge theory within the framework of BRST formalism. We concisely mention such symmetries for the 2D free Abelian 1-form and 4D free Abelian 2-form gauge theories and briefly discuss their topological aspects in our present endeavor. We conjecture that any arbitrary Abelian p-form gauge theory would respect the above cited additional symmetry in D = 2p(p = 1, 2, 3, …) dimensions of space-time. By exploiting the above inputs, we establish that the Abelian 3-form gauge theory, in six (5+1)-dimensions of space-time, is a perfect model for the Hodge theory whose discrete and continuous symmetry transformations provide the physical realizations of all aspects of the de Rham cohomological operators of differential geometry. As far as the physical utility of the above nilpotent symmetries is concerned, we demonstrate that the 2D Abelian 1-form gauge theory is a perfect model of a new class of topological theory and 4D Abelian 2-form as well as 6D Abelian 3-form gauge theories are the field theoretic models for the quasi-topological field theory.
Borel Summability of Perturbative Series in 4D N =2 and 5D N =1 Supersymmetric Theories
NASA Astrophysics Data System (ADS)
Honda, Masazumi
2016-05-01
We study weak coupling perturbative series in 4D N =2 and 5D N =1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in the zero-instanton sector are Borel summable for various observables. Our result for the 4D N =2 case supports an expectation from a recent proposal on a semiclassical realization of infrared renormalons in QCD-like theories, where the semiclassical solution does not exist in N =2 theories and the perturbative series are unambiguous, namely, Borel summable. We also prove that the perturbative series in an arbitrary number of instanton sectors are Borel summable for a wide class of theories. It turns out that exact results can be obtained by summing over the Borel resummations with every instanton number.
Gauge theories in terms of invariants
NASA Astrophysics Data System (ADS)
Kijowski, J.; Rudolph, G.; Rudolph, M.
1997-12-01
We discuss some aspects of our programme of investigating gauge theories (with fermions) in terms of local gauge invariant quantities. In the first part, the functional integral for quantum electrodynamics is discussed within our formulation. Next, the algebra of Grassmann algebra-valued invariants for one-flavour chromodynamics is investigated and, finally, the functional integral for this theory is derived within our framework.
New identities among gauge theory amplitudes
NASA Astrophysics Data System (ADS)
Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Feng, Bo; Søndergaard, Thomas
2010-08-01
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N = 4 super Yang-Mills multiplet.
4d/3d reduction of s-confining theories: the role of the "exotic" D instantons
NASA Astrophysics Data System (ADS)
Amariti, Antonio
2016-02-01
The reduction of 4d Seiberg duality to 3d by compactification on a circle is possible if finite size effects are considered. These effects boil down to the contribution of KK monopole operators acting as instantons in 3d, and they are crucial to preserve the 4d duality in 3d. This mechanism has been reproduced in string theory by T-duality on the type IIA brane setup. In some cases the 4d dual "magnetic" theories are IR confined descriptions of the UV gauge theories. In these cases the monopoles are absent in the IR dynamics and the mechanism of reduction of the 4d duality has to be modified. In this paper we investigate such modification in the brane setup. The main observation behind our analysis is that in the 4d case the superpotential of the confined theories can been obtained also from the "exotic" contribution of a D0 brane, a stringy instanton. When considering these configurations we reproduce the field theory results in the brane setup. We study both the unitary and the symplectic case. As a further check we provide the interpretation of the mechanism in terms of localization.
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.
Curving Yang-Mills-Higgs gauge theories
NASA Astrophysics Data System (ADS)
Kotov, Alexei; Strobl, Thomas
2015-10-01
We present a Yang-Mills-Higgs (YMH) gauge theory in which structure constants of the gauge group may depend on Higgs fields. The data of the theory are encoded in the bundle E →M , where the base M is the target space of Higgs fields and fibers carry information on the gauge group. M is equipped with a metric g and E carries a connection ∇. If ∇ is flat, R∇=0 , there is a local field redefinition which gives back the standard YMH gauge theory. If R∇≠0 , one obtains a new class of gauge theories. In this case, contrary to the standard wisdom of the YMH theory, the space (M ,g ) may have no isometries. We build a simple example which illustrates this statement.
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.
Graded geometry in gauge theories and beyond
NASA Astrophysics Data System (ADS)
Salnikov, Vladimir
2015-01-01
We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to the case of arbitrary Q-manifolds introducing thus the concept of equivariant Q-cohomology. Using this concept we describe a procedure for analysis of gauge symmetries of given functionals as well as for constructing functionals (sigma models) invariant under an action of some gauge group. As the main example of application of these constructions we consider the twisted Poisson sigma model. We obtain it by a gauging-type procedure of the action of an essentially infinite dimensional group and describe its symmetries in terms of classical differential geometry. We comment on other possible applications of the described concept including the analysis of supersymmetric gauge theories and higher structures.
Dimer models and quiver gauge theories
NASA Astrophysics Data System (ADS)
Pichai, Ramadevi
2013-12-01
= 1 quiver gauge theories on coincident D3 branes placed at a tip of a Calabi-Yau singularity C are dual to string theories on AdS5×X5 where X5 are Sasaki-Einstein spaces. We present a neat combinatorial approach called dimer model to understand interrelations between toric quiver gauge theories and toric data representing the Calabi-Yau singularities.
Solving flavor puzzles with quiver gauge theories
NASA Astrophysics Data System (ADS)
Antebi, Yaron E.; Nir, Yosef; Volansky, Tomer
2006-04-01
We consider a large class of models where the SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a U(5)×U(5) quiver gauge theory. An intriguing feature of these models is a relation between the gauge representation and the horizontal charge, leading to a restricted set of possible FN charges. Requiring that quark masses are hierarchical, the lepton flavor structure is uniquely determined. In particular, neutrino mass anarchy is predicted.
Lorentz Gauge Theory and Spinor Interaction
NASA Astrophysics Data System (ADS)
Carlevaro, Nakia; Lecian, Orchidea Maria; Montani, Giovanni
A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is briefly discussed. The spinor interaction with the new gauge field is then analyzed assuming the time gauge and stationary solutions, in the non-relativistic limit, are treated to generalize the Pauli equation.
Solving flavor puzzles with quiver gauge theories
Antebi, Yaron E.; Nir, Yosef; Volansky, Tomer
2006-04-01
We consider a large class of models where the SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a U(5)xU(5) quiver gauge theory. An intriguing feature of these models is a relation between the gauge representation and the horizontal charge, leading to a restricted set of possible FN charges. Requiring that quark masses are hierarchical, the lepton flavor structure is uniquely determined. In particular, neutrino mass anarchy is predicted.
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.
Nonperturbative Regulator for Chiral Gauge Theories?
Grabowska, Dorota M; Kaplan, David B
2016-05-27
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. PMID:27284646
Extracting Flavor from Quiver Gauge Theories
NASA Astrophysics Data System (ADS)
Volansky, T.
2007-04-01
We consider a large class of models where an SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a quiver gauge theory. Such quiver models are very restrictive and therefore have strong predictive power. In particular, under mild assumptions neutrino mass anarchy is predicted.
Numerical techniques for lattice gauge theories
Creutz, M.
1981-02-06
The motivation for formulating gauge theories on a lattice is reviewed. Monte Carlo simulation techniques are then discussed for these systems. Finally, the Monte Carlo methods are combined with renormalization group analysis to give strong numerical evidence for confinement of quarks by non-Abelian gauge fields.
A lattice formulation of chiral gauge theories
Bodwin, G.T.
1996-08-01
We present a method for implementing gauge theories of chiral fermions on the lattice. Discussed topics include: the lattice as a UV regulator, a chiral QED model, modification of the fermion determinant, large gauge-field momenta, and a non-perturbative problem.
NASA Astrophysics Data System (ADS)
Shi, Yan-Liang; Shrock, Robert
2015-11-01
We study asymptotically free chiral gauge theories with an SU (N ) gauge group and chiral fermions transforming according to the antisymmetric rank-k tensor representation, Ak≡[k ]N , and the requisite number, nF ¯, of copies of fermions in the conjugate fundamental representation, F ¯ ≡[1] ¯ N , to render the theories anomaly-free. We denote these as AkF ¯ theories. We take N ≥2 k +1 so that nF ¯≥1 . The A2F ¯ theories form an infinite family with N ≥5 , but we show that the A3F ¯ and A4F ¯ theories are only asymptotically free for N in the respective ranges 7 ≤N ≤17 and 9 ≤N ≤11 , and that there are no asymptotically free AkF ¯ theories with k ≥5 . We investigate the types of ultraviolet to infrared evolution for these AkF ¯ theories and find that, depending on k and N , they may lead to a non-Abelian Coulomb phase, or may involve confinement with massless gauge-singlet composite fermions, bilinear fermion condensation with dynamical gauge and global symmetry breaking, or formation of multifermion condensates that preserve the gauge symmetry. We also show that there are no asymptotically free, anomaly-free SU (N ) SkF ¯ chiral gauge theories with k ≥3 , where Sk denotes the rank-k symmetric representation.
Abelian 3-form gauge theory: Superfield approach
NASA Astrophysics Data System (ADS)
Malik, R. P.
2012-09-01
We discuss a D-dimensional Abelian 3-form gauge theory within the framework of Bonora-Tonin's superfield formalism and derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for this theory. To pay our homage to Victor I. Ogievetsky (1928-1996), who was one of the inventors of Abelian 2-form (antisymmetric tensor) gauge field, we go a step further and discuss the above D-dimensional Abelian 3-form gauge theory within the framework of BRST formalism and establish that the existence of the (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form gauge theory (discussed within the framework of BRST formalism).
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.
NASA Astrophysics Data System (ADS)
Cvetič, M.; Gubser, S. S.; Lü, H.; Pope, C. N.
2000-10-01
A class of conformally flat and asymptotically anti-de Sitter geometries involving profiles of scalar fields is studied from the point of view of gauged supergravity. The scalars involved in the solutions parametrize the SL(N,R)/SO(N) submanifold of the full scalar coset of the gauged supergravity, and are described by a symmetric potential with a universal form. These geometries descend via consistent truncation from distributions of D3-branes, M2-branes, or M5-branes in ten or eleven dimensions. We exhibit analogous solutions asymptotic to AdS6 which descend from the D4-D8-brane system. We obtain the related six-dimensional theory by consistent reduction from massive type IIA supergravity. All our geometries correspond to states in the Coulomb branch of the dual conformal field theories. We analyze linear fluctuations of minimally coupled scalars and find both discrete and continuous spectra, but always bounded below.
Cvetic, M.; Gubser, S. S.; Lu'', H.; Pope, C. N.
2000-10-15
A class of conformally flat and asymptotically anti--de Sitter geometries involving profiles of scalar fields is studied from the point of view of gauged supergravity. The scalars involved in the solutions parametrize the SL(N,R)/SO(N) submanifold of the full scalar coset of the gauged supergravity, and are described by a symmetric potential with a universal form. These geometries descend via consistent truncation from distributions of D3-branes, M2-branes, or M5-branes in ten or eleven dimensions. We exhibit analogous solutions asymptotic to AdS{sub 6} which descend from the D4-D8-brane system. We obtain the related six-dimensional theory by consistent reduction from massive type IIA supergravity. All our geometries correspond to states in the Coulomb branch of the dual conformal field theories. We analyze linear fluctuations of minimally coupled scalars and find both discrete and continuous spectra, but always bounded below.
Irregular blocks, N = 2 gauge theory and Mathieu system
NASA Astrophysics Data System (ADS)
Piatek, M. R.; Pietrykowski, A. R.
2016-01-01
The Alday-Gayotto-Tachikawa (AGT) conjecture relates 4d N = 2, SU(2) SYM theories with Nf matter hypermultiplets to 2d CFT. In case of pure 4d N = 2, SU(2) SYM there is a corresponding irregular conformal block in 2d CFT. The AGT correspondence may be extended within a certain limit (the Nekrasov-Shataschvili limit) to the correspondence between an effective twisted superpotentials of 2d N = 2 SUSY and the Zamolodchikov's “classical” conformal blocks. When narrowed to the pure 4d N = 2 SYM case its limit is related to an irregular classical conformal block. It will be shown that according to the triple correspondence (2dCFT/Gauge/Bethe - c.f. Piatek's talk) the irregular classical conformal block yields spectrum of Mathieu operator. The latter can be obtained as a “classical” limit of the null vector decoupling equation for three-point degenerate irregular block. It will also be shown that the Mathieu spectrum can be also obtained from the limit of the pure gauge theory as a solution of the saddle point equation as well as from the Bohr-Sommerfeld quantization of the Seiberg-Witten theory.
BPS index and 4d N = 2 superconformal field theories
NASA Astrophysics Data System (ADS)
Sakai, Kazuhiro
2016-07-01
We study the BPS index for the four-dimensional rank-one N = 2 superconformal field theories H 0 , H 1 , H 2 , E 6 , E 7 , E 8. We consider compactifications of the E-string theory on T 2 in which these theories arise as low energy limits. Using this realization we clarify the general structure of the BPS index. The index is characterized by two exponents and a sequence of invariants. We determine the exponents and the first few invariants.
Gauge gravitation theory: Gravity as a Higgs field
NASA Astrophysics Data System (ADS)
Sardanashvily, Gennadi
2016-05-01
Gravitation theory is formulated as gauge theory on natural bundles with spontaneous symmetry breaking, where gauge symmetries are general covariant transformations, gauge fields are general linear connections, and Higgs fields are pseudo-Riemannian metrics.
Central charge bounds in 4D conformal field theory
Rattazzi, Riccardo; Vichi, Alessandro; Rychkov, Slava
2011-02-15
We derive model-independent lower bounds on the stress tensor central charge C{sub T} in terms of the operator content of a 4-dimensional conformal field theory. More precisely, C{sub T} is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the conformal field theory. The method uses the crossing symmetry constraint of the 4-point function, analyzed by means of the conformal block decomposition.
Unifying Geometrical Representations of Gauge Theory
NASA Astrophysics Data System (ADS)
Alsid, Scott; Serna, Mario
2015-01-01
We unify three approaches within the vast body of gauge-theory research that have independently developed distinct representations of a geometrical surface-like structure underlying the vector-potential. The three approaches that we unify are: those who use the compactified dimensions of Kaluza-Klein theory, those who use Grassmannian models (also called gauge theory embedding or models) to represent gauge fields, and those who use a hidden spatial metric to replace the gauge fields. In this paper we identify a correspondence between the geometrical representations of the three schools. Each school was mostly independently developed, does not compete with other schools, and attempts to isolate the gauge-invariant geometrical surface-like structures that are responsible for the resulting physics. By providing a mapping between geometrical representations, we hope physicists can now isolate representation-dependent physics from gauge-invariant physical results and share results between each school. We provide visual examples of the geometrical relationships between each school for electric and magnetic fields. We highlight a first new result: in all three representations a static electric field (electric field from a fixed ring of charge or a sphere of charge) has a hidden gauge-invariant time dependent surface that is underlying the vector potential.
Scattering processes in lattice gauge theories
NASA Astrophysics Data System (ADS)
Alessandrini, V.; Krzywicki, A.
1980-06-01
Scattering between gauge invariant lattice excitations is studied in the framework of a 2+1 dimensional lattice theory with U(1) gauge symmetry. We put the theory in a form analogous to theories of conventional large quantum systems (spin waves in a solid, for example) and we calculate explicitly the cross section for boxiton scattering. The general strategy we have developed goes beyond the simple example of compact QED. Laboratoire associé au CNRS. Postal address: LPTHE, Bâtiment 211, Université Paris-Sud, 91405 Orsay, France.
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.
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.
Renormalization of gauge theories without cohomology
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2013-07-01
We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem.
A Gauge Theory of Massive Spin One Particles
NASA Astrophysics Data System (ADS)
Vyas, Vivek M.; Srinivasan, V.
2016-05-01
An Abelian gauge theory describing dynamics of massive spin one bosons is constructed. This is achieved by appending to the Maxwell action, a gauge invariant mass term. The theory is quantised in temporal as well as Lorentz gauge, and the corresponding Hilbert spaces are constructed. In both the gauges, it is found that, the theory respects Lorentz invariance, locality, causality and unitarity.
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.
Aspects of entanglement entropy for gauge theories
NASA Astrophysics Data System (ADS)
Soni, Ronak M.; Trivedi, Sandip P.
2016-01-01
A definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of the Hilbert space of states on each link of the lattice. This extended Hilbert space admits a tensor product decomposition by definition and allows a density matrix and entanglement entropy for the set of links of interest to be defined. Here, we continue the study of this extended Hilbert space definition with particular emphasis on the case of Non-Abelian gauge theories.
Jarzynski's theorem for lattice gauge theory
NASA Astrophysics Data System (ADS)
Caselle, Michele; Costagliola, Gianluca; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-08-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a nonequilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski's theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schrödinger functional and for simulations at finite density using reweighting techniques.
Gauge field theory of covariant strings
NASA Astrophysics Data System (ADS)
Kaku, Michio
1986-03-01
We present a gauge covariant second-quantized field theory of strings which is explicitly invariant under the gauge transformations generated by the Virasoro algebra. Unlike the old field theory strings [1] this new formulation is Lorentz covariant as well as gauge covariant under the continuous group Diff( S1) and its central extension. We derive the free action: L=Φ(X) †P[i∂ τ-(L 0-1)]PΦ(X) , in the same way that Feynman derived the Schrödinger equation from the path integral formalism. The action is manifestly invariant under the gauge transformation δΦ(X)= limit∑n=1∞ɛ -nL -nΦ(X) , where P is a projection operator which annihilates spurious states. We give three distinct formulations of this operator P to all orders, the first based on extracting the operator from the functional formulation of the Nambu-Goto action, and the second and third based on inverting the Shapovalov matrix on a Verma module. This gauge covariant formulation can be easily extended to the Green-Schwarz superstring [2,3]. One element application of these methods is to re-express the old Neveu-Schwarz-Ramond model as a field theory which is manifestly invariant under space-time supersymmetric transformations.
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
Wilson loops in supersymmetric gauge theories
NASA Astrophysics Data System (ADS)
Pestun, Vasily
This thesis is devoted to several exact computations in four-dimensional supersymmetric gauge field theories. In the first part of the thesis we prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N = 4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N = 2 and the N* = 2 supersymmetric Yang-Mills theory on a four-sphere. Circular supersymmetric Wilson loops in four-dimensional N = 2 superconformal gauge theory are treated similarly. In the second part we consider supersymmetric Wilson loops of arbitrary shape restricted to a two-dimensional sphere in the four-dimensional N = 4 supersymmetric Yang-Mills theory. We show that expectation value for these Wilson loops can be exactly computed using a two-dimensional theory closely related to the topological two-dimensional Higgs-Yang-Mills theory, or two-dimensional Yang-Mills theory for the complexified gauge group.
New Dualities in Supersymmetric Chiral Gauge Theories
Craig, Nathaniel; Essig, Rouven; Hook, Anson; Torroba, Gonzalo; /Stanford U., Phys. Dept. /SLAC
2011-08-15
We analyze the phase structure of supersymmetric chiral gauge theories with gauge group SU(N), an antisymmetric, and F {le} N + 3 flavors, in the presence of a cubic superpotential. When F = N + 3 the theory flows to a superconformal fixed point in the infrared, and new dual descriptions of this theory are uncovered. The theory with odd N admits a self-dual magnetic description. For general N, we find an infinite family of magnetic dual descriptions, characterized by arbitrarily large gauge groups and additional classical global symmetries that are truncated by nonperturbative effects. The infrared dynamics of these theories are analyzed using a-maximization, which supports the claim that all these theories flow to the same superconformal fixed point. A very rich phase structure is found when the number of flavors is reduced below N + 3, including a new self-dual point, transitions from conformal to confining, and a nonperturbative instability for F {le} N. We also give examples of chiral theories with antisymmetrics that have nonchiral duals.
Supersymmetric instanton calculus (gauge theories with matter)
Vainshtein, A.I.; Zakharov, V.I.; Novikov, V.A.; Shifman, M.A.
1985-12-01
We consider instantons in supersymmetric gauge theories with matter. We show that if the vacuum average of the scalar field is different from zero, the number of collective coordinates necessary for describing the matter superfields associated with an instanton changes. We obtain explicit expressions for these superfields. We introduce the concept of an instanton dimension which is invariant with respect to supertransformations.
Computer techniques for lattice gauge theories
NASA Astrophysics Data System (ADS)
Martin, Olivier; Moriarty, K. J. M.; Samuel, Stuart
1986-06-01
Quenched SU(3) gauge theory is simulated on a CDC CYBER 205. We describe how to deal with large data sets and discuss the performance of the machine for the two main tasks involved: Monte Carlo updating and Gauss-Seidel inversion.
Quantum critical behavior of semisimple gauge theories
NASA Astrophysics Data System (ADS)
Esbensen, Jacob Kamuk; Ryttov, Thomas A.; Sannino, Francesco
2016-02-01
We study the perturbative phase diagram of semisimple fermionic gauge theories resembling the Standard Model. We investigate an S U (N ) gauge theory with M Dirac flavors where we gauge first an S U (M )L and then an S U (2 )L⊂S U (M )L of the original global symmetry S U (M )L×S U (M )R×U (1 ) of the theory. To avoid gauge anomalies we add leptonlike particles. At the two-loop level an intriguing phase diagram appears. We uncover phases in which one, two or three fixed points exist and discuss the associated flows of the coupling constants. We discover a phase featuring complete asymptotic freedom and simultaneously an interacting infrared fixed point in both couplings. The analysis further reveals special renormalization group trajectories along which one coupling displays asymptotic freedom and the other asymptotic safety, while both flowing in the infrared to an interacting fixed point. These are safety free trajectories. We briefly sketch out possible phenomenological implications, among which an independent way to generate near-conformal dynamics à la walking is investigated.
Passing to an effective 4D phantom cosmology from 5D vacuum theory of gravity
NASA Astrophysics Data System (ADS)
Aguilar, José Edgar Madriz; Bellini, Mauricio
2008-02-01
Starting from a five-dimensional (5D) vacuum theory of gravity where the extra coordinate is considered as non-compact, we investigate the possibility of inducing four-dimensional (4D) phantom scenarios by applying form-invariance symmetry transformations. In particular we obtain phantom scenarios for two cosmological frameworks. In the first framework we deal with an induced 4D de Sitter expansion and in the second one a 4D induced model where the expansion of the universe is dominated by a decreasing cosmological parameter Λ(t) is discussed.
Gauge Theory Gravity: Outline and Utility
NASA Astrophysics Data System (ADS)
Francis, Matthew; Kosowsky, Arthur
2003-04-01
Gauge Theory Gravity, as formulated by Lasenby, Doran, and Gull, is a reformulation of gravitation as a gauge theory in Minkowski spacetime. This picture makes gravitation look formally analogous to the other forces of nature. It is locally equivalent to general relativity (the basic field equations are equivalent in form to the Cartan formulation of general relativity), but presents significant conceptual differences and certain calculational advantages. We provide an overview of the theory, its explicit relation to general relativity, and outline a constructive method for generating solutions. As an illustration, we obtain the most general spherically symmetric stationary vaccum solution, which explicitly displays all coordinate freedom and contains as special cases all common forms of the spherically symmetric vacuum metric.
Gravity as the Square of Gauge Theory
NASA Astrophysics Data System (ADS)
Kiermaier, M.
The BCJ squaring relations provide a simple prescription for thecomputation of gravity amplitudes in terms of gauge theory ingredients. Unlike the KLT relations, the squaring relations are directly applicable both at tree and loop level. We review the derivation of these relations from on-shell recursion relations, and discuss an off-shell approach to these relations in which the interactions of the gravity Lagrangian arise as the square of the gauge-theory interactions. This article is based on work with Zvi Bern, Tristan Dennen and Yu-tin Huang [Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Phys. Rev. D textbf{82} (2010), 065003, arXiv:1004.0693 (Ref. 1))] which was presented at String Field Theory and Related Aspects 2010.
Strong dynamics and lattice gauge theory
NASA Astrophysics Data System (ADS)
Schaich, David
In this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new, strongly-interacting force. Strong interactions invalidate the standard analytical approach of perturbation theory, making these models difficult to study. Lattice gauge theory is the premier method for obtaining quantitatively-reliable, nonperturbative predictions from strongly-interacting theories. In this approach, we replace spacetime by a regular, finite grid of discrete sites connected by links. The fields and interactions described by the theory are likewise discretized, and defined on the lattice so that we recover the original theory in continuous spacetime on an infinitely large lattice with sites infinitesimally close together. The finite number of degrees of freedom in the discretized system lets us simulate the lattice theory using high-performance computing. Lattice gauge theory has long been applied to quantum chromodynamics, the theory of strong nuclear interactions. Using lattice gauge theory to study dynamical EWSB, as I do in this dissertation, is a new and exciting application of these methods. Of particular interest is non-perturbative lattice calculation of the electroweak S parameter. Experimentally S ≈ -0.15(10), which tightly constrains dynamical EWSB. On the lattice, I extract S from the momentum-dependence of vector and axial-vector current correlators. I created and applied computer programs to calculate these correlators and analyze them to determine S. I also calculated the masses
Quantum walks and discrete gauge theories
NASA Astrophysics Data System (ADS)
Arnault, Pablo; Debbasch, Fabrice
2016-05-01
A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A family of two-dimensional walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac fermion coupled to arbitrary electromagnetic fields. The electromagnetic interpretation is extended beyond the continuous limit by proving that these discrete-time quantum walks (DTQWs) exhibit an exact discrete local U(1) gauge invariance and possess a discrete gauge-invariant conserved current. A discrete gauge-invariant electromagnetic field is also constructed and that field is coupled to the conserved current by a discrete generalization of Maxwell equations. The dynamics of the DTQWs under crossed electric and magnetic fields is finally explored outside the continuous limit by numerical simulations. Bloch oscillations and the so-called E ×B drift are recovered in the weak-field limit. Localization is observed for some values of the gauge fields.
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.
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.
Strong Coupling Gauge Theories in LHC ERA
NASA Astrophysics Data System (ADS)
Fukaya, H.; Harada, M.; Tanabashi, M.; Yamawaki, K.
2011-01-01
AdS/QCD, light-front holography, and the nonperturbative running coupling / Stanley J. Brodsky, Guy de Teramond and Alexandre Deur -- New results on non-abelian vortices - Further insights into monopole, vortex and confinement / K. Konishi -- Study on exotic hadrons at B-factories / Toru Iijima -- Cold compressed baryonic matter with hidden local symmetry and holography / Mannque Rho -- Aspects of baryons in holographic QCD / T. Sakai -- Nuclear force from string theory / K. Hashimoto -- Integrating out holographic QCD back to hidden local symmetry / Masayasu Harada, Shinya Matsuzaki and Koichi Yamawaki -- Holographic heavy quarks and the giant Polyakov loop / Gianluca Grignani, Joanna Karczmarek and Gordon W. Semenoff -- Effect of vector-axial-vector mixing to dilepton spectrum in hot and/or dense matter / Masayasu Harada and Chihiro Sasaki -- Infrared behavior of ghost and gluon propagators compatible with color confinement in Yang-Mills theory with the Gribov horizon / Kei-Ichi Kondo -- Chiral symmetry breaking on the lattice / Hidenori Fukaya [for JLQCD and TWQCD collaborations] -- Gauge-Higgs unification: Stable Higgs bosons as cold dark matter / Yutaka Hosotani -- The limits of custodial symmetry / R. Sekhar Chivukula ... [et al.] -- Higgs searches at the tevatron / Kazuhiro Yamamoto [for the CDF and D[symbol] collaborations] -- The top triangle moose / R. S. Chivukula ... [et al.] -- Conformal phase transition in QCD like theories and beyond / V. A. Miransky -- Gauge-Higgs unification at LHC / Nobuhito Maru and Nobuchika Okada -- W[symbol]W[symbol] scattering in Higgsless models: Identifying better effective theories / Alexander S. Belyaev ... [et al.] -- Holographic estimate of Muon g - 2 / Deog Ki Hong -- Gauge-Higgs dark matter / T. Yamashita -- Topological and curvature effects in a multi-fermion interaction model / T. Inagaki and M. Hayashi -- A model of soft mass generation / J. Hosek -- TeV physics and conformality / Thomas Appelquist -- Conformal
Anomaly nucleation constrains SU(2) gauge theories.
Halverson, James
2013-12-27
We argue for the existence of additional constraints on SU(2) gauge theories in four dimensions when realized in ultraviolet completions admitting an analog of D-brane nucleation. In type II string compactifications these constraints are necessary and sufficient for the absence of cubic non-Abelian anomalies in certain nucleated SU(N>2) theories. It is argued that they appear quite broadly in the string landscape. Implications for particle physics are discussed; most realizations of the standard model in this context are inconsistent, unless extra electroweak fermions are added. PMID:24483790
Spinning black holes in a gauge theory of gravitation
NASA Astrophysics Data System (ADS)
BabeÅ£i (Pretorian), Simona
2013-11-01
Spinning black holes are presented in terms of gauge fields in a commutative gauge theory of gravitation. The field strength tensor comes as a consequence of the particular ansatz for gauge fields. In order to obtain spinning black holes in a noncommutative gauge theory of gravitation is used an analytical procedure conceived in GRTensorII. To calculate the leading noncommutative corrections and to choose an appropriate noncommutative parameter are used recursive relations. The gauge fields and the field strength tensor for a spinning mass preserves some features of other cosmological solutions in the gauge theory of gravitation and the noncommutative corrections are expected to provide some important physical insights.
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. PMID:25215973
A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua
NASA Astrophysics Data System (ADS)
Taylor, Washington; Wang, Yi-Nan
2016-01-01
We use Monte Carlo methods to explore the set of toric threefold bases that support elliptic Calabi-Yau fourfolds for F-theory compactifications to four dimensions, and study the distribution of geometrically non-Higgsable gauge groups, matter, and quiver structure. We estimate the number of distinct threefold bases in the connected set studied to be ˜ 1048. The distribution of bases peaks around h 1,1 ˜ 82. All bases encountered after "thermalization" have some geometric non-Higgsable structure. We find that the number of non-Higgsable gauge group factors grows roughly linearly in h 1,1 of the threefold base. Typical bases have ˜ 6 isolated gauge factors as well as several larger connected clusters of gauge factors with jointly charged matter. Approximately 76% of the bases sampled contain connected two-factor gauge group products of the form SU(3) × SU(2), which may act as the non-Abelian part of the standard model gauge group. SU(3) × SU(2) is the third most common connected two-factor product group, following SU(2) × SU(2) and G 2 × SU(2), which arise more frequently.
Monte Carlo methods in lattice gauge theories
Otto, S.W.
1983-01-01
The mass of the O/sup +/ glueball for SU(2) gauge theory in 4 dimensions is calculated. This computation was done on a prototype parallel processor and the implementation of gauge theories on this system is described in detail. Using an action of the purely Wilson form (tract of plaquette in the fundamental representation), results with high statistics are obtained. These results are not consistent with scaling according to the continuum renormalization group. Using actions containing higher representations of the group, a search is made for one which is closer to the continuum limit. The choice is based upon the phase structure of these extended theories and also upon the Migdal-Kadanoff approximation to the renormalizaiton group on the lattice. The mass of the O/sup +/ glueball for this improved action is obtained and the mass divided by the square root of the string tension is a constant as the lattice spacing is varied. The other topic studied is the inclusion of dynamical fermions into Monte Carlo calculations via the pseudo fermion technique. Monte Carlo results obtained with this method are compared with those from an exact algorithm based on Gauss-Seidel inversion. First applied were the methods to the Schwinger model and SU(3) theory.
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.
Perturbative gauge theory at null infinity
NASA Astrophysics Data System (ADS)
Adamo, Tim; Casali, Eduardo
2015-06-01
We describe a theory living on the null conformal boundary I of four-dimensional Minkowski space, the states of which include the radiative modes of Yang-Mills theory. The action of a Kac-Moody symmetry algebra on the correlators of these states leads to a Ward identity for asymptotic "large" gauge transformations which is equivalent to the soft gluon theorem. The subleading soft gluon behavior is also obtained from a Ward identity for charges acting as vector fields on the sphere of null generators of I . Correlation functions of the Yang-Mills states are shown to produce the full classical S-matrix of Yang-Mills theory. The model contains additional states arising from nonunitary gravitational degrees of freedom, indicating a relationship with the twistor string of Berkovits and Witten.
Lattice gauge theories and Monte Carlo algorithms
Creutz, M.
1988-10-01
Lattice gauge theory has become the primary tool for non-perturbative calculations in quantum field theory. These lectures review some of the foundations of this subject. The first lecture reviews the basic definition of the theory in terms of invariant integrals over group elements on lattice bonds. The lattice represents an ultraviolet cutoff, and renormalization group arguments show how the bare coupling must be varied to obtain the continuum limit. Expansions in the inverse of the coupling constant demonstrate quark confinement in the strong coupling limit. The second lecture turns to numerical simulation, which has become an important approach to calculating hadronic properties. Here I discuss the basic algorithms for obtaining appropriately weighted gauge field configurations. The third lecture turns to algorithms for treating fermionic fields, which still require considerably more computer time than needed for purely bosonic simulations. Some particularly promising recent approaches are based on global accept-reject steps and should display a rather favorable dependence of computer time on the system volume. 34 refs.
Continuum regularization of gauge theory with fermions
Chan, H.S.
1987-03-01
The continuum regularization program is discussed in the case of d-dimensional gauge theory coupled to fermions in an arbitrary representation. Two physically equivalent formulations are given. First, a Grassmann formulation is presented, which is based on the two-noise Langevin equations of Sakita, Ishikawa and Alfaro and Gavela. Second, a non-Grassmann formulation is obtained by regularized integration of the matter fields within the regularized Grassmann system. Explicit perturbation expansions are studied in both formulations, and considerable simplification is found in the integrated non-Grassmann formalism.
NASA Astrophysics Data System (ADS)
Bergshoeff, Eric A.; Fernández-Melgarejo, J. J.; Rosseel, Jan; Townsend, Paul K.
2012-04-01
We construct a four-dimensional (4D) gauge theory that propagates, unitarily, the five polarization modes of a massive spin-2 particle. These modes are described by a "dual" graviton gauge potential and the Lagrangian is 4th-order in derivatives. As the construction mimics that of 3D "new massive gravity", we call this 4D model (linearized) "new massive dual gravity". We analyse its massless limit, and discuss similarities to the Eddington-Schrödinger model.
Black hole attractors and gauge theories
NASA Astrophysics Data System (ADS)
Huang, Lisa Li Fang
2007-12-01
This thesis is devoted to the study of supersymmetric black holes that arise from string compactifications. We begin by studying the R 2 corrections to the entropy of two solutions of five dimensional supergravity, the supersymmetric black ring and the spinning black hole. Using Wald's formula we compute the R2 corrections to the entropy of the black ring and BMPV black hole. We study N D4-branes wrapping a 4 cycle and M DO-branes on the quintic. For N D4-branes, we resolve the naive mismatch between the moduli space of the Higgs branch of the gauge theory and the moduli of a degree N hypersurface which the D4-brane wraps. The degree N surface must admit a holomorphic divisor and is a determinantal variety. Adding a single DO brane to probe the deformed geometry, we recover the determinant equation from F and D flatness condition which was previously discovered from a classical geometry approach. We next generalize the qunitic story for Calabi-Yau manifolds arising from complete intersections in toric varieties. We recover the moduli space of N D4-branes in terms of the moduli space of a U( N) x U(N) gauge theory with bi-fundamentals com ing from a D6 - D6 system. We also recast the tachyon condensation of the D6 - D6 system in the language of open string gauged linear sigma model. We obtain the determinant equation from F-term constraints arising from a boundary coupling. We set out to understand the Ooguri-Strominger-Vafa conjecture directly in the D4-DO black hole attractor geometry. We show that the lift to the euclidean IIA attractor geometry gives a complexified M-theory geometry whose asymptotic boundary is a torus. Employing AdS3/CFT 2 duality, we argue that the string partition function computes the elliptic genus of the Maldacena-Strominger-Witten conformal field theory. We evaluate the IIA partition function using the Green-Schwarz formalism and show that it gives ZtopZ top, coming from instantons and anti-instantons respectively. Finally, we determine
Probing the ground state in gauge theories
Heinzl, T.; Ilderton, A.; Langfeld, K.; Lavelle, M.; McMullan, D.; Lutz, W.
2008-03-01
We consider two very different models of the flux tube linking two heavy quarks: a string linking the matter fields and a Coulombic description of two separately gauge invariant charges. We compare how close they are to the unknown true ground state in compact U(1) and the SU(2) Higgs model. Simulations in compact U(1) show that the string description is better in the confined phase but the Coulombic description is best in the deconfined phase; the last result is shown to agree with analytical calculations. Surprisingly in the nonabelian theory the Coulombic description is better in both the Higgs and confined phases. This indicates a significant difference in the width of the flux tubes in the two theories.
The Origins of Lattice Gauge Theory
Wilson, Kenneth
2004-06-23
The main focus of this talk is an anecdotal account of the history underlying my 1974 article entitled 'Confinement of Quarks.' In preparing this talk, I will draw on a historical interview conducted by the project for History of Recent Science and Technology at the Dibner Institute for the History of Science and Technology at MIT, and on a theory of invention proposed by Peter Drucker in his book 'Innovation and Entrepreneurship.' I will explain this theory; no background is needed. The account will start with related work in the 1960's. I will end the talk with a plea for lattice gauge researchers to be alert for unexpected scalar or vector colored particles that are invisible to experimentalists yet could start to spoil the agreement of computations with experiment. Note: In association with the Symposium ' 'Lattice 2004,' June 21 to June 26, 2004.
CP nonconservation in dynamically broken gauge theories
Lane, K.
1981-01-01
The recent proposal of Eichten, Lane, and Preskill for CP nonconservation in electroweak gauge theories with dynamical symmetry breaking is reviewed. Through the alignment of the vacuum with the explicit chiral symmetry breaking Hamiltonian, these theories provide a natural way to understand the dynamical origin of CP nonconservation. Special attention is paid to the problem of strong CP violation. Even through all vacuum angles are zero, this problem is not automatically avoided. In the absence of strong CP violation, the neutron electric dipole moment is expected to be 10/sup -24/-10/sup -26/ e-cm. A new class of models is proposed in which both strong CP violation and large /..delta..S/ = 2 effects may be avoided. In these models, /..delta..C/ = 2 processes such as D/sup o/ D/sup -o/ mixing may be large enough to observe.
Towards gauge theories in four dimensions
NASA Astrophysics Data System (ADS)
Hernández-Pinto, Roger J.; Sborlini, Germán F. R.; Rodrigo, Germán
2016-02-01
The abundance of infrared singularities in gauge theories due to unresolved emission of massless particles (soft and collinear) represents the main difficulty in perturbative calculations. They are typically regularized in dimensional regularization, and their subtraction is usually achieved independently for virtual and real corrections. In this paper, we introduce a new method based on the loop-tree duality (LTD) theorem to accomplish the summation over degenerate infrared states directly at the integrand level such that the cancellation of the infrared divergences is achieved simultaneously, and apply it to reference examples as a proof of concept. Ultraviolet divergences, which are the consequence of the point-like nature of the theory, are also reinterpreted physically in this framework. The proposed method opens the intriguing possibility of carrying out purely four-dimensional implementations of higher-order perturbative calculations at next-to-leading order (NLO) and beyond free of soft and final-state collinear subtractions.
a Note on the - Invariant Lagrangian Densities for the Free Abelian 2-FORM Gauge Theory
NASA Astrophysics Data System (ADS)
Gupta, Saurabh; Malik, R. P.
We show that the previously known off-shell nilpotent (s(a)b2 = 0) and absolutely anticommuting (sb sab + sab sb = 0) Becchi-Rouet-Stora-Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3+1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci-Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler-Lagrange equations of motion of our present theory and ensures the absolute anticommutativity of the transformations s(a)b. Thus, the coupled Lagrangian densities, proposed in our present investigation, are aesthetically more appealing and more economical.
Coupled Cluster Methods in Lattice Gauge Theory
NASA Astrophysics Data System (ADS)
Watson, Nicholas Jay
Available from UMI in association with The British Library. Requires signed TDF. The many body coupled cluster method is applied to Hamiltonian pure lattice gauge theories. The vacuum wavefunction is written as the exponential of a single sum over the lattice of clusters of gauge invariant operators at fixed relative orientation and separation, generating excitations of the bare vacuum. The basic approximation scheme involves a truncation according to geometrical size on the lattice of the clusters in the wavefunction. For a wavefunction including clusters up to a given size, all larger clusters generated in the Schrodinger equation are discarded. The general formalism is first given, including that for excited states. Two possible procedures for discarding clusters are considered. The first involves discarding clusters describing excitations of the bare vacuum which are larger than those in the given wavefunction. The second involves rearranging the clusters so that they describe fluctuations of the gauge invariant excitations about their self-consistently calculated expectation values, and then discarding fluctuations larger then those in the given wavefunction. The coupled cluster method is applied to the Z_2 and Su(2) models in 2 + 1D. For the Z_2 model, the first procedure gives poor results, while the second gives wavefunctions which explicitly display a phase transition with critical couplings in good agreement with those obtained by other methods. For the SU(2) model, the first procedure also gives poor results, while the second gives vacuum wavefunctions valid at all couplings. The general properties of the wavefunctions at weak coupling are discussed. Approximations with clusters spanning up to four plaquettes are considered. Excited states are calculated, yielding mass gaps with fair scaling properties. Insight is obtained into the form of the wavefunctions at all couplings.
S-folds and 4d mathcal{N} = 3 superconformal field theories
NASA Astrophysics Data System (ADS)
Aharony, Ofer; Tachikawa, Yuji
2016-06-01
S-folds are generalizations of orientifolds in type IIB string theory, such that the geometric identifications are accompanied by non-trivial S-duality transformations. They were recently used by García-Etxebarria and Regalado to provide the first construction of four dimensional mathcal{N} =3 superconformal theories. In this note, we classify the different variants of these mathcal{N} =3-preserving S-folds, distinguished by an analog of discrete torsion, using both a direct analysis of the different torsion classes and the compactification of the S-folds to three dimensional M-theory backgrounds. Upon adding D3-branes, these variants lead to different classes of mathcal{N} =3 superconformal field theories. We also analyze the holographic duals of these theories, and in particular clarify the role of discrete gauge and global symmetries in holography.
The Higgs sector of gravitational gauge theories
Leclerc, M. . E-mail: mleclerc@phys.uoa.gr
2006-03-15
Gravitational gauge theories with de Sitter, Poincare and affine symmetry group are investigated under the aspect of the breakdown of the initial symmetry group down to the Lorentz subgroup. As opposed to the nonlinear realization approach, in the dynamical symmetry breaking procedure, the structure subgroup is not chosen arbitrarily, but is dictated by the symmetry of the groundstate of a Higgs field. We review the theory of spontaneously broken de Sitter gravity by Stelle and West and apply a similar approach to the case of the Poincare and affine groups. We will find that the Poincare case is almost trivial. The translational Higgs field reveals itself as pure gauge, i.e., it is expressed entirely in terms of the Nambu-Goldstone bosons and does not appear in the Lagrangian after the symmetry breaking. The same holds for the translational part of the affine group. The Higgs field provoking the breakdown of the general linear group leads to the determination of the Lorentzian signature of the metric in the groundstate. We show that the Higgs field remains in its groundstate, i.e., that the metric will have Lorentzian signature, unless we introduce matter fields that explicitely couple to the symmetric part of the connection. Furthermore, we present arguments that the Lorentzian signature is actually the only possible choice for physical spacetime, since the symmetry breaking mechanism works only if the stability subgroup is taken to be the Lorentz group. The other four-dimensional rotation groups are therefore ruled out not only on physical, but also on theoretical grounds. Finally, we show that some features, like the necessity of the introduction of a dilaton field, that seem artificial in the context of the affine theory, appear most natural if the gauge group is taken to be the special linear group in five dimensions. We also present an alternative model which is based on the spinor representation of the Lorentz group and is especially adopted to the
GAUGE INVARIANCE IN A Z2 HAMILTONIAN LATTICE GUAGE THEORY.
SUGIHARA, T.
2005-07-25
We propose an efficient variational method for Z{sub 2} lattice gauge theory based on the matrix product ansatz. The method is applied to ladder and square lattices. The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. On the ladder lattice, we identify gauge invariant low-lying states by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian. On the square lattice, the second order phase transition is well reproduced.
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.
A gauge field theory of fermionic continuous-spin particles
NASA Astrophysics Data System (ADS)
Bekaert, X.; Najafizadeh, M.; Setare, M. R.
2016-09-01
In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang-Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.
Conformal field theory dual of the RS model with gauge fields in the bulk
NASA Astrophysics Data System (ADS)
Agashe, K.; Delgado, A.
2003-02-01
It has been conjectured that the (weakly coupled) Randall-Sundrum (RS) model with gauge fields in the bulk is dual to a (strongly coupled) 4D conformal field theory (CFT) with an UV cutoff and in which global symmetries of the CFT are gauged. We elucidate features of this dual CFT which are crucial for a complete understanding of the proposed duality. We argue that the limit of no (or small) brane-localized kinetic term for bulk gauge field on the RS side (often studied in the literature) is dual to no bare kinetic term for the gauge field which is coupled to the CFT global current. In this limit, the kinetic term for this gauge field in the dual CFT is “induced” by CFT loops. Then, this CFT loop contribution to the gauge field 1PI two-point function is dual (on the RS side) to the full gauge propagator (i.e., including the contribution of Kaluza-Klein and zero modes) with both external points on the Planck brane. We also emphasize that loop corrections to the gauge coupling on the RS side are dual to subleading effects in a large-N expansion on the CFT side; these subleading corrections to the gauge coupling in the dual CFT are (in general) sensitive to the strong dynamics of the CFT.
Nonquadratic gauge fixing and ghosts for gauge theories on the hypersphere
NASA Astrophysics Data System (ADS)
Brandt, F. T.; McKeon, D. G. C.
2011-10-01
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.
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.
Hydrodynamic gradient expansion in gauge theory plasmas.
Heller, Michal P; Janik, Romuald A; Witaszczyk, Przemysław
2013-05-24
We utilize the fluid-gravity duality to investigate the large order behavior of hydrodynamic gradient expansion of the dynamics of a gauge theory plasma system. This corresponds to the inclusion of dissipative terms and transport coefficients of very high order. Using the dual gravity description, we calculate numerically the form of the stress tensor for a boost-invariant flow in a hydrodynamic expansion up to terms with 240 derivatives. We observe a factorial growth of gradient contributions at large orders, which indicates a zero radius of convergence of the hydrodynamic series. Furthermore, we identify the leading singularity in the Borel transform of the hydrodynamic energy density with the lowest nonhydrodynamic excitation corresponding to a 'nonhydrodynamic' quasinormal mode on the gravity side. PMID:23745858
The renormalon diagram in gauge theories on
NASA Astrophysics Data System (ADS)
Anber, Mohamed M.; Sulejmanpasic, Tin
2015-01-01
We analyze the renormalon diagram of gauge theories on . In particular, we perform exact one loop calculations for the vacuum polarization in QCD with adjoint matter and observe that all infrared logarithms, as functions of the external momentum, cancel between the vacuum part and finite volume part, which eliminates the IR renormalon problem. We argue that the singularities in the Borel plane, arising from the topological neutral bions, are not associated with the renormalon diagram, but with the proliferation of the Feynman diagrams. As a byproduct, we obtain, for the first time, an exact one-loop result of the vacuum polarization which can be adapted to the case of thermal compactification of QCD.
NASA Astrophysics Data System (ADS)
Rauhala, U. A.
2013-12-01
Array algebra of photogrammetry and geodesy unified multi-linear matrix and tensor operators in an expansion of Gaussian adjustment calculus to general matrix inverses and solutions of inverse problems to find all, or some optimal, parametric solutions that satisfy the available observables. By-products in expanding array and tensor calculus to handle redundant observables resulted in general theories of estimation in mathematical statistics and fast transform technology of signal processing. Their applications in gravity modeling and system automation of multi-ray digital image and terrain matching evolved into fast multi-nonlinear differential and integral array calculus. Work since 1980's also uncovered closed-form inverse Taylor and least squares Newton-Raphson-Gauss perturbation solutions of nonlinear systems of equations. Fast nonlinear integral matching of array wavelets enabled an expansion of the bundle adjustment to 4-D stereo imaging and range sensing where real-time stereo sequence and waveform phase matching enabled data-to-info conversion and compression on-board advanced sensors. The resulting unified array calculus of spacetime sensing is applicable in virtually any math and engineering science, including recent work in spacetime physics. The paper focuses on geometric spacetime reconstruction from its image projections inspired by unified relativity and string theories. The collinear imaging equations of active object space shutter of special relativity are expanded to 4-D Lorentz transform. However, regular passive imaging and shutter inside the sensor expands the law of special relativity by a quantum geometric explanation of 4-D photogrammetry. The collinear imaging equations provide common sense explanations to the 10 (and 26) dimensional hyperspace concepts of a purely geometric string theory. The 11-D geometric M-theory is interpreted as a bundle adjustment of spacetime images using 2-D or 5-D membrane observables of image, string and
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 discrete gauge symmetries in F-theory
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Pugh, Tom G.; Regalado, Diego
2016-02-01
The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the expectations for the kinetic mixing of seven-branes and is unchanged if the gaugings are absent.
Gauge Invariance and Gauge-Factor Group in Causal Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Emmenegger, N.
2001-11-01
In the present work the gauge invariance of causal Yang-Mills theory will be proven with the aid of the gauge-factor group. For that purpose it must be shown, that the operator valued distributions T_n and D_n(ret) occurring in the causal S-matrix construction can be written, after applying the gauge variation d_Q, as a divergence. Since merely local terms lead to gauge destroying expressions, one has to focus on them exclusively. In the first part of the work the local gauge-factor group will be defined in the style of the concept of gauge cohomology theory. It will be shown, that every element out of the so defined factor group under the transformation d_Q leads to a divergence of the entire operator valued distribution d_Q(T_n). In the second part all local terms arising in causal Yang-Mills theory are systematically investigated. Without further restrictions there can be proven, that every local operator valued distribution is an element of the gauge factor group or equal to zero. This concludes the demonstration of gauge invariance of causal Yang-Mills theory.
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.
Chern-Simons gauge theory: Ten years after
Labastida, J. M. F.
1999-07-13
A brief review on the progress made in the study of Chern-Simons gauge theory since its relation to knot theory was discovered ten years ago is presented. Emphasis is made on the analysis of the perturbative study of the theory and its connection to the theory of Vassiliev invariants. It is described how the study of the quantum field theory for three different gauge fixings leads to three different representations for Vassiliev invariants. Two of these gauge fixings lead to well known representations: the covariant Landau gauge corresponds to the configuration space integrals while the non-covariant light-cone gauge to the Kontsevich integral. The progress made in the analysis of the third gauge fixing, the non-covariant temporal gauge, is described in detail. In this case one obtains combinatorial expressions, instead of integral ones, for Vassiliev invariants. The approach based on this last gauge fixing seems very promising to obtain a full combinatorial formula. We collect the combinatorial expressions for all the Vassiliev invariants up to order four which have been obtained in this approach.
Quantization of higher abelian gauge theory in generalized differential cohomology
NASA Astrophysics Data System (ADS)
Szabo, R.
We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger-Simons cohomology, and of Ramond-Ramond fields in Type II superstring theory and differential K-theory.
SDiff gauge theory and the M2 condensate
NASA Astrophysics Data System (ADS)
Bandos, Igor A.; Townsend, Paul K.
2009-02-01
We develop a general formalism for the construction, in D-dimensional Minkowski space, of gauge theories for which the gauge group is the infinite-dimensional group SDiffn of volume-preserving diffeomorphisms of some closed n-dimensional manifold. We then focus on the D = 3 SDiff3 superconformal gauge theory describing a condensate of M2-branes; in particular, we derive its Script N = 8 superfield equations from a pure-spinor superspace action, and we describe its relationship to the D = 3 SDiff2 super-Yang-Mills theory describing a condensate of D2-branes.
Ward-Takahashi identities for Abelian chiral gauge theories
NASA Astrophysics Data System (ADS)
de Lima, Ana Paula Cardoso Rodrigues; Dias, Sebastião Alves
2016-04-01
By considering a general Abelian chiral gauge theory, we investigate the behavior of anomalous Ward-Takahashi (WT) identities concerning their prediction for the usual relationship between the vertex and two-point fermion functions. Using gauge anomaly vanishing results, we show that the usual (in the nonanomalous case) WT identity connecting the vertex and two-point fermion 1PI functions is modified for Abelian chiral gauge theories. The modification, however, implies a relation between fermion and charge renormalization constants that can be important in a future study of renormalization of such theories.
Evidence for a Family of SO(8) Gauged Supergravity Theories
NASA Astrophysics Data System (ADS)
Dall'Agata, G.; Inverso, G.; Trigiante, M.
2012-11-01
In this note we discuss the classification of duality orbits of N=8 gauged supergravity models. Using tensor classifiers, we show that there is a one-parameter family of inequivalent SO(8) gauged supergravity theories. We briefly discuss the couplings of such models and show that, although the maximally symmetric vacuum has the same quadratic spectrum, the supersymmetry transformations, the couplings, and the scalar potential are parameter dependent. We also comment on the possible M theory uplift and on the meaning of the parameter for the dual gauge theories.
Topics in Noncommutative Gauge Theories and Deformed Relativistic Theories
NASA Astrophysics Data System (ADS)
Chandra, Nitin
2013-01-01
This is my PhD thesis. In this thesis we study the gauge theories on noncommutative Moyal space. We find new static solitons and instantons in terms of the so called generalized Bose operators. Generalized Bose operators are constructed to describe reducible representation of the oscillator algebra. They create/annihilate k-quanta, k being a positive integer. We start with giving an alternative description to the already found static magnetic flux tube solutions of the noncommutative gauge theories in terms of generalized Bose operators. The Nielsen-Olesen vortex solutions found in terms of these operators reduce to the already found ones. On the contrary we find a class of new instaton solutions which are unitarily inequivalant to the the ones found from ADHM construction on noncommutative space. The charge of the instaton has a description in terms of the index representing the reducibility of the Fock space, i.e., k. After studying the static solitonic solutions in noncommutative Minkowski space and the instaton solutions in noncommutative Euclidean space we go on to study the implications of the time-space noncommutativity in Minkowski space. To understand it properly we study the time-dependent transitions of a forced harmonic oscillator in noncommutative 1+1 dimensional spacetime. We also try to understand the implications of the found results in the context of quantum optics. We then shift to the so called DSR theories which are related to a different kind of noncommutative (kappa-Minkowski) space. DSR (Doubly/Deformed Special Relativity) aims to search for an alternate relativistic theory which keeps a length/energy scale (the Planck scale) and a velocity scale (the speed of light scale) invariant. We study thermodynamics of an ideal gas in such a scenario.
Investigation of gauge-fixed pure U(1) theory at strong coupling
NASA Astrophysics Data System (ADS)
Basak, S.; De, Asit K.
2002-03-01
We numerically investigate the phase diagram of pure U(1) gauge theory with gauge fixing at strong gauge coupling. The FM-FMD phase transition, which proved useful in defining Abelian lattice chiral gauge theory, persists also at strong gauge coupling. However, there the transition seems no longer to be continuous. At large gauge couplings we find evidences for confinement.
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.
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
Phase diagram of 4D field theories with chiral anomaly from holography
NASA Astrophysics Data System (ADS)
Ammon, Martin; Leiber, Julian; Macedo, Rodrigo P.
2016-03-01
Within gauge/gravity duality, we study the class of four dimensional CFTs with chiral anomaly described by Einstein-Maxwell-Chern-Simons theory in five dimensions. In particular we determine the phase diagram at finite temperature, chemical potential and magnetic field. At high temperatures the solution is given by an electrically and magnetically charged AdS Reissner-Nordstroem black brane. For sufficiently large Chern-Simons coupling and at sufficiently low temperatures and small magnetic fields, we find a new phase with helical order, breaking translational invariance spontaneously. For the Chern-Simons couplings studied, the phase transition is second order with mean field exponents. Since the entropy density vanishes in the limit of zero temperature we are confident that this is the true ground state which is the holographic version of a chiral magnetic spiral.
Two-color gauge theory with novel infrared behavior.
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
2014-03-21
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. PMID:24702347
Non-Abelian gauge field theory in scale relativity
NASA Astrophysics Data System (ADS)
Nottale, Laurent; Célérier, Marie-Noëlle; Lehner, Thierry
2006-03-01
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.
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.
U([infinity]) gauge theory from higher dimensions
Shiraishi, K. )
1992-09-30
In this paper, the authors show that classical U[infinity] gauge theories can be obtained from the dimensional reduction of a certain class of higher-derivative theories. In general, the exact symmetry is attained in the limit of degenerate metric; otherwise, the infinite-dimensional symmetry can be taken as spontaneously broken. Monopole solutions are examined in the model for scalar and gauge fields. An extension to gravity is also discussed.
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.}
NASA Astrophysics Data System (ADS)
Nakamura, K.
2007-01-01
Following the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. 110 (2003), 723; ibid. 113 (2005), 481], we formulate second-order gauge invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe. We consider perturbations both in the universe dominated by a single perfect fluid and in that dominated by a single scalar field. We derive all the components of the Einstein equations in the case that the first-order vector and tensor modes are negligible. All equations are derived in terms of gauge invariant variables without any gauge fixing. These equations imply that second-order vector and tensor modes may be generated due to the mode-mode coupling of the linear-order scalar perturbations. We also briefly discuss the main progress of this work through comparison with previous works.
Gauge theory of Virasoro-Kac-Moody group
NASA Astrophysics Data System (ADS)
Cho, Y. M.; Zoh, S. W.
1992-10-01
We present a prototype gauge theory of the Virasoro-Kac-Moody symmetry associated with an arbitrary grand unified group G, which could be interpreted as an effective field theory of a colored string. The theory automatically breaks the symmetry down to H⊗U(1), where H is a subgroup of G and U(1) is the Cartan subgroup of the Virasoro group. After the inevitable spontaneous symmetry breaking the particle spectrum of the theory consists of an infinite tower of massive spin-one fields, the massless gauge fields of the unbroken subgroup, and the light scalar fields which become the pseudo-Goldstone fields of the symmetry breaking
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.
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).
The M-theory origin of global properties of gauge theories
NASA Astrophysics Data System (ADS)
Amariti, Antonio; Klare, Claudius; Orlando, Domenico; Reffert, Susanne
2015-12-01
We show that global properties of gauge groups can be understood as geometric properties in M-theory. Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with AN-1 gauge algebra and different unitary groups. The classical properties of the wrappings determine the global properties of the gauge theories without the need to impose any quantum conditions. We count the inequivalent wrappings as they fall into orbits of the modular group of the torus, which correspond to the S-duality orbits of the gauge theories.
Dynamics of N = 2 Supersymmetric Gauge Theories in Three Dimensions
de Boer, J.; Hori, K.; Oz, Y.
1997-03-21
We study the structure of the moduli spaces of vacua and superpotentials of N = 2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N = 2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U(N{sub c}) and SU(N{sub c}) with N{sub f} flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.
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.
Ward identities and renormalization of general gauge theories
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2004-02-01
We introduce the concept of general gauge theory which includes Yang-Mills models. We use the framework of the causal approach and show that the anomalies can appear only in the vacuum sector of the identities obtained from the gauge invariance condition by applying derivatives with respect to the basic fields. For the Yang-Mills model we provide these identities in the lowest orders of the perturbation theory and prove that they are valid. The investigation of higher orders of the perturbation theory is still an open problem.
Thermodynamics of quasiconformal theories from gauge/gravity duality
Alanen, Janne; Kajantie, Keijo; Tuominen, Kimmo
2010-09-01
We use gauge/gravity duality to study the thermodynamics of a generic almost conformal theory, specified by its beta function. Three different phases are identified, a high temperature phase of massless partons, an intermediate quasiconformal phase and a low temperature confining phase. The limit of a theory with infrared fixed point, in which the coupling does not run to infinity, is also studied. The transitions between the phases are of first order or continuous, depending on the parameters of the beta function. The results presented follow from gauge/gravity duality; no specific boundary theory is assumed, only its beta function.
Gauging nonrelativistic field theories using the coset construction
NASA Astrophysics Data System (ADS)
Karananas, Georgios K.; Monin, Alexander
2016-03-01
We discuss how nonrelativistic spacetime symmetries can be gauged in the context of the coset construction. We consider theories invariant under the centrally extended Galilei algebra as well as the Lifshitz one, and we investigate under what conditions they can be supplemented by scale transformations. We also clarify the role of torsion in these theories.
Variational Study of SU(3) Gauge Theory by Stationary Variance
NASA Astrophysics Data System (ADS)
Siringo, Fabio
2015-07-01
The principle of stationary variance is advocated as a viable variational approach to gauge theories. The method can be regarded as a second-order extension of the Gaussian Effective Potential (GEP) and seems to be suited for describing the strong-coupling limit of non-Abelian gauge theories. The single variational parameter of the GEP is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the solution of a set of coupled integral equations. The stationary conditions can be easily derived by the self-energy, without having to write the effective potential, making use of a general relation between self-energy and functional derivatives that has been proven to any order. The low- energy limit of pure Yang-Mills SU(3) gauge theory has been studied in Feynman gauge, and the stationary equations are written as integral equations for the gluon and ghost propagators. A physically sensible solution is found for any strength of the coupling. The gluon propagator is finite in the infrared, with a dynamical mass that decreases as a power at high energies. At variance with some recent findings in Feynman gauge, the ghost dressing function does not vanish in the infrared limit and a decoupling scenario emerges as recently reported for the Landau gauge.
Higher derivatives and brane-localised kinetic terms in gauge theories on orbifolds
NASA Astrophysics Data System (ADS)
Ghilencea, Dumitru M.; Lee, Hyun Min; Schmidt-Hoberg, Kai
2006-08-01
We perform a detailed analysis of one-loop corrections to the self-energy of the (off-shell) gauge bosons in six-dimensional Script N = 1 supersymmetric gauge theories on orbifolds. After discussing the Abelian case in the standard Feynman diagram approach, we extend the analysis to the non-Abelian case by employing the method of an orbifold-compatible one-loop effective action for a classical background gauge field. We find that bulk higher derivative and brane-localised gauge kinetic terms are required to cancel one-loop divergences of the gauge boson self energy. After their renormalisation we study the momentum dependence of both the higher derivative coupling h(k2) and the effective gauge coupling geff(k2). For momenta smaller than the compactification scales, we obtain the 4D logarithmic running of geff(k2), with suppressed power-like corrections, while the higher derivative coupling is constant. We present in detail the threshold corrections to the low energy gauge coupling, due to the massive bulk modes. At momentum scales above the compactification scales, the higher derivative operator becomes important and leads to a power-like running of geff(k2) with respect to the momentum scale. The coefficient of this running is at all scales equal to the renormalised coupling of the higher derivative operator which ensures the quantum consistency of the model. We discuss the relation to the similar one-loop correction in the heterotic string, to show that the higher derivative operators are relevant in that case too, since the field theory limit of the one-loop string correction does not commute with the infrared regularisation of the (on-shell) string result.
Cosmologies with null singularities and their gauge theory duals
Das, Sumit R.; Michelson, Jeremy; Narayan, K.; Trivedi, Sandip P.
2007-01-15
We investigate backgrounds of Type IIB string theory with null singularities and their duals proposed in S. R. Das, J. Michelson, K. Narayan, S. P. Trivedi, hep-th/0602107. The dual theory is a deformed N=4 Yang-Mills theory in 3+1 dimensions with couplings dependent on a lightlike direction. We concentrate on backgrounds which become AdS{sub 5}xS{sup 5} at early and late times and where the string coupling is bounded, vanishing at the singularity. Our main conclusion is that in these cases the dual gauge theory is nonsingular. We show this by arguing that there exists a complete set of gauge invariant observables in the dual gauge theory whose correlation functions are nonsingular at all times. The two-point correlator for some operators calculated in the gauge theory does not agree with the result from the bulk supergravity solution. However, the bulk calculation is invalid near the singularity where corrections to the supergravity approximation become important. We also obtain pp-waves which are suitable Penrose limits of this general class of solutions, and construct the matrix membrane theory which describes these pp-wave backgrounds.
Monte Carlo simulations of lattice gauge theories
Rebbi, C
1980-02-01
Monte Carlo simulations done for four-dimensional lattice gauge systems are described, where the gauge group is one of the following: U(1); SU(2); Z/sub N/, i.e., the subgroup of U(1) consisting of the elements e 2..pi..in/N with integer n and N; the eight-element group of quaternions, Q; the 24- and 48-element subgroups of SU(2), denoted by T and O, which reduce to the rotation groups of the tetrahedron and the octahedron when their centers Z/sub 2/, are factored out. All of these groups can be considered subgroups of SU(2) and a common normalization was used for the action. The following types of Monte Carlo experiments are considered: simulations of a thermal cycle, where the temperature of the system is varied slightly every few Monte Carlo iterations and the internal energy is measured; mixed-phase runs, where several Monte Carlo iterations are done at a few temperatures near a phase transition starting with a lattice which is half ordered and half disordered; measurements of averages of Wilson factors for loops of different shape. 5 figures, 1 table. (RWR)
Dualities between semiclassical strings and quantum gauge field theories
NASA Astrophysics Data System (ADS)
Ouyang, Peter
In this thesis we study several examples of the correspondence between gauge field theories and string theories. A recurrent theme of these studies is that distinctively quantum mechanical behavior on the gauge theory side of the correspondence can have a classical or semiclassical description in terms of string calculations, as one might expect from general considerations of open/closed duality. We begin in Chapter 1 by reviewing the simplest duality, which relates Type IIB supergravity in AdS5 x S5 to N = 4 SU(N) gauge theory at large N. Working with this background spacetirne, we turn to a study of D-brane probes with large quantum numbers in Chapter 2. We employ semiclassical methods to compute the excitation spectrum of these D-branes, including corrections of order 1/N, which are related to loop effects in the dual field theory. In Chapter 3 we discuss the gauge/gravity duals with N = 1 supersymmetry which arise from placing D-branes at a conifold singularity. The inclusion of fractional D3-branes breaks conformal invariance, leading to a rich variety of phenomena in the gauge theory, among them chiral anomalies, a cascade of Seiberg dualities and confinement in the infrared. We pay particular attention to the chiral anomalies of the gauge theory and show that they can be described in terms of classical spontaneous symmetry breaking in the dual string theory. In accord with low-energy confinement in the field theory, almost all of the moduli of the supergravity solution are fixed; we conclude Chapter 3 with some observations on the possibility of stabilizing the volume of the compact space in which the conifold is embedded. Finally, in Chapter 4 we study versions of the conifold theory with D7-branes, which introduce fundamental matter into the gauge theory. By solving the classical supergravity equations of motion we identify a variant of the Klebanov-Strassler duality cascade where the rate of the cascade decreases as the theory flows to low energies.
Conformal gauge-Yukawa theories away from four dimensions
NASA Astrophysics Data System (ADS)
Codello, Alessandro; Langæble, Kasper; Litim, Daniel F.; Sannino, Francesco
2016-07-01
We present the phase diagram and associated fixed points for a wide class of Gauge-Yukawa theories in d = 4 + ɛ dimensions. The theories we investigate involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten limit. The analysis is performed in steps, we start with QCD d and then we add Yukawa interactions and scalars which we study at next-to- and next-to-next-to-leading order. Interacting infrared fixed points naturally emerge in dimensions lower than four while ultraviolet ones appear above four. We also analyse the stability of the scalar potential for the discovered fixed points. We argue for a very rich phase diagram in three dimensions while in dimensions higher than four certain Gauge-Yukawa theories are ultraviolet complete because of the emergence of an asymptotically safe fixed point.
Towards a gauge theory interpretation of the real topological string
NASA Astrophysics Data System (ADS)
Hayashi, Hirotaka; Piazzalunga, Nicolò; Uranga, Angel M.
2016-03-01
We consider the real topological string on certain noncompact toric Calabi-Yau three-folds X , in its physical realization describing an orientifold of type IIA on X with an O4-plane and a single D4-brane stuck on top. The orientifold can be regarded as a new kind of surface operator on the gauge theory with 8 supercharges arising from the singular geometry. We use the M-theory lift of this system to compute the real Gopakumar-Vafa invariants (describing wrapped M2-brane Bogomol'nyi-Prasad-Sommerfield (BPS) states) for diverse geometries. We show that the real topological string amplitudes pick up certain signs across flop transitions, in a well-defined pattern consistent with continuity of the real BPS invariants. We further give some preliminary proposals of an intrinsically gauge theoretical description of the effect of the surface operator in the gauge theory partition function.
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.
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.
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.
Conformally flat black holes in Poincaré gauge theory
NASA Astrophysics Data System (ADS)
Blagojević, M.; Cvetković, B.
2016-02-01
General criteria for the existence of conformally flat Riemannian solutions in three-dimensional Poincaré gauge theory without matter are formulated. Using these criteria, we show that the Oliva-Tempo-Troncoso black hole, a solution of the Bergshoeff-Hohm-Townsend gravity, is also an exact vacuum solution of the Poincaré gauge theory. The related conserved charges, calculated from the Hamiltonian boundary term, are shown to satisfy the first law of black hole thermodynamics. The form of the boundary term is verified by using the covariant Hamiltonian approach.
Gauges and functional measures in quantum gravity I: Einstein theory
NASA Astrophysics Data System (ADS)
Ohta, N.; Percacci, R.; Pereira, A. D.
2016-06-01
We perform a general computation of the off-shell one-loop divergences in Einstein gravity, in a two-parameter family of path integral measures, corresponding to different ways of parametrizing the graviton field, and a two-parameter family of gauges. Trying to reduce the gauge- and measure-dependence selects certain classes of measures and gauges respectively. There is a choice of two parameters (corresponding to the exponential parametrization and the partial gauge condition that the quantum field be traceless) that automatically eliminates the dependence on the remaining two parameters and on the cosmological constant. We observe that the divergences are invariant under a Z 2 "duality" transformation that (in a particularly important special case) involves the replacement of the densitized metric by a densitized inverse metric as the fundamental quantum variable. This singles out a formulation of unimodular gravity as the unique "self-dual" theory in this class.
Massive gravity as a quantum gauge theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Scharf, G.
2005-06-01
We present a new point of view on the quantization of the massive gravitational field, namely we use exclusively the quantum framework of the second quantization. The Hilbert space of the many-gravitons system is a Fock space F+ (Hgraviton) where the one-particle Hilbert space Hgraviton carries the direct sum of two unitary irreducible representations of the Poincaré group corresponding to two particles of mass m > 0 and spins 2 and 0, respectively. This Hilbert space is canonically isomorphic to a space of the type Ker(Q)/Im(Q) where Q is a gauge charge defined in an extension of the Hilbert space Hgraviton generated by the gravitational field hμν and some ghosts fields uμ, ũμ (which are vector Fermi fields) and vμ (which is a vector Bose field).
Quantum equivalence of noncommutative and Yang-Mills gauge theories in 2D and matrix theory
Ydri, Badis
2007-05-15
We construct noncommutative U(1) gauge theory on the fuzzy sphere S{sub N}{sup 2} as a unitary 2Nx2N matrix model. In the quantum theory the model is equivalent to a non-Abelian U(N) Yang-Mills theory on a two-dimensional lattice with two plaquettes. This equivalence holds in the 'fuzzy sphere' phase where we observe a 3rd order phase transition between weak-coupling and strong-coupling phases of the gauge theory. In the matrix phase we have a U(N) gauge theory on a single point.
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.
Gauge transformation of double field theory for open string
NASA Astrophysics Data System (ADS)
Ma, Chen-Te
2015-09-01
We combine symmetry structures of ordinary (parallel directions) and dual (transversal directions) coordinates to construct the Dirac-Born-Infeld theory. The ordinary coordinates are associated with the Neumann boundary conditions and the dual coordinates are associated with the Dirichlet boundary conditions. Gauge fields become scalar fields by exchanging the ordinary and dual coordinates. A gauge transformation of a generalized metric is governed by the generalized Lie derivative. The gauge transformation of the massless closed string theory gives the C -bracket, but the gauge transformation of the open string theory gives the F -bracket. The F -bracket with the strong constraints is different from the Courant bracket by an exact one-form. This exact one-form should come from the one-form gauge field. Based on a symmetry point of view, we deduce a suitable action with a nonzero H -flux at the low-energy level. From an equation of motion of the scalar dilaton, it defines a generalized scalar curvature. Finally, we construct a double sigma model with a boundary term and show that this model with constraints is classically equivalent to the ordinary sigma model.
Noncommutative gauge theory and symmetry breaking in matrix models
Grosse, Harald; Steinacker, Harold; Lizzi, Fedele
2010-04-15
We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than four dimensions, an SU(n) gauge theory on a Moyal-Weyl space arises with all matter and fields in the adjoint of the gauge group. We show how this gauge symmetry can be broken spontaneously down to SU(3){sub c}xSU(2){sub L}xU(1){sub Q}[resp. SU(3){sub c}xU(1){sub Q}], which couples appropriately to all fields in the standard model. An additional U(1){sub B} gauge group arises which is anomalous at low energies, while the trace-U(1) sector is understood in terms of emergent gravity. A number of additional fields arise, which we assume to be massive, in a pattern that is reminiscent of supersymmetry. The symmetry breaking might arise via spontaneously generated fuzzy spheres, in which case the mechanism is similar to brane constructions in string theory.
Regularized path integrals and anomalies: U(1) chiral gauge theory
NASA Astrophysics Data System (ADS)
Kopper, Christoph; Lévêque, Benjamin
2012-02-01
We analyze the origin of the Adler-Bell-Jackiw anomaly of chiral U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge symmetry. It is known how (nonanomalous) gauge symmetry can be recovered in the renormalized theory in this case [Kopper, C. and Müller, V. F., "Renormalization of spontaneously broken SU(2) Yang-Mills theory with flow equations," Rev. Math. Phys. 21, 781 (2009)], 10.1142/S0129055X0900375X. Here we analyze U(1) chiral gauge theory to show how the appearance of anomalies manifests itself in such a context. We show that the three-photon amplitude leads to a violation of the Slavnov-Taylor identities which cannot be restored on taking the UV limit in the renormalized theory. We point out that this fact is related to the nonanalyticity of this amplitude in the infrared region.
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.
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.
Gauge theory of disclinations on fluctuating elastic surfaces
NASA Astrophysics Data System (ADS)
Kochetov, E. A.; Osipov, V. A.
1999-03-01
A variant of a gauge theory is formulated to describe disclinations on Riemannian surfaces that may change both the Gaussian (intrinsic) and mean (extrinsic) curvatures, which implies that both internal strains and a location of the surface in 0305-4470/32/10/013/img1 may vary. Moreover, originally distributed disclinations are taken into account. For the flat surface, an extended variant of the Edelen-Kadic gauge theory is obtained. Within the linear scheme our model recovers the von Karman equations for membranes, with a disclination-induced source being generated by gauge fields. For a single disclination on an arbitrary elastic surface a covariant generalization of the von Karman equations is derived.
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.
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.
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.
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.
Exponentiation of eikonal cross sections in nonabelian gauge theories
NASA Astrophysics Data System (ADS)
Gatheral, J. G. M.
1983-12-01
A theorem is presented which generalises the well-known exponentiation property of eikonal cross sections in abelian gauge theories to the nonabelian case. Address after September 1, 1983: Bank of America, 25 Cannon Street, London EC4P 4HN, UK.
Finite-Temperature Gauge Theory from the Transverse Lattice
Dalley, S.; Sande, B. van de
2005-10-14
Numerical computations are performed and analytic bounds are obtained on the excited spectrum of glueballs in SU({infinity}) gauge theory, by transverse lattice Hamiltonian methods. We find an exponential growth of the density of states, implying a finite critical (Hagedorn) temperature. It is argued that the Nambu-Goto string model lies in a different universality class.
Nonlocal Hamiltonian gauge theories and their connection with lattice Hamiltonians
Ktorides, C.N.; Mavromatos, N.E.
1985-06-15
We introduce the concept of primitive Hamiltonian density for nonlocal Abelian gauge theories. We subsequently study the local limit both with respect to the continuum and with respect to a lattice structure introduced via hypercubic cells. The non-Abelian case is also discussed.
Spatial Dependence of Condensates in Strongly Coupled Gauge Theories
Brodsky, Stanley J.; Shrock, Robert; /SUNY, Stony Brook
2008-03-25
We analyze quark and gluon condensates in quantum chromodynamics. We suggest that these are localized inside hadrons, because the particles whose interactions are responsible for them are confined within these hadrons. This can explain the results of recent studies of gluon condensate contributions to vacuum correlators. We also give a general discussion of condensates in asymptotically free vectorial and chiral gauge theories.
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.
Weighted power counting and Lorentz violating gauge theories. II: Classification
Anselmi, Damiano
2009-05-15
We classify the local, polynomial, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. We study the structure of such theories and prove that renormalization does not generate higher time derivatives. We work out the conditions to renormalize vertices that are usually non-renormalizable, such as the two scalar-two fermion interactions and the four fermion interactions. A number of four-dimensional examples are presented.
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.
On a gauge covariant formulation of string field theories
NASA Astrophysics Data System (ADS)
Ju-Fei, Tang; Chuan-Jie, Zhu
1986-11-01
It is shown that the Neveu-Nicolai-West formulation of the gauge covariant string field theories and that of Banks and Peskin can be obtained by different consistent truncation of the BRST multiplets. A proof is given to show the equivalence of light-cone formulation and the gauge covariant formulation without using the property of trivial cohomology of string differential forms. We would like to thank D.D. Wu and X.J. Zhou for discussion and Yi-Bing Ding for careful reading of the manuscript.
Sasakian quiver gauge theories and instantons on the conifold
NASA Astrophysics Data System (ADS)
Geipel, Jakob C.; Lechtenfeld, Olaf; Popov, Alexander D.; Szabo, Richard J.
2016-06-01
We consider Spin (4)-equivariant dimensional reduction of Yang-Mills theory on manifolds of the form Md ×T 1 , 1, where Md is a smooth manifold and T 1 , 1 is a five-dimensional Sasaki-Einstein manifold Spin (4) / U (1). We obtain new quiver gauge theories on Md extending those induced via reduction over the leaf spaces CP1 × CP1 in T 1 , 1. We describe the Higgs branches of these quiver gauge theories as moduli spaces of Spin (4)-equivariant instantons on the conifold which is realized as the metric cone over T 1 , 1. We give an explicit construction of these moduli spaces as Kähler quotients.
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.
Grand unified string theories with SU(3) gauge family symmetry
NASA Astrophysics Data System (ADS)
Maslikov, A. A.; Sergeev, S. M.; Volkov, G. G.
1994-06-01
In the framework of four dimensional heterotic superstring with free fermions we investigate the rank eight Grand Unified String Theories (GUST) which contain the SU(3) H-gauge family symmetry. We explicitly construct GUSTs with gauge symmetry G = SU(5) × U(1) × ( SU(3) × U(1)) H ⊂ SO(16) ⊂ E(8) in free complex fermion formulation. We solve the problem of the GUST symmetry breaking taking for the observable gauge symmetry the diagonal subgroup Gsym of rank 16 group G × G ⊂ SO(16) × SO(16) ⊂ E(8) × E(8). In this approach the observed electromagnetic charge Qem can be viewed as a sum of two Q1- and Q2-charges of each G-group. In this case the model spectrum does not contain particles with exotic fractional charges.
Vortex dynamics in superfluids governed by an interacting gauge theory
NASA Astrophysics Data System (ADS)
Butera, Salvatore; Valiente, Manuel; Öhberg, Patrik
2016-08-01
We study the dynamics of a vortex in a quasi two-dimensional Bose gas consisting of light-matter coupled atoms forming two-component pseudo spins. The gas is subject to a density dependent gauge potential, hence governed by an interacting gauge theory, which stems from a collisionally induced detuning between the incident laser frequency and the atomic energy levels. This provides a back-action between the synthetic gauge potential and the matter field. A Lagrangian approach is used to derive an expression for the force acting on a vortex in such a gas. We discuss the similarities between this force and the one predicted by Iordanskii, Lifshitz and Pitaevskii when scattering between a superfluid vortex and the thermal component is taken into account.
Microscopic quantum superpotential in Script N = 1 gauge theories
NASA Astrophysics Data System (ADS)
Ferrari, Frank
2007-10-01
We consider the Script N = 1 super Yang-Mills theory with gauge group U(N), adjoint chiral multiplet X and tree-level superpotential Tr W(X). We compute the quantum effective superpotential Wmic as a function of arbitrary off-shell boundary conditions at infinity for the scalar field X. This effective superpotential has a remarkable property: its critical points are in one-to-one correspondence with the full set of quantum vacua of the theory, providing in particular a unified picture of solutions with different ranks for the low energy gauge group. In this sense, Wmic is a good microscopic effective quantum superpotential for the theory. This property is not shared by other quantum effective superpotentials commonly used in the literature, like in the strong coupling approach or the glueball superpotentials. The result of this paper is a first step in extending Nekrasov's microscopic derivation of the Seiberg-Witten solution of Script N = 2 super Yang-Mills theories to the realm of Script N = 1 gauge theories.
Lattice Gauge Theory for Nuclear Physics
Konstantinos Orginos
2012-12-01
Quantum Chromodynamcs (QCD) is now established as the theory of strong interactions. A plethora of hadronic physics phenomena can be explained and described by QCD. From the early days of QCD, it was clear that low energy phenomena require a non-perturbative approach. Lattice QCD is a non-perturbative formulation of QCD that is particularly suited for numerical calculations. Today, supercomputers have achieved performance cabable of performing calculations that allow us to understand complex phenomana that arise from QCD. In this talk I will review the most recent results, relevant to nuclear physics. In particular, I will focus on results relevant to the structure and interactions of hadrons. Finally, I will comment on the opportunities opening up as we approach the era of exaflop computing.
Brane webs in the presence of an O5--plane and 4 d class S theories of type D
NASA Astrophysics Data System (ADS)
Zafrir, Gabi
2016-07-01
In this article we conjecture a relationship between 5 d SCFT's, that can be engineered by 5-brane webs in the presence of an O5--plane, and 4 d class S theories of type D. The specific relation is that compactification on a circle of the former leads to the latter. We present evidence for this conjecture. One piece of evidence, which is also an interesting application of this, is that it suggests identifications between different class S theories. This can in turn be tested by comparing their central charges.
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.
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.
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
Flavor Gauge Theory, and Masses of Top and Neutrino
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 by a new (Higgsless) flavor gauge theory (FGT). We investigate this possibility by studying the renormalization group equations for the Yukawa couplings of SM with two Higgs doublets for various mt and υU/υD. With appropriate flavor democratic boundary conditions at ΛFGT, we derive the bounds on masses of top and tau-neutrino, which are compatible with experimental bounds.
Gauge-invariant cosmological perturbation theory with seeds
Durrer, R. )
1990-10-15
Gauge-invariant cosmological perturbation theory is extended to handle perturbations induced by seeds. A calculation of the Sachs-Wolfe effect is presented. A second-order differential equation for the growth of density perturbations is derived and the perturbation of Liouville's equation for collisionless particles is also given. The results are illustrated by a simple analytic example of a single texture knot, where we calculate the induced perturbations of the energy of microwave photons, of baryonic matter, and of collisionless particles.
Gauge approach to gravitation and regular Big Bang theory
NASA Astrophysics Data System (ADS)
Minkevich, A. V.
2006-03-01
Field theoretical scheme of regular Big Bang in 4-dimensional physical space-time, built in the framework of gauge approach to gravitation, is discussed. Regular bouncing character of homogeneous isotropic cosmological models is ensured by gravitational repulsion effect at extreme conditions without quantum gravitational corrections. The most general properties of regular inflationary cosmological models are examined. Developing theory is valid, if energy density of gravitating matter is positive and energy dominance condition is fulfilled.
Enhanced gauge symmetry and winding modes in double field theory
NASA Astrophysics Data System (ADS)
Aldazabal, G.; Graña, M.; Iguri, S.; Mayo, M.; Nuñez, C.; Rosabal, J. A.
2016-03-01
We provide an explicit example of how the string winding modes can be incorporated in double field theory. Our guiding case is the closed bosonic string compactified on a circle of radius close to the self-dual point, where some modes with non-zero winding or discrete momentum number become massless and enhance the U(1) × U(1) symmetry to SU(2) × SU(2). We compute three-point string scattering amplitudes of massless and slightly massive states, and extract the corresponding effective low energy gauge field theory. The enhanced gauge symmetry at the self-dual point and the Higgs-like mechanism arising when changing the compactification radius are examined in detail. The extra massless fields associated to the enhancement are incorporated into a generalized frame with Oleft(d+3,d+3right)/Oleft(d+3right)× Oleft(d+3right) structure, where d is the number of non-compact dimensions. We devise a consistent double field theory action that reproduces the low energy string effective action with enhanced gauge symmetry. The construction requires a truly non-geometric frame which explicitly depends on both the compact coordinate along the circle and its dual.
Role of division algebra in seven-dimensional gauge theory
NASA Astrophysics Data System (ADS)
Kalauni, Pushpa; Barata, J. C. A.
2015-03-01
The algebra of octonions 𝕆 forms the largest normed division algebra over the real numbers ℝ, complex numbers ℂ and quaternions ℍ. The usual three-dimensional vector product is given by quaternions, while octonions produce seven-dimensional vector product. Thus, octonionic algebra is closely related to the seven-dimensional algebra, therefore one can extend generalization of rotations in three dimensions to seven dimensions using octonions. An explicit algebraic description of octonions has been given to describe rotational transformation in seven-dimensional space. We have also constructed a gauge theory based on non-associative algebra to discuss Yang-Mills theory and field equation in seven-dimensional space.
Gauge theory, topological strings, and S-duality
NASA Astrophysics Data System (ADS)
Kapustin, Anton
2004-09-01
We offer a derivation of the duality between the topological U(1) gauge theory on a Calabi-Yau 3-fold and the topological A-model on the same manifold. This duality was conjectured recently by Iqbal, Nekrasov, Okounkov, and Vafa. We deduce it from the S-duality of the IIB superstring. We also argue that the mirror version of this duality relates the topological B-model on a Calabi-Yau 3-fold and a topological sector of the Type IIA Little String Theory on the same manifold.
[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...
Local gauge transformation for the quark propagator in an SU(N) gauge theory
NASA Astrophysics Data System (ADS)
Aslam, M. Jamil; Bashir, A.; Gutiérrez-Guerrero, L. X.
2016-04-01
In an S U (N ) gauge field theory, the n -point Green functions, namely, propagators and vertices, transform under the simultaneous local gauge variations of the gluon vector potential and the quark matter field in such a manner that the physical observables remain invariant. In this article, we derive this intrinsically nonperturbative transformation law for the quark propagator within the system of covariant gauges. We carry out its explicit perturbative expansion up to O (gs6) and, for some terms, up to O (gs8) . We study the implications of this transformation for the quark-antiquark condensate, multiplicative renormalizability of the massless quark propagator, as well as its relation with the quark-gluon vertex at the one-loop order. Setting the color factors CF=1 and CA=0 , Landau-Khalatnikov-Fradkin transformation for the Abelian case of quantum electrodynamics is trivially recovered. We also test whether the usually employed proposals for the truncations of Schwinger-Dyson equations are consistent with what the Landau-Khalatnikov-Fradkin transformations entail for the massless quark propagator.
D-branes, gauge/string duality and noncommutative theories
NASA Astrophysics Data System (ADS)
Mateos, Toni
2004-09-01
In this thesis we elaborate on the three subjects of the title. We first show that supertubes exist and still preserve some supersymmetry in a large variety of curved backgrounds. Within the AdS/CFT correspondence we study the supersymmetry of rotating strings with 3 angular momenta, and we consider the possibility of adding matter in a stable but non-supersymmetric way. We contribute to the extension of the duality to more realistic YM theories by constructing the sugra dual of an N=2 pure SYM in 3d, given in terms of a Calabi-Yau four-fold in M-theory. We study the unitarity of noncommutative nonrelativistic field theories, we construct the sugra dual of noncommutative pure SYM theories with N=1 in 4d and N=2 in 3d, and we study holographically properties like UV/IR mixing, confinement, chiral symmetry breaking and moduli spaces.
On Chern-Simons theory with an inhomogeneous gauge group and BF theory knot invariants
Naot, Gad
2005-12-15
We study the Chern-Simons topological quantum field theory with an inhomogeneous gauge group, a non-semi-simple group obtained from a semisimple one by taking its semidirect product with its Lie algebra. We find that the standard knot observable (i.e., trace of the holonomy along the knot) essentially vanishes, and yet, the non-semi-simplicity of the gauge group allows us to consider a class of unorthodox observables which breaks gauge invariance at one point and leads to a nontrivial theory on long knots in R{sup 3}. We have two main morals. (1) In the non-semi-simple case there is more to observe in Chern-Simons theory. There might be other interesting non-semi-simple gauge groups to study in this context beyond our example. (2) In the case of an inhomogeneous gauge group, we find that Chern-Simons theory with the unorthodox observable is actually the same as three-dimensional BF theory with the Cattaneo-Cotta-Ramusino-Martellini knot observable. This leads to a simplification of their results and enables us to generalize and solve a problem they posed regarding the relation between BF theory and the Alexander-Conway polynomial. We prove that the most general knot invariant coming from pure BF topological quantum field theory is in the algebra generated by the coefficients of the Alexander-Conway polynomial.
A combinatorial approach to diffeomorphism invariant quantum gauge theories
Zapata, J.A.
1997-11-01
Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical states are gauge and diffeomorphism invariant distributions on the space of functions of the holonomies of the edges of a certain family of graphs. Then a family of graphs embedded in the space manifold (satisfying certain properties) induces a representation of the algebra of physical observables. We construct a quantum model from the set of piecewise linear graphs on a piecewise linear manifold, and another manifestly combinatorial model from graphs defined on a sequence of increasingly refined simplicial complexes. Even though the two models are different at the kinematical level, they provide unitarily equivalent representations of the algebra of physical observables in {ital separable} Hilbert spaces of physical states (their s-knot basis is countable). Hence, the combinatorial framework is compatible with the usual interpretation of quantum field theory. {copyright} {ital 1997 American Institute of Physics.}
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.
2014-01-01
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
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.
Simulation of non-Abelian gauge theories with optical lattices.
Tagliacozzo, L; Celi, A; Orland, P; Mitchell, M W; Lewenstein, M
2013-01-01
Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may provide such tools. Here we show how to engineer quantum simulators of non-Abelian lattice gauge theories. The systems we consider have several applications: they can be used to mimic quark confinement or to study dimer and valence-bond states (which may be relevant for high-temperature superconductors). PMID:24162080
Simulation of non-Abelian gauge theories with optical lattices
NASA Astrophysics Data System (ADS)
Tagliacozzo, L.; Celi, A.; Orland, P.; Mitchell, M. W.; Lewenstein, M.
2013-10-01
Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may provide such tools. Here we show how to engineer quantum simulators of non-Abelian lattice gauge theories. The systems we consider have several applications: they can be used to mimic quark confinement or to study dimer and valence-bond states (which may be relevant for high-temperature superconductors).
New fuzzy extra dimensions from S U (N ) gauge theories
NASA Astrophysics Data System (ADS)
KürkçüoÇ§lu, Seçkin
2015-07-01
We start with an S U (N ) Yang-Mills theory on a manifold M , suitably coupled to scalar fields in the adjoint representation of S U (N ) , which are forming a doublet and a triplet, respectively, under a global S U (2 ) symmetry. We show that a direct sum of fuzzy spheres SF2 Int≔SF2(ℓ)⊕SF2(ℓ)⊕SF2(ℓ+1/2 )⊕SF2(ℓ-1/2 ) emerges as the vacuum solution after the spontaneous breaking of the gauge symmetry and paves the way for us to interpret the spontaneously broken model as a U (n ) gauge theory over M ×SF2 Int . Focusing on a U (2 ) gauge theory, we present complete parametrizations of the S U (2 )-equivariant, scalar, spinor and vector fields characterizing the effective low energy features of this model. Next, we direct our attention to the monopole bundles SF2 ±≔SF2(ℓ)⊕SF2(ℓ±1/2 ) over SF2(ℓ) with winding numbers ±1 , which naturally come forth through certain projections of SF2 Int , and give the parametrizations of the S U (2 )-equivariant fields of the U (2 ) gauge theory over M ×SF2 ± as a projected subset of those of the parent model. Referring to our earlier work [1], we explain the essential features of the low energy effective action that ensues from this model after dimensional reduction. Replacing the doublet with a k -component multiplet of the global S U (2 ), we provide a detailed study of vacuum solutions that appear as direct sums of fuzzy spheres as a consequence of the spontaneous breaking of S U (N ) gauge symmetry in these models and obtain a class of winding number ±(k -1 )∈Z monopole bundles SF2 ,±(k -1 ) over SF2(ℓ) as certain projections of these vacuum solutions and briefly discuss their equivariant field content. We make the observation that SF2 Int is indeed the bosonic part of the N =2 fuzzy supersphere with O S P (2 ,2 ) supersymmetry and construct the generators of the o s p (2 ,2 ) Lie superalgebra in two of its irreducible representations using the matrix content of the vacuum solution SF2 Int
Pauli-Villars Regularization of Non-Abelian Gauge Theories
NASA Astrophysics Data System (ADS)
Hiller, J. R.
2016-04-01
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.
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.
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.
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.
Simple U (1 ) gauge theory explanation of the diphoton excess
NASA Astrophysics Data System (ADS)
Chang, Spencer
2016-03-01
The recent ATLAS and CMS diphoton resonance excesses are explored in a simple U (1 ) gauge theory extension of the Standard Model where the resonance is the Higgs boson of the U (1 ) symmetry breaking, ϕ . This particle couples to exotic quarks which, through loops, can produce a large enough rate to explain the excess. Due to the choice of U (1 ) charges, flavor constraints are naturally suppressed, allowing arbitrary flavor violation in the decays of the new quarks to up-type quarks, modifying their signal topologies. An additional heavy quark in the model decays to the lighter exotic quark by emitting either ϕ or the U (1 ) gauge boson Ax, giving extra signals containing diphoton and digluon resonances. Finally, the new Higgs can decay into γ Ax and Z Ax, followed by Ax decaying into Standard Model fermions through kinetic mixing. Thus, this model gives interesting modified signals to the general class of exotic quark models explaining the diphoton resonance.
Search for a Minimal N =1 Superconformal Field Theory in 4D
NASA Astrophysics Data System (ADS)
Xie, Dan; Yonekura, Kazuya
2016-07-01
We discuss a candidate for a minimal interacting four-dimensional N =1 superconformal field theory. The model contains a chiral primary operator u satisfying the chiral ring relation u2=0 , and its scaling dimension is Δ (u )=1.5 . The model is derived by turning on a N =1 preserving deformation of N =2 A2 Argyres-Douglas theory. The central charges are given by (a ,c )=(263 /768 ,271 /768 )≃(0.342 ,0.353 ) . There is no moduli space of vacua, no flavor symmetry, and the chiral ring is finite.
Classical irregular block, = 2 pure gauge theory and Mathieu equation
NASA Astrophysics Data System (ADS)
Piątek, Marcin; Pietrykowski, Artur R.
2014-12-01
Combining the semiclassical/Nekrasov-Shatashvili limit of the AGT conjecture and the Bethe/gauge correspondence results in a triple correspondence which identifies classical conformal blocks with twisted superpotentials and then with Yang-Yang functions. In this paper the triple correspondence is studied in the simplest, yet not completely understood case of pure SU(2) super-Yang-Mills gauge theory. A missing element of that correspondence is identified with the classical irregular block. Explicit tests provide a convincing evidence that such a function exists. In particular, it has been shown that the classical irregular block can be recovered from classical blocks on the torus and sphere in suitably defined decoupling limits of classical external conformal weights. These limits are "classical analogues" of known decoupling limits for corresponding quantum blocks. An exact correspondence between the classical irregular block and the SU(2) gauge theory twisted superpotential has been obtained as a result of another consistency check. The latter determines the spectrum of the 2-particle periodic Toda (sin-Gordon) Hamiltonian in accord with the Bethe/gauge correspondence. An analogue of this statement is found entirely within 2 d CFT. Namely, considering the classical limit of the null vector decoupling equation for the degenerate irregular block a celebrated Mathieu's equation is obtained with an eigenvalue determined by the classical irregular block. As it has been checked this result reproduces a well known weak coupling expansion of Mathieu's eigenvalue. Finally, yet another new formulae for Mathieu's eigenvalue relating the latter to a solution of certain Bethe-like equation are found.
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.
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. PMID:19519096
Classical probes of string/gauge theory duality
NASA Astrophysics Data System (ADS)
Ishizeki, Riei
The AdS/CFT correspondence has played an important role in the recent development of string theory. The reason is that it proposes a description of certain gauge theories in terms of string theory. It is such that simple string theory computations give information about the strong coupling regime of the gauge theory. Vice versa, gauge theory computations give information about string theory and quantum gravity. Although much is known about AdS/CFT, the precise map between the two sides of the correspondence is not completely understood. In the unraveling of such map classical string solutions play a vital role. In this thesis, several classical string solutions are proposed to help understand the AdS/CFT duality. First, rigidly rotating strings on a two-sphere are studied. Taking special limits of such solutions leads to two cases: the already known giant magnon solution, and a new solution which we call the single spike solution. Next, we compute the scattering phase shift of the single spike solutions and compare the result with the giant magnon solutions. Intriguingly, the results are the same up to non-logarithmic terms, indicating that the single spike solution should have the same rich spin chain structure as the giant magnon solution. Afterward, we consider open string solutions ending on the boundary of AdS5. The lines traced by the ends of such open strings can be viewed as Wilson loops in N = 4 SYM theory. After applying an inversion transformation, the open Wilson loops become closed Wilson loops whose expectation value is consistent with previously conjectured results. Next, several Wilson loops for N = 4 SYM in an AdS5 pp-wave background are considered and translated to the pure AdS 5 background and their interpretation as forward quark-gluon scattering is suggested. In the last part of this thesis, a class of classical solutions for closed strings moving in AdS3 x S 1 ⊂ AdS5 x S5 with energy E and spin S in AdS3 and angular momentum J and winding m
Monopole Condensation and Confining Phase of N=1 Gauge Theories Via M Theory Fivebrane
de Boer, Jan; Oz, Yaron
1997-08-07
The fivebrane of M theory is used in order to study the moduli space of vacua of confining phase N=1 supersymmetric gauge theories in four dimensions. The supersymmetric vacua correspond to the condensation of massless monopoles and confinement of photons. The monopole and meson vacuum expectation values are computed using the fivebrane configuration. The comparison of the fivebrane computation and the field theory analysis shows that at vacua with a classically enhanced gauge group SU(r) the effective superpotential obtained by the"integrating in" method is exact for r=2 but is not exact for r> 2. The fivebrane configuration corresponding to N=1 gauge theories with Landau-Ginzburg type superpotentials is studied. N=1 non-trivial fixed points are analyzed using the brane geometry.
Naturalness and ultraviolet structure of gauge theories with massive fermions
NASA Astrophysics Data System (ADS)
Gellas, G. C.; Karanikas, A. I.; Ktorides, C. N.
1997-04-01
According to the principle of naturalness a small, with respect to the cutoff, mass parameter entering a quantum field system is natural only when it is compatible with some symmetry in the limit where it vanishes. In this paper, advantage is taken of the liberty afforded by the renormalization procedure in order to harmonize the cutoff with the physical mass in a non-Abelian gauge field theory with spin-1/2 matter fields. The ultraviolet structure of the theory, from such a vantage point, is explored at the level of the full fermionic propagator, as well as the vertex function, using the world line approach. An interplay between this ultraviolet structure and the infrared behavior of the same system, but from the customary viewpoint ``cutoff much greater than mass,'' is pointed out. Direct implications for open fermionic lines in the world line path integral casting of field theories are also made.
NASA Astrophysics Data System (ADS)
Gupta, S.; Kumar, R.; Malik, R. P.
2010-11-01
We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the four (3+1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated ( B∧ F) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci-Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion which are derived from the above coupled Lagrangian densities. We show the invariance of the action from the point of view of the symmetry considerations as well as superfield formulation. We discuss, furthermore, the topological term within the framework of superfield formalism and provide the geometrical meaning of its invariance under the (anti-)BRST symmetry transformations.
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.
Perturbative vacuum wavefunctional for gauge theories in the Milne space
NASA Astrophysics Data System (ADS)
Jeon, Sangyong; Epelbaum, Thomas
2016-01-01
The spectrum of vacuum fluctuations in the Milne space (i.e. the τ - η coordinate system) is an important ingredient in the thermalization studies in relativistic heavy ion collisions. In this paper, the Schrödinger functional for the gauge theory perturbative vacuum is derived for the Milne space. The Wigner-transform of the corresponding vacuum density functional is also found together with the propagators. We finally identify the fluctuation spectrum in vacuum, and show the equivalence between the present approach and the symplectic product based method (Dusling et al., 2011; Epelbaum and Gelis, 2013).
Orbifold family unification in SO(2N) gauge theory
Kawamura, Yoshiharu; Miura, Takashi
2010-04-01
We study the possibility of family unification on the basis of SO(2N) gauge theory on the five-dimensional space-time, M{sup 4}xS{sup 1}/Z{sub 2}. Several SO(10), SU(4)xSU(2){sub L}xSU(2){sub R}, or SU(5) multiplets come from a single bulk multiplet of SO(2N) after the orbifold breaking. Other multiplets including brane fields are necessary to compose three families of quarks and leptons.
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.
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.
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.
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.
Exact WKB analysis of {N} = 2 gauge theories
NASA Astrophysics Data System (ADS)
Ashok, Sujay K.; Jatkar, Dileep P.; John, Renjan R.; Raman, M.; Troost, Jan
2016-07-01
We study {N} = 2 supersymmetric gauge theories with gauge group SU(2) coupled to fundamental flavours, covering all asymptotically free and conformal cases. We re-derive, from the conformal field theory perspective, the differential equations satisfied by ɛ 1- and ɛ 2-deformed instanton partition functions. We confirm their validity at leading order in ɛ 2 via a saddle-point analysis of the partition function. In the semi-classical limit we show that these differential equations take a form amenable to exact WKB analysis. We compute the monodromy group associated to the differential equations in terms of ɛ 1-deformed and Borel resummed Seiberg-Witten data. For each case, we study pairs of Stokes graphs that are related by flips and pops, and show that the monodromy groups allow one to confirm the Stokes automorphisms that arise as the phase of ɛ 1 is varied. Finally, we relate the Borel resummed monodromies with the traditional Seiberg-Witten variables in the semi-classical limit.
Geometry and topology of bubble solutions from gauge theory
NASA Astrophysics Data System (ADS)
Chen, Heng-Yu; Correa, Diego H.; Silva, Guillermo A.
2007-07-01
We study how geometrical and topological aspects of certain (1)/(2)-BPS type IIB supergravity solutions are captured by the N=4 super Yang-Mills gauge theory in the AdS/CFT context. The type IIB solutions are completely characterized by arbitrary droplets in a plane and we consider, in particular, concentric droplets. We probe the dual (1)/(2)-BPS operators of the gauge theory with single traces and extract their one-loop anomalous dimensions. The action of the one-loop dilatation operator can be reformulated as the Hamiltonian of a bosonic lattice. The operators defining the Hamiltonian encode the topology of the droplet. The axial symmetry of the droplets turns out to be essential for obtaining the spectrum of the Hamiltonians. In appropriate BMN limits, the near-BPS spectrum reproduces the spectrum of near-BPS string excitations propagating along each individual edge of the droplet of the dual geometric background. We also study semiclassical regimes for the Hamiltonians. We show that, for droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.
Instanton calculus and loop operator in supersymmetric gauge theory
Kanno, Hiroaki; Moriyama, Sanefumi
2008-06-15
We compute the one-point function of the glueball loop operator in the maximally confining phase of supersymmetric gauge theory using instanton calculus. In the maximally confining phase the residual symmetry is the diagonal U(1) subgroup and the localization formula implies that the chiral correlation functions are the sum of the contributions from each fixed point labeled by the Young diagram. The summation can be performed exactly by operator formalism of free fermions, which is also featured in the equivariant Gromov-Witten theory of P{sup 1}. By taking the Laplace transformation of the glueball loop operator, we find an exact agreement with the previous results for the generating function (resolvent) of the glueball one-point functions.
/N=2 gauge theories from wrapped five-branes
NASA Astrophysics Data System (ADS)
Bigazzi, F.; Cotrone, A. L.; Zaffaroni, A.
2001-11-01
We present string duals of four-dimensional N=2 pure SU(N) SYM theory. The theory is obtained as the low energy limit of D5-branes wrapped on non-trivial two-cycles. Using seven-dimensional gauged supergravity and uplifting the result to ten dimensions, we obtain solutions corresponding to various points of the N=2 moduli space. The more symmetric solution may correspond to a point with rotationally invariant classical vevs. By turning on seven-dimensional scalar fields, we find a solution corresponding to a linear distribution of vevs. Both solutions are conveniently studied with a D5-probe, which also confirms many of the standard expectations for N=2 solutions.
Dynamic universality class of large-N gauge theories
Natsuume, Makoto; Okamura, Takashi
2011-02-15
In dynamic critical phenomena, singular behaviors appear not only in the order parameter but also in the other transport coefficients (due to the mode-mode coupling). However, this effect has not been observed in the AdS/CFT duality. We point out that this mode-mode coupling is suppressed by 1/N{sup 2} in the large-N gauge theories which correspond to model H in the classification of Hohenberg and Halperin. Thus, the effect cannot be seen in the classical supergravity approximation. We illustrate this point using the example of the N=4 super-Yang-Mills theory at a finite chemical potential. We also discuss the implications of this result to heavy-ion collisions.
Investigations in gauge theories, topological solitons and string theories. Final report
Not Available
1993-06-01
This is the Final Report on a supported research project on theoretical particle physics entitled ``Investigations in Gauge Theories, Topological Solitons and String Theories.`` The major theme of particle theory pursued has been within the rubric of the standard model, particularly on the interplay between symmetries and dynamics. Thus, the research has been carried out primarily in the context of gauge with or without chiral fermions and in effective chiral lagrangian field theories. The topics studied include the physical implications of abelian and non-abelian anomalies on the spectrum and possible dynamical symmetry breaking in a wide range of theories. A wide range of techniques of group theory, differential geometry and function theory have been applied to probe topological and conformal properties of quantum field theories in two and higher dimensions, the breaking of global chiral symmetries by vector-like gauge theories such as QCD,the phenomenology of a possibly strongly interacting Higgs sector within the minimal standard model, and the relevance of solitonic ideas to non-perturbative phenomena at SSC energies.
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].
CERN Winter School on Supergravity, Strings, and Gauge Theory 2010
None
2011-10-06
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
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.
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.
Noncommutative SO(2,3) gauge theory and noncommutative gravity
NASA Astrophysics Data System (ADS)
Dimitrijević, Marija; Radovanović, Voja
2014-06-01
In this paper noncommutative gravity is constructed as a gauge theory of the noncommutative SO(2,3)⋆ group, while the noncommutativity is canonical (constant). The Seiberg-Witten map is used to express noncommutative fields in terms of the corresponding commutative fields. The commutative limit of the model is the Einstein-Hilbert action with the cosmological constant term and the topological Gauss-Bonnet term. We calculate the second order correction to this model and obtain terms that are of zeroth to fourth power in the curvature tensor and torsion. Trying to relate our results with f(R) and f(T) models, we analyze different limits of our model. In the limit of big cosmological constant and vanishing torsion we obtain an x-dependent correction to the cosmological constant; i.e. noncommutativity leads to an x-dependent cosmological constant. We also discuss the limit of small cosmological constant and vanishing torsion and the teleparallel limit.
Topological susceptibility near Tc in SU(3) gauge theory
NASA Astrophysics Data System (ADS)
Xiong, Guang-Yi; Zhang, Jian-Bo; Chen, Ying; Liu, Chuan; Liu, Yu-Bin; Ma, Jian-Ping
2016-01-01
Topological charge susceptibility χt for pure gauge SU(3) theory at finite temperature is studied using anisotropic lattices. The over-improved stout-link smoothing method is utilized to calculate the topological charge. Near the phase transition point we find a rapid declining behavior for χt with values decreasing from (188 (1) MeV) 4 to (67 (3) MeV) 4 as the temperature increased from zero temperature to 1.9Tc which demonstrates the existence of topological excitations far above Tc. The 4th order cumulant c4 of topological charge, as well as the ratio c4 /χt is also investigated. Results of c4 show step-like behavior near Tc while the ratio at high temperature agrees with the value as predicted by the diluted instanton gas model.
Generalization of trinification to theories with 3N SU(3) gauge groups
Carone, Christopher D.
2005-04-01
We consider a natural generalization of trinification to theories with 3N SU(3) gauge groups. These theories have a simple moose representation and a gauge boson spectrum that can be interpreted via the deconstruction of a 5D theory with unified symmetry broken on a boundary. Although the matter and Higgs sectors of the theory have no simple extra-dimensional analog, gauge unification retains features characteristic of the 5D theory. We determine possible assignments of the matter and Higgs fields to unified multiplets and present theories that are viable alternatives to minimal trinified GUTs.
Geometric Structure of the Translation Gauge Theory of Gravitation
NASA Astrophysics Data System (ADS)
Yoshida, H.
1982-04-01
In the translation gauge theory of gravitation, we give a general expression of the affine connexion coefficient satisfying the following conditions: (i) It is a function of the vierbien b_kμ and of its first derivative bμk,ν. (ii) It is linear in bμk,ν. (iii) It satisfies the metricity condition. Our expression includes both of the connexion coefficients of the Riemann and Weitzenböck space-times as special ones, and hence, the space-time in the translation gauge theory is of Riemann-Cartan type. We fix the gravitational interaction of matter fields following Hayashi's method. The most general quadratic Lagrangian density of b_kμ is represented in terms of the curvature scalar and of the torsion tensor. In the case of electromagnetic field interacting with gravitational field, it is pointed out that the torsion tensor can give rise to observable effects if the field strength Fμν of the electromagnetic field is given by Fμν=nablaμAν-nablaνAμ. Besides the electric charge of the matter field there is a charge which is associated both with the gravitational and electromagnetic fields. In the case of the electromagnetic and gravitational fields produced by a spherically symmetric massive charged matter, the effects of the torsion tensor appear in the post-Newtonian term in the gravitational potential and in the ``post-Coulombian term'' in the electric field strength. We point out the available experimental data in the astronomy impose no restriction on the connexion coefficient.
Wilson loops in noncompact U(1) gauge theories at criticality
Metlitski, Max A.
2008-04-15
We study the properties of Wilson loops in three-dimensional noncompact U(1) gauge theories with global Abelian symmetries. We use duality in the continuum and on the lattice to argue that, close to the critical point between the Higgs and Coulomb phases, all correlators of the Wilson loops are periodic functions of the Wilson loop charge, Q. The period depends on the global symmetry of the theory, which determines the magnetic flux carried by the dual particles. For single flavor scalar electrodynamics, the emergent period is Q=1. In the general case of N complex scalars with a U(1){sup N-1} global symmetry, the period is Q=N. We also give some arguments why this phenomenon does not generalize to theories with a full non-Abelian SU(N) symmetry, where no periodicity in Q is expected. Implications for lattice simulations, as well as for physical systems, such as easy-plane antiferromagnets and disordered superfluids, are noted.
Perturbative Quantum Gravity as a Double Copy of Gauge Theory and Implications for UV Properties
NASA Astrophysics Data System (ADS)
Bern, Zvi
2015-01-01
The talk will review recent developments showing that in a precise sense gravity scattering amplitudes are double copies of corresponding gauge theory ones used to describe the strong subnuclear interactions. Underlying this is a correspondence between the color charges and kinematic numerators appearing in gauge theory scattering amplitudes. An application of these ideas will be given, demonstrating that within perturbation theory standard supergravity theories are much tamer in the ultraviolet than had been believed possible.
Model of the N-quark potential in SU(N) gauge theory using gauge-string duality
NASA Astrophysics Data System (ADS)
Andreev, Oleg
2016-05-01
We use gauge-string duality to model the N-quark potential in pure Yang-Mills theories. For SU (3), the result agrees remarkably well with lattice simulations. The model smoothly interpolates between almost the Δ-law at short distances and the Y-law at long distances.
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.
Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories
NASA Astrophysics Data System (ADS)
Wiese, U.-J.
2013-11-01
Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is non-perturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.
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.
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.
The arithmetic of elliptic fibrations in gauge theories on a circle
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis
2016-06-01
The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.
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
Theory of structural trends within 4d and 5d transition metal topologically close-packed phases
NASA Astrophysics Data System (ADS)
Seiser, B.; Hammerschmidt, T.; Kolmogorov, A. N.; Drautz, R.; Pettifor, D. G.
2011-06-01
A combination of electronic-structure methodologies from density functional theory (DFT) through a tight-binding (TB) model to analytic bond-order potentials (BOPs) has been used to investigate structural trends within TCP phases, which we recently discussed using an empirical structure map [Acta MaterialiaACMAFD1359-645410.1016/j.actamat.2010.10.013 59, 749 (2011)]. First, DFT is used to calculate the structural energy differences across the elemental 4d and 5d transition metal series and the heats of formation of the binary alloys Mo-Re, Mo-Ru, Nb-Re, and Nb-Ru, where we show that the valence electron concentration stabilizes A15, σ, and χ phases but destabilizes μ and Laves phases. Second, a one-parameter canonical d-band TB model in combination with the structural energy difference theorem is found to reproduce the observed elemental DFT structural trends. The structural energy difference theorem is also used to rationalize the influence of the relative size differences on the stability of μ and Laves phases in binary systems. Third, analytic BOP theory using the TB bond integrals as input is shown to converge to the TB structural energy difference curves as the number of moments in the BOP expansion is increased. In order to provide a simple interpretation of these structural energy difference curves in terms of analytic response functions and the differences in the moments of the density of states (DOS), an expression is used for the difference in the band energy that is correct to first order in the Fermi energy differences. We find that the fourth-moment contribution separates the A15, σ, and χ phases from the μ and Laves phases in agreement with the empirical structure map due to difference in the bimodality of the corresponding DOS caused mainly by distortions in their coordination polyhedra from ideal Frank-Kasper polyhedra. Finally, it is shown that at least six moments are needed to predict the structural trend A15→σ→χ.
Ultraviolet and infrared zeros of gauge theories at the four-loop order and beyond
Pica, Claudio; Sannino, Francesco
2011-02-01
We unveil the general features of the phase diagram for any gauge theory with fermions transforming according to distinct representations of the underlying gauge group, at the four-loop order. We classify and analyze the zeros of the perturbative beta function and discover the existence of a rich phase diagram. The anomalous dimension of the fermion masses, at the infrared stable fixed point, are presented. We show that the infrared fixed point, and associated anomalous dimension, are well described by the all-orders beta function for any theory. We also argue the possible existence, to all orders, of a nontrivial ultraviolet fixed point for gauge theories at large number of flavors.
Some constraints on dynamical fermion mass generation in simple gauge theories
NASA Astrophysics Data System (ADS)
Hellman, William S.; Srikanth, M. L.
1980-11-01
Consistency conditions concerning dynamical fermion mass generation in simple gauge theories are examined in lowest order using the procedure of Nambu and Joma-Lasinio. The emerging constraints place strong limitations on the number of fermion multiplets and gauge groups allowed.
Constraint Structure and Quantization of a Non-Abelian Gauge Theory by Means of Dirac Brackets
NASA Astrophysics Data System (ADS)
Bracken, Paul
An SO(3) non-Abelian gauge theory is introduced. The Hamiltonian density is determined and the constraint structure of the model is derived. The first-class constraints are obtained and gauge-fixing constraints are introduced into the model. Finally, using the constraints, the Dirac brackets can be determined and a canonical quantization is found using Dirac's procedure.
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.
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.
Dynamical cosmic strings from a gauge theory of gravity
Furlong, R.C.
1988-09-15
A new dynamical realization of O(5) gauge Euclidean gravity is proposed and shown to possess topologically nontrivial features, cosmic-string flux tubes and dark-matter solitons, of a purely gravitational origin (no Higgs particle needed).
The energy-momentum tensor(s) in classical gauge theories
Gieres, Francois; Blaschke, Daniel N.; Reboud, Meril; Schweda, Manfred
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. Here, the relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
Electric-magnetic dualities in non-abelian and non-commutative gauge theories
NASA Astrophysics Data System (ADS)
Ho, Jun-Kai; Ma, Chen-Te
2016-08-01
Electric-magnetic dualities are equivalence between strong and weak coupling constants. A standard example is the exchange of electric and magnetic fields in an abelian gauge theory. We show three methods to perform electric-magnetic dualities in the case of the non-commutative U (1) gauge theory. The first method is to use covariant field strengths to be the electric and magnetic fields. We find an invariant form of an equation of motion after performing the electric-magnetic duality. The second method is to use the Seiberg-Witten map to rewrite the non-commutative U (1) gauge theory in terms of abelian field strength. The third method is to use the large Neveu Schwarz-Neveu Schwarz (NS-NS) background limit (non-commutativity parameter only has one degree of freedom) to consider the non-commutative U (1) gauge theory or D3-brane. In this limit, we introduce or dualize a new one-form gauge potential to get a D3-brane in a large Ramond-Ramond (R-R) background via field redefinition. We also use perturbation to study the equivalence between two D3-brane theories. Comparison of these methods in the non-commutative U (1) gauge theory gives different physical implications. The comparison reflects the differences between the non-abelian and non-commutative gauge theories in the electric-magnetic dualities. For a complete study, we also extend our studies to the simplest abelian and non-abelian p-form gauge theories, and a non-commutative theory with the non-abelian structure.
On {N} = 2 supersymmetric gauge theories on S 2 × S 2
NASA Astrophysics Data System (ADS)
Sinamuli, Musema
2016-05-01
We construct a supergeometry based on S 2× S 2 on which four dimensional {N} = 2 gauge theories can be placed supersymmetrically while preserving all supersymmetries. By embedding the supergeometry in four dimensional {N} = 2 supergravity we are able to construct an arbitrary {N} = 2 gauge theory on S 2 × S 2. We show that {N} = 2 gauge theories are invariant under the exceptional superalgebra D(2 , 1 , α), where α is the ratio of the radii of the two S 2's. We solve the supersymmetry fixed points equations for a choice of supercharge in D(2 , 1 , α). The solution of these BPS equations, which we find, would serve as the exact saddle point configurations of a localization computation of the partition function of {N} = 2 gauge theories on S 2 × S 2.
Relative weights approach to SU(3) gauge theories with dynamical fermions at finite density
NASA Astrophysics Data System (ADS)
Greensite, Jeff; Höllwieser, Roman
2016-07-01
We derive effective Polyakov line actions for SU(3) gauge theories with staggered dynamical fermions, for a small sample of lattice couplings, lattice actions, and lattice extensions in the time direction. The derivation is via the method of relative weights, and the theories are solved at finite chemical potential by mean field theory. We find in some instances that the long-range couplings in the effective action are very important to the phase structure, and that these couplings are responsible for long-lived metastable states in the effective theory. Only one of these states corresponds to the underlying lattice gauge theory.
NASA Astrophysics Data System (ADS)
Rey, Soo-Jong; Suyama, Takao
2011-01-01
Using localization, matrix model and saddle-point techniques, we determine exact behavior of circular Wilson loop in mathcal{N} = 2 superconformal (quiver) gauge theories in the large number limit of colors. Focusing at planar and large `t Hooft couling limits, we compare its asymptotic behavior with well-known exponential growth of Wilson loop in mathcal{N} = 4 super Yang-Mills theory with respect to `t Hooft coupling. For theory with gauge group SU( N) coupled to 2 N fundamental hypermultiplets, we find that Wilson loop exhibits non-exponential growth — at most, it can grow as a power of `t Hooft coupling. For theory with gauge group SU( N)×SU( N) and bifundamental hypermultiplets, there are two Wilson loops associated with two gauge groups. We find Wilson loop in untwisted sector grows exponentially large as in mathcal{N} = 4 super Yang-Mills theory. We then find Wilson loop in twisted sector exhibits non-analytic behavior with respect to difference of the two `t Hooft coupling constants. By letting one gauge coupling constant hierarchically larger/smaller than the other, we show that Wilson loops in the second type theory interpolate to Wilson loops in the first type theory. We infer implications of these findings from holographic dual description in terms of minimal surface of dual string worldsheet. We suggest intuitive interpretation that in both classes of theory holographic dual background must involve string scale geometry even at planar and large `t Hooft coupling limit and that new results found in the gauge theory side are attributable to worldsheet instantons and infinite resummation therein. Our interpretation also indicates that holographic dual of these gauge theories is provided by certain non-critical string theories.
On the Potentials of Supersymmetric Theories with Gauge-Field Mixing Terms
NASA Astrophysics Data System (ADS)
Nunes Ferreira, Cristine
2004-12-01
In this letter, we reconsider the delicate issue of symmetry and supersymmetry breakings for gauge theories with gauge-field mixings. The purpose is to study generalyzed potentials in the presence of more than a single gauge potential. In this work, following a stream of investigation on supersymmetric gauge theories without flat directions, we contemplate the possibility of building up D- and F-term potentials by means of a gauge-field mixing in connection with a U(1)×U(1)' -symmetry. We investigate a generalized potential including an N=1 supersymmetric extension of the Maxwell-Chern-Simons model focusing on the study of cosmic string configurations. This analysis sheds some light on the formation of cosmic strings for model with violation of Lorentz symmetry.
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).
Masslessness of ghosts in equivariantly gauge-fixed Yang-Mills theories
Golterman, Maarten; Zimmerman, Leah
2005-06-01
We show that the one-loop ghost self-energy in an equivariantly gauge-fixed Yang-Mills theory vanishes at zero momentum. A ghost mass is forbidden by equivariant BRST symmetry, and our calculation confirms this explicitly. The four-ghost self interaction which appears in the equivariantly gauge-fixed Yang-Mills theory is needed in order to obtain this result.
Gauge theory dynamics and Kähler potential for Calabi-Yau complex moduli
NASA Astrophysics Data System (ADS)
Doroud, Nima; Gomis, Jaume
2013-12-01
We compute the exact two-sphere partition function and matrix of two-point functions of operators in the chiral ring with their complex conjugates in two-dimensional supersymmetric gauge theories. For gauge theories that flow in the infrared to a CalabiYau nonlinear sigma model, these renormalization group invariant observables determine the exact Kähler potential and associated Zamolodchikov metric in the complex structure moduli space of the Calabi-Yau manifold.
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.
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. PMID:25166817
Noncommutative Chern-Simons gauge and gravity theories and their geometric Seiberg-Witten map
NASA Astrophysics Data System (ADS)
Aschieri, Paolo; Castellani, Leonardo
2014-11-01
We use a geometric generalization of the Seiberg-Witten map between noncommutative and commutative gauge theories to find the expansion of noncommutative Chern-Simons (CS) theory in any odd dimension D and at first order in the noncommutativity parameter θ. This expansion extends the classical CS theory with higher powers of the curvatures and their derivatives.
Chiral gauge theories and a dirac neutrino - Dark matter connection
NASA Astrophysics Data System (ADS)
Hernandez, Daniel
2016-06-01
It is proposed that all light fermionic degrees of freedom, including the Standard Model (SM) fermions and all possible light beyond-the-standard model fields, are chiral with respect to some spontaneously broken abelian gauge symmetry. A new gauge symmetry U(1)ν is required if light fermionic new states are to exist. Anomaly cancellations mandate the existence of several new fields with nontrivial U(1)ν charges. A general technique to write down chiral-fermions-only models that are at least anomaly-free under a U(1) gauge symmetry is described. A concrete example that provides a Dark Matter candidate and leads to parametrically small Dirac neutrino masses is further developed.
Confluent Heun functions in gauge theories on thick braneworlds
Cunha, M. S.; Christiansen, H. R.
2011-10-15
We investigate the propagation modes of gauge fields in an infinite Randall-Sundrum scenario. In this model a sine-Gordon soliton represents our thick four-dimensional braneworld while an exponentially coupled scalar acts for the dilaton field. For the gauge-field motion we find a differential equation which can be transformed into a confluent Heun equation. By means of another change of variables we obtain a related Schroedinger equation with a family of symmetric rational ({gamma}-{omega}z{sup 2})/(1-z{sup 2}){sup 2} potential functions. We discuss both results and present the infinite spectrum of analytical solutions for the gauge field. Finally, we assess the existence and the relative weights of Kaluza-Klein modes in the present setup.
Disk relations for tree amplitudes in minimal coupling theory of gauge field and gravity
NASA Astrophysics Data System (ADS)
Chen, Yi-Xin; Du, Yi-Jian; Ma, Qian
2010-07-01
KLT relations on S factorize closed string amplitudes into product of open string tree amplitudes. The field theory limits of KLT factorization relations hold in minimal coupling theory of gauge field and gravity. In this paper, we consider the field theory limits of relations on D. Though the relations on D and KLT factorization relations hold on worldsheets with different topologies, we find the field theory limits of D relations also hold in minimal coupling theory of gauge field and gravity. We use the D relations to give three- and four-point tree amplitudes where gluons are minimally coupled to gravitons. We also give a further discussion on general tree amplitudes in minimal coupling theory of gauge field and gravity. In general, any tree amplitude with M gravitons in addition to N gluons can be given by pure-gluon tree amplitudes with N+2M legs.
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.
Cluster Algebras from Dualities of 2d = (2, 2) Quiver Gauge Theories
NASA Astrophysics Data System (ADS)
Benini, Francesco; Park, Daniel S.; Zhao, Peng
2015-11-01
We interpret certain Seiberg-like dualities of two-dimensional = (2,2) quiver gauge theories with unitary groups as cluster mutations in cluster algebras, originally formulated by Fomin and Zelevinsky. In particular, we show how the complexified Fayet-Iliopoulos parameters of the gauge group factors transform under those dualities and observe that they are in fact related to the dual cluster variables of cluster algebras. This implies that there is an underlying cluster algebra structure in the quantum Kähler moduli space of manifolds constructed from the corresponding Kähler quotients. We study the S 2 partition function of the gauge theories, showing that it is invariant under dualities/mutations, up to an overall normalization factor, whose physical origin and consequences we spell out in detail. We also present similar dualities in = (2,2)* quiver gauge theories, which are related to dualities of quantum integrable spin chains.
Evidence that centre vortices underpin dynamical chiral symmetry breaking in SU (3) gauge theory
NASA Astrophysics Data System (ADS)
Trewartha, Daniel; Kamleh, Waseem; Leinweber, Derek
2015-07-01
The link between dynamical chiral symmetry breaking and centre vortices in the gauge fields of pure SU (3) gauge theory is studied using the overlap-fermion quark propagator in Lattice QCD. Overlap fermions provide a lattice realisation of chiral symmetry and consequently offer a unique opportunity to explore the interplay of centre vortices, instantons and dynamical mass generation. Simulations are performed on gauge fields featuring the removal of centre vortices, identified through gauge transformations maximising the center of the gauge group. In contrast to previous results using the staggered-fermion action, the overlap-fermion results illustrate a loss of dynamical chiral symmetry breaking coincident with vortex removal. This result is linked to the overlap-fermion's sensitivity to the subtle manner in which instanton degrees of freedom are compromised through the process of centre vortex removal. Backgrounds consisting solely of the identified centre vortices are also investigated. After smoothing the vortex-only gauge fields, we observe dynamical mass generation on the vortex-only backgrounds consistent within errors with the original gauge-field ensemble following the same smoothing. Through visualizations of the instanton-like degrees of freedom in the various gauge-field ensembles, we find evidence of a link between the centre vortex and instanton structure of the vacuum. While vortex removal destabilizes instanton-like objects under O (a4)-improved cooling, vortex-only backgrounds provide gauge-field degrees of freedom sufficient to create instantons upon cooling.
Tricritical points in a compact U (1 ) lattice gauge theory at strong coupling
NASA Astrophysics Data System (ADS)
De, Asit K.; Sarkar, Mugdha
2016-06-01
Pure compact U (1 ) lattice gauge theory exhibits a phase transition at gauge coupling g ˜O (1 ) separating a familiar weak coupling Coulomb phase, having free massless photons, from a strong coupling phase. However, the phase transition was found to be of first order, ruling out any nontrivial theory resulting from a continuum limit from the strong coupling side. In this work, a compact U (1 ) lattice gauge theory is studied with addition of a dimension-two mass counterterm and a higher derivative (HD) term that ensures a unique vacuum and produces a covariant gauge-fixing term in the naive continuum limit. For a reasonably large coefficient of the HD term, now there exists a continuous transition from a regular ordered phase to a spatially modulated ordered phase. For weak gauge couplings, a continuum limit from the regular ordered phase results in a familiar theory consisting of free massless photons. For strong gauge couplings with g ≥O (1 ), this transition changes from first order to continuous as the coefficient of the HD term is increased, resulting in tricritical points which appear to be a candidate in this theory for a possible nontrivial continuum limit.
Note on the Dual BRST Symmetry in Gauge Theory
NASA Astrophysics Data System (ADS)
Gaete, Patricio
We analyze the relation between the Lagrangian and Hamiltonian BRST symmetry generators for a recently proposed two-dimensional symmetry. In particular it is shown that this symmetry may be obtained from a canonical transformation in the ghost sector in a gauge-independent way.
Remarks on worldsheet theories dual to free large N gauge theories
Aharony, Ofer; David, Justin R.; Gopakumar, Rajesh; Komargodski, Zohar; Razamat, Shlomo S.
2007-05-15
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 [R. Gopakumar, Phys. Rev. D 70, 025009 (2004); ibid.70, 025010 (2004); C. R. Physique 5, 1111 (2004); Phys. Rev. D 72, 066008 (2005)]. 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.
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.
On gauge enhancement and singular limits in G 2 compactifications of M-theory
NASA Astrophysics Data System (ADS)
Halverson, James; Morrison, David R.
2016-04-01
We study the physics of singular limits of G 2 compactifications of M-theory, which are necessary to obtain a compactification with non-abelian gauge symmetry or massless charged particles. This is more difficult than for Calabi-Yau compactifications, due to the absence of calibrated two-cycles that would have allowed for direct control of W-boson masses as a function of moduli. Instead, we study the relationship between gauge enhancement and singular limits in G 2 moduli space where an associative or coassociative submanifold shrinks to zero size; this involves the physics of topological defects and sometimes gives indirect control over particle masses, even though they are not BPS. We show how a lemma of Joyce associates the class of a three-cycle to any U(1) gauge theory in a smooth G 2 compactification. If there is an appropriate associative submanifold in this class then in the limit of nonabelian gauge symmetry it may be interpreted as a gauge theory worldvolume and provides the location of the singularities associated with non-abelian gauge or matter fields. We identify a number of gauge enhancement scenarios related to calibrated submanifolds, including Coulomb branches and non-isolated conifolds, and also study examples that realize them.
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.
Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
NASA Astrophysics Data System (ADS)
van Tongeren, Stijn J.
2016-03-01
We give an AdS/CFT interpretation to homogeneous Yang-Baxter deformations of the AdS5 ×S5 superstring as noncommutative deformations of the dual gauge theory, going well beyond the canonical noncommutative case. These homogeneous Yang-Baxter deformations can be of so-called abelian or jordanian type. While abelian deformations have a clear interpretation in string theory and many already had well understood gauge theory duals, jordanian deformations appear novel on both counts. We discuss the symmetry structure of the deformed string from the uniformizing perspective of Drinfeld twists and indicate that this structure can be realized on the gauge theory side by considering theories on various noncommutative spaces. We then conjecture that these are the gauge theory duals of our strings, modulo subtleties involving singularities. We support this conjecture by a brane construction for two jordanian examples, corresponding to noncommutative spaces with [x- , ⋆xi ] ∼xi (i = 1 , 2). We also discuss κ-Minkowski type deformations of AdS5 ×S5, one of which may be the gravity dual of gauge theory on spacelike κ-Minkowski space.
Mirror symmetry in three-dimensional gauge theories, quivers and D-branes
NASA Astrophysics Data System (ADS)
de Boer, Jan; Hori, Kentaro; Ooguri, Hirosi; Oz, Yaron
1997-02-01
We construct and analyze dual N = 4 supersymmetric gauge theories in three dimensions with unitary and symplectic gauge groups. The gauge groups and the field content of the theories are encoded in quiver diagrams. The duality exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters. We analyze the classical and the quantum moduli spaces of the theories and construct an explicit mirror map between the mass parameters and the Fayet-Iliopoulos parameters of the dual. The results generalize the relation between ALE spaces and moduli spaces of SU( n) and SO(2 n) instantons. We interpret some of these results from the string theory viewpoint, for SU( n) by analyzing T-duality and extremal transitions in type II string compactifications, for SO(2 n) by using D-branes as probes. Finally, we make a proposal for the moduli space of vacua of these theories in the absence of matter.
An Interacting Gauge Field Theoretic Model for Hodge Theory: Basic Canonical Brackets
NASA Astrophysics Data System (ADS)
R., Kumar; Gupta, S.; R. P., Malik
2014-06-01
We derive the basic canonical brackets amongst the creation and annihilation operators for a two (1 + 1)-dimensional (2D) gauge held theoretic model of an interacting Hodge theory where a U(1) gauge field (Aμ) is coupled with the fermionic Dirac fields (ψ and bar psi). In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries (and the concept of their generators) that are present in the theory. We do not use the definition of the canonical conjugate momenta (corresponding to the basic fields of the theory) anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries (and corresponding generators) provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.
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.
Trilinear neutral gauge boson couplings in effective theories
NASA Astrophysics Data System (ADS)
Larios, F.; Pérez, M. A.; Tavares-Velasco, G.; Toscano, J. J.
2001-06-01
We list all the lowest dimension effective operators inducing off-shell trilinear neutral gauge boson couplings ZZγ, Zγγ, and ZZZ within the effective Lagrangian approach, both in the linear and nonlinear realizations of SU(2)L × U(1)Y gauge symmetry. In the linear scenario we find that these couplings can be generated only by dimension-8 operators necessarily including the Higgs boson field, whereas in the nonlinear case they are induced by dimension-6 operators. We consider the impact of these couplings on some precision measurements such as the magnetic and electric dipole moments of fermions, as well as the Z boson rare decay Z-->νν¯γ. If the underlying new physics is of a decoupling nature, it is not expected that trilinear neutral gauge boson couplings may affect considerably any of these observables. On the contrary, it is just in the nonlinear scenario where these couplings have the more promising prospects of being perceptible through high precision experiments.
Application of double-dimensional regularization in a nonabelian gauge theory
Karnaukhov, S.N.
1986-04-01
Calculations of the polarization operator and vertex function in a nonabelian gauge theory are performed in second order of perturbation theory on the basis of the method of I. V. Tyutin (JETP Lett. 35, 428 (1982)). In this calculation the formal contribution of the ghosts disappears, but the expressions for the polarization operator and vertex function are modified in such a way that this leads to automatic allowance for the contribution of the ghosts. For the gauge-invariant ..beta..-function the answer coincides with the known expression, but for the polarization operator and vertex function the dependence on the gauge parameter differs from that in standard calculations. It is shown that the calculations can be performed in the framework of dimensional regularization with a special choice of gauge condition.
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.
Emergence of Supersymmetry, Gauge Theory and String in Condensed Matter Systems
NASA Astrophysics Data System (ADS)
Lee, Sung-Sik
2012-11-01
The lecture note consists of four parts. In the first part, we review a 2+1 dimensional lattice model which realizes emergent supersymmetry at a quantum critical point. The second part is devoted to a phenomenon called fractionalization where gauge boson and fractionalized particles emerge as low energy excitations as a result of strong interactions between gauge neutral particles. In the third part, we discuss about stability and low energy effective theory of a critical spin liquid state where stringy excitations emerge in a large N limit. In the last part, we discuss about an attempt to come up with a prescription to derive holographic theory for general quantum field theory.
The free energy of higher representation sources in lattice gauge theories
NASA Astrophysics Data System (ADS)
Damgaard, P. H.
1987-07-01
Deconfinement of higher representation sources in SU(2) lattice gauge theory is studied by a Monte Carlo simulation on an 83×2 lattice. Results for the free energy are compared with expectations from the effective theory of thermal Polyakov loops, and critical exponents for the magnetization of different representations in SU(2) are computed. We also compare the predictions for higher representations in SU(3) lattice gauge theory with some recent Monte Carlo data. Finally, possible phenomenological consequences of the deconfinement associated with higher representation sources are discussed. I would like to thank Urs Heller and Alan Luther for helpful discussions.
Study of Z(N) gauge theories on a three-dimensional pseudorandom lattice
Pertermann, D.; Ranft, J. )
1988-01-01
Using the simplicial pseudorandom version of lattice gauge theory the authors study simple Z(eta) gauge models in D = 3 dimensions. In this formulation it is possible to interpolate continuously between a regular simplicial lattice and a pseudorandom lattice. Calculating average plaquette expectation values they look for the phase transitions of the Z(eta) gauge models with eta = 2 and 3. They find all the phase transitions to be of first order, also in the case of the Z(2) model. The critical couplings increase with the irregularity of the lattice.
Non-Abelian SU(2) Lattice Gauge Theories in Superconducting Circuits.
Mezzacapo, A; Rico, E; Sabín, C; Egusquiza, I L; Lamata, L; Solano, E
2015-12-11
We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure SU(2) gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulation of non-Abelian physics with solid-state quantum platforms. PMID:26705616
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. PMID:27337339
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.
Symmetry breaking and restoration for interacting scalar and gauge fields in Lifshitz type theories
NASA Astrophysics Data System (ADS)
Farakos, K.; Metaxas, D.
2012-05-01
We consider the one-loop effective potential at zero and finite temperature in field theories with anisotropic space-time scaling, with critical exponent z = 2, including both scalar and gauge fields. Depending on the relative strength of the coupling constants for the gauge and scalar interactions, we find that there is a symmetry breaking term induced at one loop at zero temperature and we find symmetry restoration through a first-order phase transition at high temperature.
Local existence of N=1 supersymmetric gauge theory in four Dimensions
Akbar, Fiki T.; Gunara, Bobby E.; Zen, Freddy P.; Triyanta
2015-04-16
In this paper, we shall prove the local existence of N=1 supersymmetry gauge theory in 4 dimension. We start from the Lagrangian for coupling chiral and vector multiplets with constant gauge kinetic function and only considering a bosonic part by setting all fermionic field to be zero at level equation of motion. We consider a U(n) model as isometry for scalar field internal geometry. And we use a nonlinear semigroup method to prove the local existence.
Path ordered operator formalism of gauge theories in two-dimensional space-time
NASA Astrophysics Data System (ADS)
Kikkawa, K.
1980-05-01
Two-dimensional gauge theories, both abelian and non-belian, are formulated in terms of gauge invariant path ordered operators (POO). The generators of the Poincaré group are constructed with POO's. An exact equation of motion for POO's is derived and is shown to reduce to the 't Hooft eigenvalue equation in QCD in the large N limit. Nowhere appear infrared problems.
Aspects of non-commutative gauge theory and the AdS/CFT correspondance
NASA Astrophysics Data System (ADS)
Thomas, Keith S.
Non-commutative gauge theory with a non-constant non-commutativity parameter can be formulated as a decoupling limit of open strings ending on D3-branes wrapping a Melvin universe. We identify this model as a simple Melvin twist of flat D3 branes. Along similar lines, one recognizes the model of Hashimoto and Sethi as being the Melvin null twist, and the model of Dolan and Nappi as being the null Melvin twist, of the flat D3-brane. This construction therefore offers a unified perspective on most of the known explicit constructions of non-commutative gauge theories as a decoupled theory of D-branes in a, B-field background. In order to gain insight into the type of physics embodied in such theories, we describe the world volume theory on a D3-brane embedded in a Melvin universe which is decaying via the nucleation of monopole anti-monopole pairs. Further, focusing on the gauge theory properties and dynamics, we construct the action explicitly for the Melvin twist non-commutative gauge theory and discuss various physical features of the model. The decoupled field theory is not supersymmetric. Nonetheless, the Coulomb branch appears to remain flat at least in the large N and large 't Hooft coupling limit. We also find the analogue of Prasad-Sommerfield monopoles whose size scales with the non-commutativity parameter and is therefore position dependent.
The Black Hole in the Throat - Thermodynamics of Strongly Coupled Cascading Gauge Theories
Aharony, Ofer; Buchel, Alex; Kerner, Patrick; /Western Ontario U.
2007-06-14
We numerically construct black hole solutions corresponding to the deconfined, chirally symmetric phase of strongly coupled cascading gauge theories at various temperatures. We compute the free energy as a function of the temperature, and we show that it becomes positive below some critical temperature, indicating the possibility of a first order phase transition at which the theory deconfines and restores the chiral symmetry.
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.
N=2, 4 supersymmetric gauge field theory in two-time physics
Bars, Itzhak; Kuo, Y.-C.
2009-01-15
In the context of two-time physics in 4+2 dimensions we construct the most general N=2, 4 supersymmetric Yang-Mills gauge theories for any gauge group G. This builds on our previous work for N=1 supersymmetry (SUSY). The action, the conserved SUSY currents, and the SU(N) covariant SUSY transformation laws are presented for both N=2 and N=4. When the equations of motion are used the SUSY transformations close to the supergroup SU(2,2|N) with N=1, 2, 4. The SU(2,2)=SO(4,2) subsymmetry is realized linearly on 4+2 dimensional flat spacetime. All fields, including vectors and spinors, are in 4+2 dimensions. The extra gauge symmetries in 2T field theory, together with the kinematic constraints that follow from the action, remove all the ghosts to give a unitary theory. By choosing gauges and solving the kinematic equations, the 2T field theory in 4+2 flat spacetime can be reduced to various shadows in various 3+1 dimensional (generally curved) spacetimes. These shadows are related to each other by dualities. The conformal shadows of our theories in flat 3+1 dimensions coincide with the well known counterpart N=1, 2, 4 supersymmetric massless renormalizable field theories in 3+1 dimensions. It is expected that our more symmetric new structures in 4+2 spacetime may be useful for nonperturbative or exact solutions of these theories.
Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory
Nielsen, H.B.; Rugh, H.H.; Rugh, S.E.
1996-12-31
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a {open_quote}no go{close_quotes} for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a {open_quotes}continuum limit{close_quotes} in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined.
NASA Astrophysics Data System (ADS)
Noronha, Jorge
2010-02-01
We show that in four-dimensional gauge theories dual to five-dimensional Einstein gravity coupled to a single scalar field in the bulk, the derivative of the single heavy quark free energy in the deconfined phase is dFQ(T)/dT˜-1/cs2(T), where cs(T) is the speed of sound. This general result provides a direct link between the softest point in the equation of state of strongly-coupled plasmas and the deconfinement phase transition described by the expectation value of the Polyakov loop. We give an explicit example of a gravity dual with black hole solutions that can reproduce the lattice results for the expectation value of the Polyakov loop and the thermodynamics of SU(3) Yang-Mills theory in the (nonperturbative) temperature range between Tc and 3Tc.
Adler-Bardeen theorem and manifest anomaly cancellation to all orders in gauge theories
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2014-10-01
We reconsider the Adler-Bardeen theorem for the cancellation of gauge anomalies to all orders, when they vanish at one loop. Using the Batalin-Vilkovisky formalism and combining the dimensional-regularization technique with the higher-derivative gauge invariant regularization, we prove the theorem in the most general perturbatively unitary renormalizable gauge theories coupled to matter in four dimensions, and identify the subtraction scheme where anomaly cancellation to all orders is manifest, namely no subtractions of finite local counterterms are required from two loops onwards. Our approach is based on an order-by-order analysis of renormalization, and, differently from most derivations existing in the literature, does not make use of arguments based on the properties of the renormalization group. As a consequence, the proof we give also applies to conformal field theories and finite theories.
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.
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.
Zero of the discrete beta function in SU(3) lattice gauge theory with color sextet fermions
Shamir, Yigal; Svetitsky, Benjamin; DeGrand, Thomas
2008-08-01
We have carried out a Schrodinger functional calculation for the SU(3) lattice gauge theory with two flavors of Wilson fermions in the sextet representation of the gauge group. We find that the discrete beta function, which governs the change in the running coupling under a discrete change of spatial scale, changes sign when the Schrodinger functional renormalized coupling is in the neighborhood of g{sup 2}=2.0. The simplest explanation is that the theory has an infrared-attractive fixed point, but more complicated possibilities are allowed by the data. While we compare rescalings by factors of 2 and 4/3, we work at a single lattice spacing.
Gauge fields in graphene with nonuniform elastic deformations: A quantum field theory approach
NASA Astrophysics Data System (ADS)
Arias, Enrique; Hernández, Alexis R.; Lewenkopf, Caio
2015-12-01
We investigate the low-energy continuum limit theory for electrons in a graphene sheet under strain. We use the quantum field theory in curved spaces to analyze the effect of the system deformations into an effective gauge field. We study both in-plane and out-of-plane deformations and obtain a closed expression for the effective gauge field due to arbitrary nonuniform sheet deformations. The obtained results reveal a remarkable relation between the local-pseudomagnetic field and the Riemann curvature, so far overlooked.
Gluon Productions in classical SU(3) lattice gauge theory in high energy heavy ion collisions
NASA Astrophysics Data System (ADS)
Nara, Yasushi; Krasnitz, Alex; Venugopalan, Raju
2001-10-01
A classical effective field theory approach was introduced to describe the initial conditions for the produced partons in ultra-relativistic heavy ion collisions. The importance of the productions of small x gluons are emphasized, since, in high energy heavy ion collisions, parton distributions grow rapidly and may saturate. Most of them are freed during the reactions. Krasnitz and Venugopalan performed a non-perturbative numerical computation for a SU(2) gauge theory. We present the initial gluon transverse momentum distribution from SU(3) real time lattice gauge simulation in the high energy heavy ion collisions.
Grand unified theories with dimension-5 interactions: Gauge unification and intermediate scales
Chakrabortty, Joydeep; Raychaudhuri, Amitava
2010-03-01
Dimension-5 corrections to the gauge kinetic term of grand unified theories may capture effects of quantum gravity or string compactification. Such operators modify the usual gauge coupling unification prediction in a calculable manner. Here we examine SU(5), SO(10), and E(6) grand unified theories in the light of all such permitted operators and calculate the impact on the intermediate scales and the unification program. We show that in many cases at least one intermediate scale can be lowered to even 1-10 TeV, where a neutral Z{sup '} and possibly other states are expected.
Pure gauge configurations and tachyon solutions to string field theories equations of motion
NASA Astrophysics Data System (ADS)
Aref'eva, Irina Ya.; Gorbachev, Roman V.; Grigoryev, Dmitry A.; Khromov, Pavel N.; Maltsev, Maxim V.; Medvedev, Peter B.
2009-05-01
In construction of analytical solutions to open string field theories pure gauge configurations parameterized by wedge states play an essential role. These pure gauge configurations are constructed as perturbation expansions and to guaranty that these configurations are asymptotical solutions to equations of motion one needs to study convergence of the perturbation expansions. We demonstrate that for the large parameter of the perturbation expansion these pure gauge truncated configurations give divergent contributions to the equation of motion on the subspace of the wedge states. We perform this demonstration numerically for the pure gauge configurations related to tachyon solutions for the bosonic and NS fermionic SFT. By the numerical calculations we also show that the perturbation expansions are cured by adding extra terms. These terms are nothing but the terms necessary to make valued the Sen conjectures.
Gauge invariance and anomalous theories at finite fermionic density
Roberge, A. )
1990-04-15
We investigate the issue of stability of anomalous matter at finite fermionic density using a two-dimensional toy model. In particular, we pay careful attention to the issue of gauge invariance. We find that, contrary to some recent claims, the effective free energy (obtained by integrating out the fermions) cannot be obtained by the simple inclusion of a Chern-Simons term multiplying the fermionic chemical potential. We obtain some conditions for stability of anomalous charges when some finite density of conserved charge is present as well as for the neutral case. We also show that, under reasonable conditions, no sphaleron-type solution can exist in the toy model unless the anomalous charge density vanishes. We argue that this could be the case for more realistic models as well.
Yang-Mills Gauge Theory and the Higgs Boson Family
NASA Astrophysics Data System (ADS)
Chang, Ngee-Pong
The gauge symmetry principles of the Yang-Mills field of 1954 provide the solid rock foundation for the Standard Model of particle physics. To give masses to the quarks and leptons, however, SM calls on the solitary Higgs field using a set of mysterious complex Yukawa coupling matrices. We enrich the SM by reducing the Yukawa coupling matrices to a single Yukawa coupling constant, and endowing it with a family of Higgs fields that are degenerate in mass. The recent experimental discovery of the Higgs resonance at 125.09±0.21 GeV does not preclude this possibility. Instead, it presents an opportunity to explore the interference effects in background events at the LHC. We present a study based on the maximally symmetric Higgs potential in a leading hierarchy scenario.
Yang-Mills gauge theory and the Higgs boson family
NASA Astrophysics Data System (ADS)
Chang, Ngee-Pong
2016-01-01
The gauge symmetry principles of the Yang-Mills field of 1954 provide the solid rock foundation for the Standard Model of particle physics. To give masses to the quarks and leptons, however, SM calls on the solitary Higgs field using a set of mysterious complex Yukawa coupling matrices. We enrich the SM by reducing the Yukawa coupling matrices to a single Yukawa coupling constant, and endowing it with a family of Higgs fields that are degenerate in mass. The recent experimental discovery of the Higgs resonance at 125.09 ± 0.21 GeV does not preclude this possibility. Instead, it presents an opportunity to explore the interference effects in background events at the LHC. We present a study based on the maximally symmetric Higgs potential in a leading hierarchy scenario.
The complete KLT-map between gravity and gauge theories
NASA Astrophysics Data System (ADS)
Damgaard, Poul H.; Huang, Rijun; Søndergaard, Thomas; Zhang, Yang
2012-08-01
We present the complete map of any pair of super Yang-Mills theories to supergravity theories as dictated by the KLT relations in four dimensions. Symmetries and the full set of associated vanishing identities are derived. A graphical method is introduced which simplifies counting of states, and helps in identifying the relevant set of symmetries.
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. PMID:26684222
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.
Large-N volume independence in conformal and confining gauge theories
Unsal, Mithat; Yaffe, Laurence G.; /Washington U., Seattle
2010-08-26
Consequences of large N volume independence are examined in conformal and confining gauge theories. In the large N limit, gauge theories compactified on R{sup d-k} x (S{sup 1}){sup k} are independent of the S{sup 1} radii, provided the theory has unbroken center symmetry. In particular, this implies that a large N gauge theory which, on R{sup d}, flows to an IR fixed point, retains the infinite correlation length and other scale invariant properties of the decompactified theory even when compactified on R{sup d-k} x (S{sup 1}){sup k}. In other words, finite volume effects are 1/N suppressed. In lattice formulations of vector-like theories, this implies that numerical studies to determine the boundary between confined and conformal phases may be performed on one-site lattice models. In N = 4 supersymmetric Yang-Mills theory, the center symmetry realization is a matter of choice: the theory on R{sup 4-k} x (S{sup 1}){sup k} has a moduli space which contains points with all possible realizations of center symmetry. Large N QCD with massive adjoint fermions and one or two compactified dimensions has a rich phase structure with an infinite number of phase transitions coalescing in the zero radius limit.
A Critical Review of the Research on the Extreme Male Brain Theory and Digit Ratio (2D:4D)
ERIC Educational Resources Information Center
Teatero, Missy L.; Netley, Charles
2013-01-01
Boys are more likely than girls to be diagnosed with an autism spectrum disorder (ASD). The extreme male brain (EMB) theory of ASD suggests that fetal testosterone (FT) exposure may underlie sex differences in autistic traits. A link between the organizational effects of FT on the brain and ASD is often drawn based on research using digit ratio…
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.
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.
Gauge-invariant perturbation theory for trans-Planckian inflation
Shankaranarayanan, S.; Lubo, Musongela
2005-12-15
The possibility that the scale-invariant inflationary spectrum may be modified due to the hidden assumptions about the Planck scale physics--dubbed as trans-Planckian inflation--has received considerable attention. To mimic the possible trans-Planckian effects, among various models, modified dispersion relations have been popular in the literature. In almost all the earlier analyses, unlike the canonical scalar field driven inflation, the trans-Planckian effects are introduced to the scalar/tensor perturbation equations in an ad hoc manner--without calculating the stress tensor of the cosmological perturbations from the covariant Lagrangian. In this work, we perform the gauge-invariant cosmological perturbations for the single scalar-field inflation with the Jacobson-Corley dispersion relation by computing the fluctuations of all the fields including the unit-timelike vector field which defines a preferred rest frame. We show that: (i) The nonlinear effects introduce corrections only to the perturbed energy density. The corrections to the energy density vanish in the super-Hubble scales. (ii) The scalar perturbations, in general, are not purely adiabatic. (iii) The equation of motion of the Mukhanov-Sasaki variable corresponding to the inflaton field is different from those presumed in the earlier analyses. (iv) The tensor perturbation equation remains unchanged. We perform the classical analysis for the resultant system of equations and also compute the power spectrum of the scalar perturbations in a particular limit. We discuss the implications of our results and compare with the earlier results.
SU (2) lattice gauge theory simulations on Fermi GPUs
Cardoso, Nuno; Bicudo, Pedro
2011-05-10
In this work we explore the performance of CUDA in quenched lattice SU (2) simulations. CUDA, NVIDIA Compute Unified Device Architecture, is a hardware and software architecture developed by NVIDIA for computing on the GPU. We present an analysis and performance comparison between the GPU and CPU in single and double precision. Analyses with multiple GPUs and two different architectures (G200 and Fermi architectures) are also presented. In order to obtain a high performance, the code must be optimized for the GPU architecture, i.e., an implementation that exploits the memory hierarchy of the CUDA programming model. We produce codes for the Monte Carlo generation of SU (2) lattice gauge configurations, for the mean plaquette, for the Polyakov Loop at finite T and for the Wilson loop. We also present results for the potential using many configurations (50,000) without smearing and almost 2000 configurations with APE smearing. With two Fermi GPUs we have achieved an excellent performance of 200x the speed over one CPU, in single precision, around 110 Gflops/s. We also find that, using the Fermi architecture, double precision computations for the static quark-antiquark potential are not much slower (less than 2x slower) than single precision computations.
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.
NASA Astrophysics Data System (ADS)
Sadri, Darius; Sheikh-Jabbari, Mohammad M.
2006-03-01
We consider Script N = 1, D = 4 superconformal U(N)p × q Yang-Mills theories dual to AdS5 × S5/Zp × Zq orbifolds. We construct the dilatation operator of this superconformal gauge theory at one-loop planar level. We demonstrate that a specific sector of this dilatation operator can be thought of as the transfer matrix for a two-dimensional statistical mechanical system, related to an integrable SU(3) ferromagnetic spin chain system, which in turn is equivalent to a 2+1-dimensional string theory where the spatial slices are discretized on a triangular lattice. This is an extension of the SO(6) spin chain picture of Script N = 4 super Yang-Mills theory. We comment on the integrability of this Script N = 1 gauge theory and hence the corresponding three-dimensional statistical mechanical system, its connection to three-dimensional lattice gauge theories, extensions to six-dimensional string theories, AdS/CFT type dualities and finally their construction via orbifolds and brane-box models. In the process we discover a new class of almost-BPS BMN type operators with large engineering dimensions but controllably small anomalous corrections.
The non-Abelian gauge theory of matrix big bangs
NASA Astrophysics Data System (ADS)
O'Loughlin, Martin; Seri, Lorenzo
2010-07-01
We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantization to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t = 0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat space-time also reveals some surprising features.
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.
Dyonic String-Like Solution in a Non-Abelian Gauge Theory with Two Potentials
NASA Astrophysics Data System (ADS)
Tripathi, Buddhi Vallabh; Nandan, Hemwati; Purohit, K. D.
2016-04-01
Axially symmetric dyon solutions of a non-Abelian gauge theory model with two potentials are sought. While seeking axially symmetric (flux tube like solutions) for the model, we stumbled upon an exact solution which represents an infinite string-like dyonic configuration with cylindrical symmetry.
Note on Gauge Theory on M4 × ZN with Auxiliary Field
NASA Astrophysics Data System (ADS)
Maekawa, T.; Taira, H.
1997-06-01
It is shown that the discrete gauge theory on ZN is well formulated with the auxiliary fields due to Chamseddine et al. and Okumura et al. together with the exterior algebra of Dimakis and Müller-Hoissen. A Lagrangian of the Yang-Mills-Higgs fields is also given.
PPN Metric and PPN torsion in the quadratic poincaré gauge theory of gravity
NASA Astrophysics Data System (ADS)
Gladchenko, M. S.; Ponomariov, V. N.; Zhytnikov, V. V.
1990-05-01
The post-newtonian approximation of the quadratic Poincaré gauge theory of gravity is studied. As a result of this investigation the modified PPN metric and PPN torsion is obtained. Post-newtonian equations of motion for different test bodies are analyzed and some restrictions on the parameters of the quadratic lagrangian are found.
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.
The structure of the anomalies of gauge theories in the causal approach
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2002-02-01
We consider the gauge invariance of the standard Yang-Mills model in the framework of the causal approach of Epstein-Glaser and Scharf and determine the generic form of the anomalies. The method used is based on the Epstein-Glaser approach to renormalization theory. In the case of quantum electrodynamics we obtain quite easily the absence of anomalies in all orders.
Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups
NASA Astrophysics Data System (ADS)
Lord, Eric A.
1986-12-01
The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.
On the weak field approximation of the de Sitter gauge theory of gravity
NASA Astrophysics Data System (ADS)
Ma, Meng-Sen; Huang, Chao-Guang
2013-01-01
The weak field approximation of a model of de Sitter gauge theory of gravity is studied in two cases. Without torsion and spin current, the model cannot give the right non-relativistic approximation unless the density is a constant. With small torsion, a satisfactory Newtonian approximation can be obtained.
Pure gauge configurations and solutions to fermionic superstring field theory equations of motion
NASA Astrophysics Data System (ADS)
Aref'eva, I. Ya; Gorbachev, R. V.; Medvedev, P. B.
2009-07-01
Recent results on solutions to the equation of motion of the cubic fermionic string field theory and an equivalence of nonpolynomial and cubic string field theory are discussed. To have the possibility of dealing with both GSO(+) and GSO(-) sectors in the uniform way, a matrix formulation for the NS fermionic SFT is used. In constructions of analytical solutions to open-string field theories truncated pure gauge configurations parametrized by wedge states play an essential role. The matrix form of this parametrization for NS fermionic SFT is presented. Using the cubic open superstring field theory as an example we demonstrate explicitly that for the large parameter of the perturbation expansion these truncated pure gauge configurations give divergent contributions to the equations of motion on the subspace of the wedge states. The perturbation expansion is corrected by adding extra terms that are just those necessary for the equation of motion contracted with the solution itself to be satisfied.
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.
Dunne, Gerald V; Shifman, M; Ünsal, Mithat
2015-05-15
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. PMID:26024159
Anti-De Sitter Space, Thermal Phase Transition, and Confinement in Gauge Theories
NASA Astrophysics Data System (ADS)
Witten, Edward
2014-03-01
The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of N = 4 super Yang-Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement, and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale "holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.
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.
Quantization of integrable systems and a 2d/4d duality
NASA Astrophysics Data System (ADS)
Dorey, Nick; Lee, Sungjay; Hollowood, Timothy J.
2011-10-01
We present a new duality between the F-terms of supersymmetric field theories defined in two-and four-dimensions respectively. The duality relates mathcal{N} = 2 super-symmetric gauge theories in four dimensions, deformed by an Ω-background in one plane, to mathcal{N} = left( {2,2} right) gauged linear σ-models in two dimensions. On the four dimensional side, our main example is mathcal{N} = 2 SQCD with gauge group G = SU( L) and N F = 2 L fundamental flavours. Using ideas of Nekrasov and Shatashvili, we argue that the Coulomb branch of this theory provides a quantization of the classical Heisenberg SL(2) spin chain. Agreement with the standard quantization via the Algebraic Bethe Ansatz implies the existence of an isomorphism between the chiral ring of the 4 d theory and that of a certain two-dimensional theory. The latter can be understood as the worldvolume theory on a surface operator/vortex string probing the Higgs branch of the same 4 d theory. We check the proposed duality by explicit calculation at low orders in the instanton expansion. One striking consequence is that the Seiberg-Witten solution of the 4 d theory is captured by a one-loop computation in two dimensions. The duality also has interesting connections with the AGT conjecture, matrix models and topological string theory where it corresponds to a refined version of the geometric transition.
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.
Dimensional Reduction of Gauge Theories, Spontaneous Compactification and Model Building
NASA Astrophysics Data System (ADS)
Kubyshin, Yura A.; Mourao, Jose M.; Rudolph, Gerd; Volobujev, Igor P.
This monograph presents in detail the reduction method for studying the unification of fundamental actions. The mathematical (differential geometrical) methods make extensive use of Lie Groups and the concept of homogeneous spaces. The main topic of the book is the dimensional reduction of pure Yang-Mills theories. A rather complete analysis of the structure of the scalar field potential is given and a general procedure for solving the equations of spontaneous compactification within Einstein-Yang-Mills systems is presented. The authors also discuss gravity and theories with fermions included and they review attempts to construct realistic models. The book presents the basic ideas and the calculations in detail and should be of interest to researchers and graduate students in mathematical physics.
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.
Energy-Momentum and Angular Momentum in /line{Poincaré Gauge Theory of Gravity
NASA Astrophysics Data System (ADS)
Kawai, T.
1988-04-01
In /line{Poincaré gauge theory of gravity developed in previous papers, we examine energy-momentum and angular momentum for an isolated system by fixing the asymptotic form of the Higgs-type field psi = \\{psi(k}\\) to be psi(k) =~ e((0)k) _{mu}x(mu) + psi((0)k) with constants e((0)k}_{mu) and psi((0)k) . Conservations of energy-momentum and of total angular momentum both follow from the internal /line{Poincaré gauge invariance. The orbital part of the total angular momentum arises from a term, which Kibble-type ``Poincaré gauge'' theory lacks, in the expression for the ``spin'' angular momentum density. This resolves the mystery of the isolated conesrvation of spin in gauge theory of gravity. In the present scheme, the canonical energy-momentum density and the ``orbital angular momentum'' density, introduced by considering coordinate transformations, both turn out to be trivial when they are intergrated over a space-like surface. We need not invoke coordinate transformations to get physical quantities. An alternative asymptotic form of psi is also discussed.
NASA Astrophysics Data System (ADS)
Bershtein, Mikhail; Bonelli, Giulio; Ronzani, Massimiliano; Tanzini, Alessandro
2016-07-01
We provide a contour integral formula for the exact partition function of N = 2 supersymmetric U( N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2∗ theory on {P}^2 for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.
A numerical solution to the local cohomology problem in U(1) chiral gauge theories
NASA Astrophysics Data System (ADS)
Kadoh, Daisuke; Kikukawa, Yoshio
2005-01-01
We consider a numerical method to solve the local cohomology problem related to the gauge anomaly cancellation in U(1) chiral gauge theories. In the cohomological analysis of the chiral anomaly, it is required to carry out the differentiation and the integration of the anomaly with respect to the continuous parameter for the interpolation of the admissible gauge fields. In our numerical approach, the differentiation is evaluated explicitly through the rational approximation of the overlap Dirac operator with Zolotarev optimization. The integration is performed with a Gaussian Quadrature formula, which turns out to show rather good convergence. The Poincaré lemma is reformulated for the finite lattice and is implemented numerically. We compute the current associated with the cohomologically trivial part of the chiral anomaly in two-dimensions and check its locality properties.
Non-linear gauge transformations in D = 10 SYM theory and the BCJ duality
NASA Astrophysics Data System (ADS)
Lee, Seungjin; Mafra, Carlos R.; Schlotterer, Oliver
2016-03-01
Recent progress on scattering amplitudes in super Yang-Mills and super-string theory benefitted from the use of multiparticle superfields. They universally capture tree-level subdiagrams, and their generating series solve the non-linear equations of ten-dimensional super Yang-Mills. We provide simplified recursions for multiparticle superfields and relate them to earlier representations through non-linear gauge transformations of their generating series. Moreover, we discuss the gauge transformations which enforce their Lie symmetries as suggested by the Bern-Carrasco-Johansson duality between color and kine-matics. Another gauge transformation due to Harnad and Shnider is shown to streamline the theta-expansion of multiparticle superfields, bypassing the need to use their recursion relations beyond the lowest components. The findings of this work tremendously simplify the component extraction from kinematic factors in pure spinor superspace.
Nonabelian 2D gauge theories for determinantal Calabi-Yau varieties
NASA Astrophysics Data System (ADS)
Jockers, Hans; Kumar, Vijay; Lapan, Joshua M.; Morrison, David R.; Romo, Mauricio
2012-11-01
The two-dimensional supersymmetric gauged linear sigma model (GLSM) with abelian gauge groups and matter fields has provided many insights into string theory on Calabi-Yau manifolds of a certain type: complete intersections in toric varieties. In this paper, we consider two GLSM constructions with nonabelian gauge groups and charged matter whose infrared CFTs correspond to string propagation on determinantal Calabi-Yau varieties, furnishing another broad class of Calabi-Yau geometries in addition to complete intersections. We show that these two models — which we refer to as the PAX and the PAXY model — are dual descriptions of the same low-energy physics. Using GLSM techniques, we determine the quantum Kähler moduli space of these varieties and find no disagreement with existing results in the literature.
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.; Gardner, S.; Kronfeld, A. S.; Alford, M. G.; Alkofer, R.; Butenschoen, M.; Cohen, T. D.; Erdmenger, J.; et al
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
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; 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 themore » system.« less
Noncommutative gauge theories on {R}_{\\uplambda}^3 : perturbatively finite models
NASA Astrophysics Data System (ADS)
Géré, Antoine; Jurić, Tajron; Wallet, Jean-Christophe
2015-12-01
We show that natural noncommutative gauge theory models on {R}_{\\uplambda}^3 can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of {R}_{\\uplambda}^3 and the components of the gauge invariant 1-form canonical connection. This latter object shows up naturally within the present noncommutative differential calculus. Restricting ourselves to positive actions with covariant coordinates as field variables, a suitable gauge-fixing leads to a family of matrix models with quartic interactions and kinetic operators with compact resolvent. Their perturbative behavior is then studied. We first compute the 2-point and 4-point functions at the one-loop order within a subfamily of these matrix models for which the interactions have a symmetric form. We find that the corresponding contributions are finite. We then extend this result to arbitrary order. We find that the amplitudes of the ribbon diagrams for the models of this subfamily are finite to all orders in perturbation. This result extends finally to any of the models of the whole family of matrix models obtained from the above gauge-fixing. The origin of this result is discussed. Finally, the existence of a particular model related to integrable hierarchies is indicated, for which the partition function is expressible as a product of ratios of determinants.
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.
Yang-Mills field theory in an axial field-strength gauge
NASA Astrophysics Data System (ADS)
Tyburski, Lawrence
1984-02-01
We introduce what we call an axial field-strength gauge as an alternative to the conventional Coulomb gauge in the Yang-Mills field theory. This new gauge does not share the pathologies that were shown to exist in the Coulomb gauge by Gribov and Mandelstam. We apply this new gauge to the calculation, in two special cases, of the energy possessed by sources J1,20 interacting in the presence of a background field produced by a source J30, which is assumed to be of order g-1, in the limit g goes to zero, where g is the coupling constant. In the case in which the charge density J30 consists of two infinite uniform parallel plates bearing charge densities equal in magnitude but opposite in sign, we find that the potential energy possessed by two point particles bearing charge densities J1,20 grows linearly in proportion to the distance between them at large distances when the two particles are separated along a line parallel to the background field. This is a confining potential.
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.
Effective theory of two-dimensional chiral superfluids: Gauge duality and Newton-Cartan formulation
NASA Astrophysics Data System (ADS)
Moroz, Sergej; Hoyos, Carlos
2015-02-01
We present a theory of Galilean-invariant conventional and chiral px±i py fermionic superfluids at zero temperature in two spatial dimensions in terms of a dual gauge theory. Our formulation is general coordinate invariant. The parity-violating effects are encoded in the Wen-Zee term that gives rise to the Hall viscosity and edge current. We show that the relativistic superfluid with the Euler current reduces to the chiral superfluid in the limit c →∞ . Using Newton-Cartan geometry, we construct the covariant formulation of the effective theory and calculate the energy current.
Srivastava, Y.N.; Vaughn, M.T.
1993-02-01
Work done on the following topics is summarized: (1) Coulomb potential in QED on the lattice; (2) Weyl cosmic strings and their consequences; (3) Interference between past and future events in [phi] [yields] K[bar K]; (4) Quantum effects of strong classical electromagnetic fields; (5) Application of computer algebra to calculations in supersymmetry and supergravity; (6) numerical studies of classical scalar [phi][sup 4] field theory and related nonlinear [sigma]-models; (7) Analysis of a cubic model field theory; and, (8) Renormalization group analysis of unified gauge theories.
Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops
NASA Astrophysics Data System (ADS)
Pestun, Vasily
2012-07-01
We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the {N=4} supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure {N=2} and the {N=2^*} supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional {N=2} superconformal gauge theory is treated similarly.
Massive Yang-Mills theory based on the nonlinearly realized gauge group
Bettinelli, D.; Ferrari, R.; Quadri, A.
2008-02-15
We propose a subtraction scheme for a massive Yang-Mills theory realized via a nonlinear representation of the gauge group [here SU(2)]. It is based on the subtraction of the poles in D-4 of the amplitudes, in dimensional regularization, after a suitable normalization has been performed. Perturbation theory is in the number of loops, and the procedure is stable under iterative subtraction of the poles. The unphysical Goldstone bosons, the Faddeev-Popov ghosts, and the unphysical mode of the gauge field are expected to cancel out in the unitarity equation. The spontaneous symmetry breaking parameter is not a physical variable. We use the tools already tested in the nonlinear sigma model: hierarchy in the number of Goldstone boson legs and weak-power-counting property (finite number of independent divergent amplitudes at each order). It is intriguing that the model is naturally based on the symmetry SU(2){sub L} local x SU(2){sub R} global. By construction the physical amplitudes depend on the mass and on the self-coupling constant of the gauge particle and moreover on the scale parameter of the radiative corrections. The Feynman rules are in the Landau gauge.
Phases of a two-dimensional large-N gauge theory on a torus
Mandal, Gautam; Morita, Takeshi
2011-10-15
We consider two-dimensional large N gauge theory with D adjoint scalars on a torus, which is obtained from a D+2-dimensional pure Yang-Mills theory on T{sup D+2} with D small radii. The two-dimensional model has various phases characterized by the holonomy of the gauge field around noncontractible cycles of the 2-torus. We determine the phase boundaries and derive the order of the phase transitions using a method developed in an earlier work (hep-th/0910.4526), which is nonperturbative in the 't Hooft coupling and uses a 1/D expansion. We embed our phase diagram in the more extensive phase structure of the D+2-dimensional Yang-Mills theory and match with the picture of a cascade of phase transitions found earlier in lattice calculations. We also propose a dual gravity system based on a Scherk-Schwarz compactification of a D2 brane wrapped on a 3-torus and find a phase structure which is similar to the phase diagram found in the gauge theory calculation.
Real-Time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks
NASA Astrophysics Data System (ADS)
Pichler, T.; Dalmonte, M.; Rico, E.; Zoller, P.; Montangero, S.
2016-01-01
Tensor network algorithms provide a suitable route for tackling real-time-dependent problems in lattice gauge theories, enabling the investigation of out-of-equilibrium dynamics. We analyze a U(1) lattice gauge theory in (1 +1 ) dimensions in the presence of dynamical matter for different mass and electric-field couplings, a theory akin to quantum electrodynamics in one dimension, which displays string breaking: The confining string between charges can spontaneously break during quench experiments, giving rise to charge-anticharge pairs according to the Schwinger mechanism. We study the real-time spreading of excitations in the system by means of electric-field and particle fluctuations. We determine a dynamical state diagram for string breaking and quantitatively evaluate the time scales for mass production. We also show that the time evolution of the quantum correlations can be detected via bipartite von Neumann entropies, thus demonstrating that the Schwinger mechanism is tightly linked to entanglement spreading. To present a variety of possible applications of this simulation platform, we show how one could follow the real-time scattering processes between mesons and the creation of entanglement during scattering processes. Finally, we test the quality of quantum simulations of these dynamics, quantifying the role of possible imperfections in cold atoms, trapped ions, and superconducting circuit systems. Our results demonstrate how entanglement properties can be used to deepen our understanding of basic phenomena in the real-time dynamics of gauge theories such as string breaking and collisions.
Spontaneous symmetry breaking, and strings defects in hypercomplex gauge field theories
NASA Astrophysics Data System (ADS)
Cartas-Fuentevilla, R.; Meza-Aldama, O.
2016-02-01
Inspired by the appearance of split-complex structures in the dimensional reduction of string theory, and in the theories emerging as byproducts, we study the hypercomplex formulation of Abelian gauge field theories by incorporating a new complex unit to the usual complex one. The hypercomplex version of the traditional Mexican hat potential associated with the U(1) gauge field theory, corresponds to a hybrid potential with two real components, and with U(1)× SO(1,1) as symmetry group. Each component corresponds to a deformation of the hat potential, with the appearance of a new degenerate vacuum. Hypercomplex electrodynamics will show novel properties, such as spontaneous symmetry breaking scenarios with running masses for the vectorial and scalar Higgs fields, and such as Aharonov-Bohm type strings defects as exact solutions; these topological defects may be detected only by quantum interference of charged particles through gauge invariant loop integrals. In a particular limit, the hyperbolic electrodynamics does not admit topological defects associated with continuous symmetries.
Valla, Jeffrey; Ceci, Stephen J
2011-03-01
Brain organization theory posits a cascade of physiological and behavioral changes initiated and shaped by prenatal hormones. Recently, this theory has been associated with outcomes including gendered toy preference, 2D/4D digit ratio, personality characteristics, sexual orientation, and cognitive profile (spatial, verbal, and mathematical abilities). We examine the evidence for this claim, focusing on 2D/4D and its putative role as a biomarker for organizational features that influence cognitive abilities/interests predisposing males toward mathematically and spatially intensive careers. Although massive support exists for early brain organization theory overall, there are myriad inconsistencies, alternative explanations, and outright contradictions that must be addressed while still taking the entire theory into account. Like a fractal within the larger theory, the 2D/4D hypothesis mirrors this overall support on a smaller scale while likewise suffering from inconsistencies (positive, negative, and sex-dependent correlations), alternative explanations (2D/4D related to spatial preferences rather than abilities per se), and contradictions (feminine 2D/4D in men associated with higher spatial ability). Using the debate over brain organization theory as the theoretical stage, we focus on 2D/4D evidence as an increasingly important player on this stage, a demonstrative case in point of the evidential complexities of the broader debate, and an increasingly important topic in its own right. PMID:22164187
Valla, Jeffrey; Ceci, Stephen J.
2011-01-01
Brain organization theory posits a cascade of physiological and behavioral changes initiated and shaped by prenatal hormones. Recently, this theory has been associated with outcomes including gendered toy preference, 2D/4D digit ratio, personality characteristics, sexual orientation, and cognitive profile (spatial, verbal, and mathematical abilities). We examine the evidence for this claim, focusing on 2D/4D and its putative role as a biomarker for organizational features that influence cognitive abilities/interests predisposing males toward mathematically and spatially intensive careers. Although massive support exists for early brain organization theory overall, there are myriad inconsistencies, alternative explanations, and outright contradictions that must be addressed while still taking the entire theory into account. Like a fractal within the larger theory, the 2D/4D hypothesis mirrors this overall support on a smaller scale while likewise suffering from inconsistencies (positive, negative, and sex-dependent correlations), alternative explanations (2D/4D related to spatial preferences rather than abilities per se), and contradictions (feminine 2D/4D in men associated with higher spatial ability). Using the debate over brain organization theory as the theoretical stage, we focus on 2D/4D evidence as an increasingly important player on this stage, a demonstrative case in point of the evidential complexities of the broader debate, and an increasingly important topic in its own right. PMID:22164187
Strong-weak coupling duality in non-abelian gauge theories
NASA Astrophysics Data System (ADS)
Ferrari, Frank
1997-05-01
This is a general introduction to electric-magnetic duality in non-abelian gauge theories. In chapter I, I review the general ideas which led in the late 70s to the idea of electric/magnetic duality in quantum field theory. In chapters II and III, I focus mainly on N=2 supersymmetric theories. I present the lagrangians and explain in more or less detail the non-renormalization theorems, rigid special geometry, supersymmetric instanton calculus, charge fractionization, the semiclassical theory of monopoles, duality in Maxwell theory and the famous Seiberg-Witten solution. I discuss various physical applications, as electric charge confinement, chiral symmetry breaking or non-trivial superconformal theories in four dimensions. In Section II.3 new material is presented, related to the computation of the eta invariant of certain Dirac operators coupled minimally to non-trivial monopole field configurations. I explain how these invariants can be obtained exactly by a one-loop calculation in a suitable N=2 supersymmetric gauge theory. This is an unexpected application of the holomorphy properties of N=2 supersymmetry, and constitutes a tremendous simplification of the usual computation. An expanded version of these new results will be published soon.
Real forms of extended Kac-Moody symmetries and higher spin gauge theories
NASA Astrophysics Data System (ADS)
Henneaux, Marc; Kleinschmidt, Axel; Nicolai, Hermann
2012-07-01
We consider the relation between higher spin gauge fields and real Kac-Moody Lie algebras. These algebras are obtained by double and triple extensions of real forms {{g}_0} of the finite-dimensional simple algebras {{g}} arising in dimensional reductions of gravity and supergravity theories. Besides providing an exhaustive list of all such algebras, together with their associated involutions and restricted root diagrams, we are able to prove general properties of their spectrum of generators with respect to a decomposition of the triple extension of {{g}_0} under its gravity subalgebra {{gl}(D,{R})} . These results are then combined with known consistent models of higher spin gauge theory to prove that all but finitely many generators correspond to non-propagating fields and there are no higher spin fields contained in the Kac-Moody algebra.
On higher derivatives in 3D gravity and higher-spin gauge theories
Bergshoeff, Eric A. Hohm, Olaf Townsend, Paul K.
2010-05-15
The general second-order massive field equations for arbitrary positive integer spin in three spacetime dimensions, and their 'self-dual' limit to first-order equations, are shown to be equivalent to gauge-invariant higher-derivative field equations. We recover most known equivalences for spins 1 and 2, and find some new ones. In particular, we find a non-unitary massive 3D gravity theory with a 5th order term obtained by contraction of the Ricci and Cotton tensors; this term is part of an N=2 super-invariant that includes the 'extended Chern-Simons' term of 3D electrodynamics. We also find a new unitary 6th order gauge theory for 'self-dual' spin 3.
On the relation between gauge theories, moving frames, fiber bundles, and parastatistics
NASA Astrophysics Data System (ADS)
Macrae, Kenneth I.
1985-07-01
We write down standard gauge field theory in a basis-independent manner using the ideas of moving frames (fiber bundles). Then we describe the construction of frames for gauging parafields. To do this (frames) bases for fields are replaced by Clifford matrices. These matrices are in one-to-one correspondence with the number of spinor components. We briefly examine the objects upon which they can act (through matrix multiplication on the left). These objects bear the same relations to spinors that spinors do to vectors. Finally, we show how to construct a set of inner products for the parabases that yield the same action and n-point functions as in the standard field theory.
Integrand oxidation and one-loop colour-dual numerators in {N}=4 gauge theory
NASA Astrophysics Data System (ADS)
Bjerrum-Bohr, N. Emil J.; Dennen, Tristan; Monteiro, Ricardo; O'Connell, Donal
2013-07-01
We present a systematic method to determine BCJ numerators for one-loop amplitudes that explores the global constraints on the loop momentum dependence. We apply this method to amplitudes in {N}=4 gauge theory, working out detailed examples up to seven points in both the MHV and the NMHV sectors. We see no obstruction to the application of our method to higher point one-loop amplitudes. The structure of Jacobi identities between BCJ numerators is seen to be closely connected to that of algebraic integrand reductions. We discuss the consequences for one-loop {N}=8 supergravity amplitudes obtained through the double copy prescription. Moreover, in the MHV sector, we show how to obtain simple BCJ box numerators using a relationship with amplitudes in self-dual gauge theory. We also introduce simpler trace-type formulas for integrand reductions.
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.
Post-Newtonian effects in the quadratic Poincaré gauge theory of gravitation
NASA Astrophysics Data System (ADS)
Gladchenko, M. S.; Zhytnikov, V. V.
1994-10-01
The post-Newtonian approximation of the Poincaré gauge theory (PGT) of gravitation with an arbitrary Lagrangian is calculated. The constraints on the parameters of the PGT which follow from light deflection and retardation experiments and composition-independent fifth-force data are obtained. It is shown that modern experimental data cannot rule out the existence of massive torsion particles with both large and very small masses.
Instanton calculus and nonperturbative relations in N=2 supersymmetric gauge theories
Fucito, F.; Travaglini, G.
1997-01-01
Using instanton calculus we check, in the weak coupling region, the nonperturbative relation {l_angle}Tr{phi}{sup 2}{r_angle}=i{pi}[ F{minus}(a/2){partial_derivative}{partial_derivative}a] obtained for a N=2 globally supersymmetric gauge theory. Our computations are performed for instantons of winding number k, up to k=2, and turn out to agree with previous nonperturbative results. {copyright} {ital 1997} {ital The American Physical Society}
Measuring topological charge in monte carlo simulation of SU( N) lattice gauge theories
NASA Astrophysics Data System (ADS)
Moriarty, K. J. M.; Teper, M.
1986-09-01
We describe a numerical method for measuring topological charge in SU( N) lattice gauge theories, and we outline the implementation of this method on a CDC CYBER 205. We estimate the CPU requirements of a usefully accurate calculation of the low and high temperature properties of the SU(3) topological susceptibility, Xt , which controls the mass splitting between the η particle and the pseudoscalar octet of Goldstone bosons.
Wilson loop calculations in four-dimensional lattice gauge theory on the CDC cyber 205
NASA Astrophysics Data System (ADS)
Barkai, D.; Creutz, M.; Moriarty, K. J. M.
1983-07-01
Pure SU(4) gauge theory is simulated by Monte Carlo methods on an 8 4 lattice. The method of Metropolis et al. is used to equilibriate the space-time lattice. All Wilson loops up to size 4×4 are calculated. Because of memory requirements we work on the 2 Mword CDC CYBER 205 at Colorado State University and take full advantage of the parallel processing capabilities of this vector machine.
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.
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.
Gravity as an internal Yang-Mills gauge field theory of the Poincaré group.
NASA Astrophysics Data System (ADS)
Hennig, Jörg; Nitsch, Jürgen
1981-10-01
In the framework of affine bundles we present gravity as an “internal” gauge field theory of the Poincaré group. The resulting geometry is a Riemann-Cartan space-time carrying torsion and curvature. In order to admit a nontrivial action of the translation group we formally extend the matter Lagrangian to affine field variables. Finally, we establish the relation of our approach with the formalism of Hehl et al.
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.
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.
Global asymmetry of many-qubit correlations: A lattice-gauge-theory approach
NASA Astrophysics Data System (ADS)
Williamson, Mark S.; Ericsson, Marie; Johansson, Markus; Sjöqvist, Erik; Sudbery, Anthony; Vedral, Vlatko
2011-09-01
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.
Dualities, Twists, and Gauge Theories with Non-Constant Non-Commutativity
NASA Astrophysics Data System (ADS)
Hashimoto, Akikazu
2005-01-01
We study the world volume theory of D3-branes wrapping the Melvin universe supported by background NSNS B-field. In the appropriate decoupling limit, the open string dynamics is that of non-commutative guage field theory with non-constant non-commutativity. We identify this model as a simple Melvin twist of flat D3 branes. Along similar lines, one recognizes the model of Hashimoto and Sethi as being the Melvin null twist, and the model of Dolan and Nappi as being the null Melvin twist, of the flat D3-brane. This construction therefore offers a unified perspective on most of the known explicit constructions of non-commutative gauge theories as a decoupled theory of D-branes in a B-field background. We also describe the world volume theory on the D3-brane in a Melvin universe which is decaying via the nucleation of monopole anti-monopole pair.
A chiral SU( N) gauge theory and its non-chiral Spin(8) dual
NASA Astrophysics Data System (ADS)
Pouliot, P.; Strassler, M. J.
1996-02-01
We study supersymmetric SU( N - 4) gauge theories with a symmetric tensor and N antifundamental representations. The theory with W = 0 has a dual description in terms of a non-chiral Spin(8) theory with one spinor and N vectors. This duality flows to the SO( N) duality of Seiberg and to a duality proposed by one of us. It also flows to dualities for a number of Spin( m) theories, m ≤ 8. For N = 6, when an N = 2 SUSY superpotential is added, the singularities of Seiberg and Witten are recovered. For N ≤ 6, a mass for the spinor generates the branches of SO(8) theories found by Intriligator and Seiberg. Other phenomena include a classical constraint mapped to an anomaly equation under duality and an intricate consistency check on the renormalization group flow.
Oegetbil, O.
2007-03-15
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){sub 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){sub 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.
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.
Model independent determination of the gluon condensate in four dimensional SU(3) gauge theory.
Bali, Gunnar S; Bauer, Clemens; Pineda, Antonio
2014-08-29
We determine the nonperturbative gluon condensate of four-dimensional SU(3) gauge theory in a model-independent way. This is achieved by carefully subtracting high-order perturbation theory results from nonperturbative lattice QCD determinations of the average plaquette. No indications of dimension-two condensates are found. The value of the gluon condensate turns out to be of a similar size as the intrinsic ambiguity inherent to its definition. We also determine the binding energy of a B meson in the heavy quark mass limit. PMID:25215978
On Algebraic Singularities, Finite Graphs and D-Brane Gauge Theories: A String Theoretic Perspective
NASA Astrophysics Data System (ADS)
He, Yang-Hui
2002-09-01
In this writing we shall address certain beautiful inter-relations between the construction of 4-dimensional supersymmetric gauge theories and resolution of algebraic singularities, from the perspective of String Theory. We review in some detail the requisite background in both the mathematics, such as orbifolds, symplectic quotients and quiver representations, as well as the physics, such as gauged linear sigma models, geometrical engineering, Hanany-Witten setups and D-brane probes. We investigate aspects of world-volume gauge dynamics using D-brane resolutions of various Calabi-Yau singularities, notably Gorenstein quotients and toric singularities. Attention will be paid to the general methodology of constructing gauge theories for these singular backgrounds, with and without the presence of the NS-NS B-field, as well as the T-duals to brane setups and branes wrapping cycles in the mirror geometry. Applications of such diverse and elegant mathematics as crepant resolution of algebraic singularities, representation of finite groups and finite graphs, modular invariants of affine Lie algebras, etc. will naturally arise. Various viewpoints and generalisations of McKay's Correspondence will also be considered. The present work is a transcription of excerpts from the first three volumes of the author's PhD thesis which was written under the direction of Prof. A. Hanany - to whom he is much indebted - at the Centre for Theoretical Physics of MIT, and which, at the suggestion of friends, he posts to the ArXiv pro hac vice; it is his sincerest wish that the ensuing pages might be of some small use to the beginning student.
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.
NASA Astrophysics Data System (ADS)
Fulp, R. O.; Davis, W. R.; Norris, L. K.
1986-01-01
The bundle structures required by volume-preserving and related projective properties are developed and discussed in the context ofA(4) gauge theories which may be taken as the proper framework for Poincaré gauge theories. The results of this paper include methods for extending both tensors and connections to a principal fiber bundle havingG1(4,R)xG1(4,R) as its structure group. This bundle structure is shown to be a natural arena for the generalized (±) covariant differentiation utilized by Einstein for his extended gravitational theories involving nonsymmetric connections. In particular, it is shown that this generalized (±) covariant differentiation is actually a special case of ordinary covariant differentiation with respect to a connection on theG1(4,R) xG1(4,R) bundle. These results are discussed in relation to certain properties of generalized gravitational theories based on a nonsymmetric connection which include the metric affine theories of Hehl et al. and the general requirement that it should be possible to formulate well-defined local conservation laws. In terms of the extended bundle structure considered in this paper, it is found that physically distinct particle number type conservation expressions could exist for certain given types of matter currents.
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
Planck-scale induced left-right gauge theory at LHC and experimental tests
NASA Astrophysics Data System (ADS)
Parida, M. K.; Sahoo, Biswonath
2016-05-01
Recent measurements at LHC have inspired searches for TeV scale left-right gauge theory originating from grand unified theories. We show that inclusion of Planck-scale induced effects due to dim . 5 operator not only does away with all the additional intermediate symmetries, but also it predicts the minimal set of light Higgs scalars tailored after neutrino masses and dilepton, or trilepton signals. The heavy-light neutrino mixings are predicted from charged fermion mass fits in SO (10) and LFV constraints which lead to new predictions for dilepton or trilepton production signals. Including fine-structure constant matching and two-loop, and threshold effects predict MWR =g2R10 4.3 ± 1.5 ± 0.2 GeV and proton lifetime τp =10 36.15 ± 5.8 ± 0.2 yrs with WR gauge boson coupling g2R = 0.56- 0.57. Predictions on lepton flavour and lepton number violations are accessible to ongoing experiments. Current CMS data on di-electron excess at √{ s} = 8 TeV are found to be consistent with WR gauge boson mass MWR ≥ 1.9- 2.2 TeV which also agrees with the values obtained from dijet resonance production data. We also discuss plausible explanations for diboson production excesses observed at LHC and make predictions expected at √{ s} = 14 TeV.
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.
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. PMID:27419560
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.
Z2 gauge theory description of the Mott transition in infinite dimensions
NASA Astrophysics Data System (ADS)
Žitko, Rok; Fabrizio, Michele
2015-06-01
The infinite-dimensional half-filled Hubbard model can be mapped exactly with no additional constraint onto a model of free fermions coupled in a Z2 gauge-invariant manner to auxiliary Ising spins in a transverse field. In this slave-spin representation, the zero-temperature insulator-to-metal transition translates into spontaneous breaking of the local Z2 gauge symmetry, which is not forbidden in infinite dimensions, thus endowing the Mott transition of an order parameter that is otherwise elusive in the original fermion representation. We demonstrate this interesting scenario by exactly solving the effective spin-fermion model by dynamical mean-field theory both at zero and at finite temperature.
Density of states and Fisher's zeros in compact U(1) pure gauge theory
NASA Astrophysics Data System (ADS)
Bazavov, A.; Berg, B. A.; Du, Daping; Meurice, Y.
2012-03-01
We present high-accuracy calculations of the density of states using multicanonical methods for lattice gauge theory with a compact gauge group U(1) on 44, 64, and 84 lattices. We show that the results are consistent with weak and strong coupling expansions. We present methods based on Chebyshev interpolations and Cauchy theorem to find the (Fisher’s) zeros of the partition function in the complex β=1/g2 plane. The results are consistent with reweighting methods whenever the latter are accurate. We discuss the volume dependence of the imaginary part of the Fisher’s zeros, the width and depth of the plaquette distribution at the value of β where the two peaks have equal height. We discuss strategies to discriminate between first- and second-order transitions and explore them with data at larger volume but lower statistics. Higher statistics and even larger lattices are necessary to draw strong conclusions regarding the order of the transition.
Gauge theories of partial compositeness: scenarios for Run-II of the LHC
NASA Astrophysics Data System (ADS)
Ferretti, Gabriele
2016-06-01
We continue our investigation of gauge theories in which the Higgs boson arises as a pseudo-Nambu-Goldstone boson (pNGB) and top-partners arise as bound states of three hyperfermions. All models have additional pNGBs in their spectrum that should be accessible at LHC. We analyze the patterns of symmetry breaking and present all relevant couplings of the pNGBs with the gauge fields. We discuss how vacuum misalignment and a mass for the pNGBs is generated by a loop-induced potential. Finally, we paint a very broad, qualitative, picture of the kind of experimental signatures these models give rise to, setting the stage for further analysis.
NASA Astrophysics Data System (ADS)
Wen, Xiao-Gang
2013-11-01
The standard model is a chiral gauge theory where the gauge fields couple to the right-hand and the left-hand fermions differently. The standard model is defined perturbatively and describes all elementary particles (except gravitons) very well. However, for a long time, we do not know if we can have a non-perturbative definition of the standard model as a Hamiltonian quantum mechanical theory. Here we propose a way to give a modified standard model (with 48 two-component Weyl fermions) a non-perturbative definition by embedding the modified standard model into an SO (10) chiral gauge theory. We show that the SO (10) chiral gauge theory can be put on a lattice (a 3D spatial lattice with a continuous time) if we allow fermions to interact. Such a non-perturbatively defined standard model is a Hamiltonian quantum theory with a finite-dimensional Hilbert space for a finite space volume. More generally, using the defining connection between gauge anomalies and the symmetry-protected topological orders, one can show that any truly anomaly-free chiral gauge theory can be non-perturbatively defined by putting it on a lattice in the same dimension.
Defects in Chern-Simons theory, gauged WZW models on the brane, and level-rank duality
NASA Astrophysics Data System (ADS)
Armoni, Adi; Niarchos, Vasilis
2015-07-01
We consider Hanany-Witten setups of 3- and 5-branes in type IIB string theory that realize , (2, 0) and (1, 1) gauged WZW models in 1 + 1 dimensions. The gauged WZW models arise as theories residing on the boundary of D3 branes ending on D5 branes. From the point of view of low energy dynamics the D5 branes play the role of half-BPS co-dimension-1 defects (domain walls) in 3d or Chern-Simons theories. Extending the analysis of previous works on the subject of boundary conditions in (supersymmetric) Chern-Simons theory, we discuss in detail the field theory construction of a large class of Chern-Simons domain wall theories and its embedding in open string dynamics. Finally, we exhibit how standard brane moves that result to 3d Seiberg duality, translate in our setup to a generalized level-rank duality in gauged-WZW models.
Cartan's Spiral Staircase in Physics and, in Particular, in the Gauge Theory of Dislocations
NASA Astrophysics Data System (ADS)
Lazar, Markus; Hehl, Friedrich W.
2010-10-01
In 1922, Cartan introduced in differential geometry, besides the Riemannian curvature, the new concept of torsion. He visualized a homogeneous and isotropic distribution of torsion in three dimensions (3d) by the “helical staircase”, which he constructed by starting from a 3d Euclidean space and by defining a new connection via helical motions. We describe this geometric procedure in detail and define the corresponding connection and the torsion. The interdisciplinary nature of this subject is already evident from Cartan’s discussion, since he argued—but never proved—that the helical staircase should correspond to a continuum with constant pressure and constant internal torque. We discuss where in physics the helical staircase is realized: (i) In the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d theories of gravity, namely (a) in 3d Einstein-Cartan gravity—this is Cartan’s case of constant pressure and constant intrinsic torque—and (b) in 3d Poincaré gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the gauge field theory of dislocations of Lazar et al., as we prove for the first time by arranging a suitable distribution of screw dislocations. Our main emphasis is on the discussion of dislocation field theory.
Topics in phenomenology of unified gauge theories of weak, electromagnetic, and strong interactions
Kang, Y.S.
1982-11-01
Three phenomenological analyses on the current unification theories of elementary particle interactions are presented. In Chapter I, the neutral current phenomenology of a class of supersymmetric SU(2) x U(1) x U tilde(1) models is analyzed. A model with the simplest fermion and Higgs structure allowing a realistic mass spectrum is considered first. Its neutral current sector is parametrized in terms of two mixing angles and the strength of the new U tilde(1) interactions. Expressions for low-energy model-independent parameters are derived and compared with those of the standard model. Bounds on the neutral gauge boson masses are obtained from the data for various neutrino interactions, eD scattering, and the asymmetry in e/sup +/e/sup -/ ..-->.. ..mu../sup +/..mu../sup -/. In Chapter II, the evolution of fermion mass in grand unified theories is reexamined. In particular, the question of gauge invariance of mass ratios in left-right asymmetric theories is considered. A simple expression is derived for the evolution of the Higgs-fermion-fermion coupling which essentially governs the scale dependence of fermion mass. At the one loop level the expression is gauge invariant and involves only the representation content of left- and right-handed fermions but not that of Higgs. The corresponding expression for supersymmetric theories is also given. In Chapter III, the production and the subsequent decays of a heavy lepton pair L/sup + -/ near the Z peak in e/sup +/e/sup -/ annihilation are considered as a test of the standard model. The longitudinal polarization is derived from the spin-dependent production cross-section, and the decays L ..-->.. ..pi.. nu and L ..-->.. l nu nu are used as helicity analyzers.
Probability distribution of the index in gauge theory on 2d non-commutative geometry
NASA Astrophysics Data System (ADS)
Aoki, Hajime; Nishimura, Jun; Susaki, Yoshiaki
2007-10-01
We investigate the effects of non-commutative geometry on the topological aspects of gauge theory using a non-perturbative formulation based on the twisted reduced model. The configuration space is decomposed into topological sectors labeled by the index ν of the overlap Dirac operator satisfying the Ginsparg-Wilson relation. We study the probability distribution of ν by Monte Carlo simulation of the U(1) gauge theory on 2d non-commutative space with periodic boundary conditions. In general the distribution is asymmetric under ν mapsto -ν, reflecting the parity violation due to non-commutative geometry. In the continuum and infinite-volume limits, however, the distribution turns out to be dominated by the topologically trivial sector. This conclusion is consistent with the instanton calculus in the continuum theory. However, it is in striking contrast to the known results in the commutative case obtained from lattice simulation, where the distribution is Gaussian in a finite volume, but the width diverges in the infinite-volume limit. We also calculate the average action in each topological sector, and provide deeper understanding of the observed phenomenon.
Abelian gauge symmetries and proton decay in global F-theory GUTs
Grimm, Thomas W.; Weigand, Timo
2010-10-15
The existence of Abelian gauge symmetries in four-dimensional F-theory compactifications depends on the global geometry of the internal Calabi-Yau four-fold and has important phenomenological consequences. We study conceptual and phenomenological aspects of such U(1) symmetries along the Coulomb and the Higgs branch. As one application we examine Abelian gauge factors arising after a certain global restriction of the Tate model that goes beyond a local spectral cover analysis. In SU(5) grand unified theory (GUT) models this mechanism enforces a global U(1){sub X} symmetry that prevents dimension-4 proton decay and allows for an identification of candidate right-handed neutrinos. We invoke a detailed account of the singularities of Calabi-Yau four-folds and their mirror duals starting from an underlying E{sub 8} and E{sub 7}xU(1) enhanced Tate model. The global resolutions and deformations of these singularities can be used as the appropriate framework to analyze F-theory GUT models.
Classifying BPS states in supersymmetric gauge theories coupled to higher derivative chiral models
NASA Astrophysics Data System (ADS)
Nitta, Muneto; Sasaki, Shin
2015-06-01
We study N =1 supersymmetric gauge theories coupled with higher derivative chiral models in four dimensions in the off-shell superfield formalism. We solve the equation of motion for the auxiliary fields and find two distinct on-shell structures of the Lagrangian that we call the canonical and noncanonical branches characterized by zero and nonzero auxiliary fields, respectively. We classify Bogomol'nyi-Prasado-Sommerfield (BPS) states of the models in Minkowski and Euclidean spaces. In Minkowski space, we find Abelian and non-Abelian vortices, vortex lumps (or gauged lumps with fractional lump charges) as 1 /2 BPS states in the canonical branch, and higher derivative generalization of vortices and vortex-(BPS)baby Skyrmions (or gauged BPS baby Skyrmions with fractional baby Skyrme charges) as 1 /4 BPS states in the noncanonical branch. In four-dimensional Euclidean space, we find Yang-Mills instantons trapped inside a non-Abelian vortex, intersecting vortices, and intersecting vortex-(BPS)baby Skyrmions as 1 /4 BPS states in the canonical branch but no BPS states in the noncanonical branch other than those in the Minkowski space.
Global Constraints on Anomalous Triple Gauge Couplings in the Effective Field Theory Approach
NASA Astrophysics Data System (ADS)
Falkowski, Adam; González-Alonso, Martín; Greljo, Admir; Marzocca, David
2016-01-01
We present a combined analysis of LHC Higgs data (signal strengths) together with LEP-2 W W production measurements. To characterize possible deviations from the standard model (SM) predictions, we employ the framework of an effective field theory (EFT) where the SM is extended by higher-dimensional operators suppressed by the mass scale of new physics Λ . The analysis is performed consistently at the order Λ-2 in the EFT expansion keeping all the relevant operators. While the two data sets suffer from flat directions, together they impose stringent model-independent constraints on the anomalous triple gauge couplings.
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.
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.
Chiral symmetry restoration at large chemical potential in strongly coupled SU(N) gauge theories
Tomboulis, E. T.
2013-12-15
We show that at sufficiently large chemical potential SU(N) lattice gauge theories in the strong coupling limit with staggered fermions are in a chirally symmetric phase. The proof employs a polymer cluster expansion which exploits the anisotropy between timelike and spacelike directions in the presence of a quark chemical potential μ. The expansion is shown to converge in the infinite volume limit at any temperature for sufficiently large μ. All expectations of chirally non-invariant local fermion operators vanish identically, or, equivalently, their correlations cluster exponentially, within the expansion. The expansion itself may serve as a computational tool at large μ and strong coupling.
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.
NASA Astrophysics Data System (ADS)
Braguta, V. V.; Buividovich, P. V.; Chernodub, M. N.; Kotov, A. Yu.; Polikarpov, M. I.
2012-12-01
Using numerical simulations of quenched SU (2) gauge theory we demonstrate that an external magnetic field leads to spontaneous generation of quark condensates with quantum numbers of electrically charged ρ mesons if the strength of the magnetic field exceeds the critical value eBc = 0.927 (77) GeV2 or Bc = (1.56 ± 0.13) ṡ1016 Tesla. The condensation of the charged ρ mesons in strong magnetic field is a key feature of the magnetic-field-induced electromagnetic superconductivity of the vacuum.
Global Constraints on Anomalous Triple Gauge Couplings in the Effective Field Theory Approach.
Falkowski, Adam; González-Alonso, Martín; Greljo, Admir; Marzocca, David
2016-01-01
We present a combined analysis of LHC Higgs data (signal strengths) together with LEP-2 WW production measurements. To characterize possible deviations from the standard model (SM) predictions, we employ the framework of an effective field theory (EFT) where the SM is extended by higher-dimensional operators suppressed by the mass scale of new physics Λ. The analysis is performed consistently at the order Λ(-2) in the EFT expansion keeping all the relevant operators. While the two data sets suffer from flat directions, together they impose stringent model-independent constraints on the anomalous triple gauge couplings. PMID:26799011
Infrared fixed point in SU(2) gauge theory with adjoint fermions
DeGrand, Thomas; Shamir, Yigal; Svetitsky, Benjamin
2011-04-01
We apply Schroedinger-functional techniques to the SU(2) lattice gauge theory with N{sub f}=2 flavors of fermions in the adjoint representation. Our use of hypercubic smearing enables us to work at stronger couplings than did previous studies, before encountering a critical point and a bulk phase boundary. Measurement of the running coupling constant gives evidence of an infrared fixed point g{sub *} where 1/g{sub *}{sup 2}=0.20(4)(3). At the fixed point, we find a mass anomalous dimension {gamma}{sub m}(g{sub *})=0.31(6).
A highly optimized vectorized code for Monte Carlo simulations of Su(3) lattice gauge theories
NASA Astrophysics Data System (ADS)
Barkai, D.; Moriarty, K. J. M.; Rebbi, C.
1984-04-01
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 μs/link for 8 hits per iteration (40.9 μs for 10 hits) or 101.5 MFLOPS.
Spin transistor action from Onsager reciprocity and SU(2) gauge theory
NASA Astrophysics Data System (ADS)
Adagideli, Inanc
2012-02-01
We construct a local gauge transformation to show how a generic, nonhomogeneous SU(2) spin-orbit Hamiltonian reduces to two U(1) Hamiltonians for spinless fermions at opposite magnetic fields, to leading order in the spin-orbit strength. Using an Onsager reciprocity relation, we show how the resulting spin conductance vanishes in a two-terminal setup, and how it is turned on by either weakly breaking time-reversal symmetry by applied magnetic fields or opening additional transport terminals. We numerically illustrate our theory for diffusive conductors, ballistic mesoscopic cavities as well as Aharonov-Bohm rings.
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.
Correlation functions of the energy-momentum tensor in SU(2) gauge theory at finite temperature
Huebner, K.; Pica, C.; Karsch, F.
2008-11-01
We calculate correlation functions of the energy-momentum tensor in the vicinity of the deconfinement phase transition of (3+1)-dimensional SU(2) gauge theory and discuss their critical behavior in the vicinity of the second order deconfinement transition. We show that correlation functions of the trace of the energy-momentum tensor diverge uniformly at the critical point in proportion to the specific heat singularity. Correlation functions of the pressure, on the other hand, stay finite at the critical point. We discuss the consequences of these findings for the analysis of transport coefficients, in particular, the bulk viscosity, in the vicinity of a second order phase transition point.
A relation between gauge-invariant formulation of QCD and string theory in two dimensions
NASA Astrophysics Data System (ADS)
Nakamura, Akihiro; Odaka, Kazuhiko
1982-08-01
We have studied the explicit relation between the gauge-invariant path-ordered operator (POO) and a string field in two dimensions. For this purpose, we use the hamiltonian of two-dimensional quantum chromodynamics reformulated in terms of POO. POO is expanded in a power series of a non-local bosonic operator. We show that such a bosonic operator describes Bars and Hanson's free string field in the second quantization. Interactions among bosonic operators are treated in perturbation theory. The coupling constant is proportional to 1/√ Nc.
Renormalization group and phase transitions in spin, gauge, and QCD like theories
NASA Astrophysics Data System (ADS)
Liu, Yuzhi
In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG). We use the two dimensional nearest neighbor Ising model to introduce many conventional yet important concepts. We then generalize the model to Dyson's hierarchical model (HM), which has rich phase properties depending on the strength of the interaction. The partition function zeros (Fisher zeros) of the HM model in the complex temperature plane is calculated and their connection with the complex RG flows is discussed. The two lattice matching method is used to construct both the complex RG flows and calculate the discrete beta functions. The motivation of calculating the discrete beta functions for various HM models is to test the matching method and to show how physically relevant fixed points emerge from the complex domain. We notice that the critical exponents calculated from the HM depend on the blocking parameter b. This motivated us to analyze the connection between the discrete and continuous RG transformation. We demonstrate numerical calculations of the ERG equations. We discuss the relation between Litim and Wilson-Polchinski equation and the effect of the cut-off functions in the ERG calculation. We then apply methods developed in the spin models to more complicated and more physically relevant lattice gauge theories and lattice quantum chromodynamics (QCD) like theories. Finite size scaling (FSS) technique is used to analyze the Binder cumulant of the SU(2) lattice gauge model. We calculate the critical exponent nu and omega of the model and show that it is in the same universality class as the three dimensional Ising model. Motivated by the walking technicolor theory, we study the strongly coupled gauge theories with conformal or near conformal properties. We compare
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.
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.
Deconfinement phase transition in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
NASA Astrophysics Data System (ADS)
Reinhardt, H.; Campagnari, D.; Heffner, J.
2014-04-01
Recent results obtained for the deconfinement phase transition within the Hamiltonian approach to Yang-Mills theory are reviewed. Assuming a quasiparticle picture for the grand canonical gluon ensemble the thermal equilibrium state is found by minimizing the free energy with respect to the quasi-gluon energy. The deconfinement phase transition is accompanied by a drastic change of the infrared exponents of the ghost and gluon propagators. Above the phase transition the ghost form factor remains infrared divergent but its infrared exponent is approximately halved. The gluon energy being infrared divergent in the confined phase becomes infrared finite in the deconfined phase. Furthermore, the effective potential of the order parameter for confinement is calculated for SU(N) Yang-Mills theory in the Hamiltonian approach by compactifying one spatial dimension and using a background gauge fixing. In the simplest truncation, neglecting the ghost and using the ultraviolet form of the gluon energy, we recover the Weiss potential. From the full non-perturbative potential (with the ghost included) we extract a critical temperature of the deconfinement phase transition of 269 MeV for the gauge group SU(2) and 283 MeV for SU(3).
Gauge theory duals of cosmological backgrounds and their energy momentum tensors
Awad, Adel; Das, Sumit R.; Narayan, K.; Trivedi, Sandip P.
2008-02-15
We revisit type IIB supergravity backgrounds with null and spacelike singularities with natural gauge theory duals proposed in [S. R. Das, J. Michelson, K. Narayan, and S. P. Trivedi, Phys. Rev. D 74, 026002 (2006)] and [S. R. Das, J. Michelson, K. Narayan, and S. P. Trivedi, Phys. Rev. D 75, 026002 (2007)]. We show that for these backgrounds there are always choices of the boundaries of these deformed AdS{sub 5}xS{sup 5} space-times, such that the dual gauge theories live on flat metrics and have space-time dependent couplings. We present a new time dependent solution of this kind where the effective string coupling is always bounded and vanishes at a spacelike singularity in the bulk, and the space-time becomes AdS{sub 5}xS{sup 5} at early and late times. The holographic energy momentum tensor calculated with a choice of flat boundary is shown to vanish for null backgrounds and to be generically nonzero for time dependent backgrounds.
Xiang, Liangzhong; Wang, Bo; Ji, Lijun; Jiang, Huabei
2013-01-01
Photoacoustic tomography (PAT) offers three-dimensional (3D) structural and functional imaging of living biological tissue with label-free, optical absorption contrast. These attributes lend PAT imaging to a wide variety of applications in clinical medicine and preclinical research. Despite advances in live animal imaging with PAT, there is still a need for 3D imaging at centimeter depths in real-time. We report the development of four dimensional (4D) PAT, which integrates time resolutions with 3D spatial resolution, obtained using spherical arrays of ultrasonic detectors. The 4D PAT technique generates motion pictures of imaged tissue, enabling real time tracking of dynamic physiological and pathological processes at hundred micrometer-millisecond resolutions. The 4D PAT technique is used here to image needle-based drug delivery and pharmacokinetics. We also use this technique to monitor 1) fast hemodynamic changes during inter-ictal epileptic seizures and 2) temperature variations during tumor thermal therapy. PMID:23346370
NASA Astrophysics Data System (ADS)
Xiang, Liangzhong; Wang, Bo; Ji, Lijun; Jiang, Huabei
2013-01-01
Photoacoustic tomography (PAT) offers three-dimensional (3D) structural and functional imaging of living biological tissue with label-free, optical absorption contrast. These attributes lend PAT imaging to a wide variety of applications in clinical medicine and preclinical research. Despite advances in live animal imaging with PAT, there is still a need for 3D imaging at centimeter depths in real-time. We report the development of four dimensional (4D) PAT, which integrates time resolutions with 3D spatial resolution, obtained using spherical arrays of ultrasonic detectors. The 4D PAT technique generates motion pictures of imaged tissue, enabling real time tracking of dynamic physiological and pathological processes at hundred micrometer-millisecond resolutions. The 4D PAT technique is used here to image needle-based drug delivery and pharmacokinetics. We also use this technique to monitor 1) fast hemodynamic changes during inter-ictal epileptic seizures and 2) temperature variations during tumor thermal therapy.
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.
Instantons and the 5D U(1) gauge theory with extra adjoint
NASA Astrophysics Data System (ADS)
Poghossian, Rubik; Samsonyan, Marine
2009-07-01
In this paper, we compute the partition function of 5D supersymmetric U(1) gauge theory with extra adjoint matter in general Ω background. It is well known that such partition functions encode very rich topological information. We show in particular that unlike the case with no extra matter, the partition function with extra adjoint at some special values of the parameters directly reproduces the generating function for the Poincare polynomial of the moduli space of instantons. We compare our results with those recently obtained by Iqbal et al (Refined topological vertex, cylindric partitions and the U(1) adjoint theory, arXiv:0803.2260), who used the so-called refined topological vertex method.
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.
Stability of D brane-anti D brane systems in confining gauge theories
NASA Astrophysics Data System (ADS)
Ghoroku, Kazuo; Nakamura, Akihiro; Toyoda, Fumihiko
2011-01-01
We study the stability of a special form of D brane embedding which is regarded as a bound state of D n and anti-D n brane embedded in a 10D supergravity background which is dual to a confining gauge theory. For D5 branes with U(1) flux, their bound-state configuration can be regarded as the baryonium vertex. For D branes of n=6 and 8 without the U(1) flux, their bound states have been used to introduce flavor quarks in the dual supersymmetric Yang-Mills theory. In any case, it would be important to ensure that they are free from tachyon instability. For all these cases, we could show their stability with respect to this point.
String tension scaling in high-temperature confined SU(N) gauge theories
Meisinger, Peter N.; Ogilvie, Michael C.
2010-01-15
SU(N) gauge theories, extended with adjoint fermions having periodic boundary conditions, are confining at high temperature for sufficiently light fermion mass m. In the high-temperature confining region, the one-loop effective potential for Polyakov loops has a Z(N)-symmetric confining minimum. String tensions associated with Polyakov loops are calculable in perturbation theory, and display a novel scaling behavior in which higher representations have smaller string tensions than the fundamental representation. In the magnetic sector, the Polyakov loop plays a role similar to a Higgs field, leading to an apparent breaking of SU(N) to U(1){sup N-1}. This in turn yields a dual effective theory where magnetic monopoles give rise to string tensions for spatial Wilson loops. The spatial string tensions arise semiclassically from kink solutions of the dual system. We prove that the spatial string tensions {sigma}{sub k}{sup (s)} associated with each N-ality k are constrained by a rigorous upper bound. This bound is saturated for N=2 and 3, but is insufficient to determine the spatial string tension scaling law for N{>=}4. Lattice simulations indicate that the high-temperature confining region is smoothly connected to the confining region of low-temperature pure SU(N) gauge theory. However, our results show that the string tension scaling behavior of the low-temperature region does not hold for the electric sector in the high-temperature region, and may not hold in the magnetic sector. The predicted change in the behavior of the electric sector should be readily distinguishable in lattice simulations.
Dirichlet branes and nonperturbative aspects of supersymmetric string and gauge theories
Yin, Zheng
1999-05-01
In chapter 1 the author reviews some elements of string theory relevant to the rest of this report. He touches on both the classical, i.e. perturbative, string physics before D-branes rise to prominence, and some of the progresses they brought forth. In chapter 2 he proceeds to give an exact algebraic formulation of D-branes in curved spaces. This allows one to classify them in backgrounds of interest and study their geometric properties. He applies this formalism to string theory on Calabi-Yau and other supersymmetry preserving manifolds. Then he studies the behavior of the D-branes under mirror symmetry in chapter 3. Mirror symmetry is known to be a symmetry of string theory perturbatively. He finds evidence for its nonperturbative validity when D-branes are also considered and compute some dynamical consequences. In chapter 4 he turns to examine the consistency of curved and/or intersecting D-brane configurations. They have been used recently to extract information about the field theories that arise in certain limits. It turns out that there are potential quantum mechanical inconsistencies associated with them. What saves the day are certain subtle topological properties of D-branes. This resolution has implications for the conserved charges carried by the D-branes, which he computes for the cases studied in chapter 2. In chapter 5 he uses intersecting brane configurations to study three dimensional supersymmetric gauge theories. There is also a mirror symmetry there that, among other things, exchanges classical and quantum mechanical quantities of a (mirror) pair of theories. It has an elegant realization in term of a symmetry of string theory involving D-branes. The author employs it to study a wide class of 3d models. He also predicts new mirror pairs and unconventional 3d field theories without Lagrangian descriptions.
Origin of Abelian gauge symmetries in heterotic/F-theory duality
NASA Astrophysics Data System (ADS)
Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; Poretschkin, Maximilian; Song, Peng
2016-04-01
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, we derive both the Calabi-Yau geometry as well as 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) × U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU( m) × Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E8 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. 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 Stückelberg mechanism in the lower-dimensional effective theory. 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.
Berube, D.; Kroeger, H.; Lafrance, R.; Marleau, L. )
1991-02-15
We discuss properties of a noncompact formulation of gauge theories with fermions on a momentum ({ital k}) lattice. (a) This formulation is suitable to build in Fourier acceleration in a direct way. (b) The numerical effort to compute the action (by fast Fourier transform) goes essentially like log{ital V} with the lattice volume {ital V}. (c) For the Yang-Mills theory we find that the action conserves gauge symmetry and chiral symmetry in a weak sense: On a finite lattice the action is invariant under infinitesimal transformations with compact support. Under finite transformations these symmetries are approximately conserved and they are restored on an infinite lattice and in the continuum limit. Moreover, these symmetries also hold on a finite lattice under finite transformations, if the classical fields, instead of being {ital c}-number valued, take values from a finite Galois field. (d) There is no fermion doubling. (e) For the {phi}{sup 4} model we investigate the transition towards the continuum limit in lattice perturbation theory up to second order. We compute the two- and four-point functions and find local and Lorentz-invariant results. (f) In QED we compute a one-loop vacuum polarization and find in the continuum limit the standard result. (g) As a numerical application, we compute the propagator {l angle}{phi}({ital k}){phi}({ital k}{prime}){r angle} in the {phi}{sup 4} model, investigate Euclidean invariance, and extract {ital m}{sub {ital R}} as well as {ital Z}{sub {ital R}}. Moreover we compute {l angle}{ital F}{sub {mu}{nu}}({ital k}){ital F}{sub {mu}{nu}}({ital k}{prime}){r angle} in the SU(2) model.
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.
Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes
NASA Astrophysics Data System (ADS)
Bern, Z.; Carrasco, J. J. M.; Dixon, L. J.; Johansson, H.; Roiban, R.
2012-05-01
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/Nc2 single-trace divergence in N=4 super-Yang-Mills theory.
Mills, R.
1989-06-01
This article is a survey of the history and ideas of gauge theory. Described here are the gradual emergence of symmetry as a driving force in the shaping of physical theory; the elevation of Noether's theorem, relating symmetries to conservation laws, to a fundamental principle of nature; and the force of the idea (''the gauge principle'') that the symmetries of nature, like the interactions themselves, should be local in character. The fundamental role of gauge fields in mediating the interactions of physics springs from Noether's theorem and the gauge principle in a remarkably clean and elegant way, leaving, however, some tantalizing loose ends that might prove to be the clue to a future deeper level of understanding. The example of the electromagnetic field as the prototype gauge theory is discussed in some detail and serves as the basis for examining the similarities and differences that emerge in generalizing to non-Abelian gauge theories. The article concludes with a brief examination of the dream of total unification: all the forces of nature in a single unified gauge theory, with the differences among the forces due to the specific way in which the fundamental symmetries are broken in the local environment.
Lattice gauge theory for condensed matter physics: ferromagnetic superconductivity as its example
NASA Astrophysics Data System (ADS)
Ichinose, Ikuo; Matsui, Tetsuo
2014-09-01
Recent theoretical studies of various strongly-correlated systems in condensed matter physics reveal that the lattice gauge theory (LGT) developed in high-energy physics is quite a useful tool to understand physics of these systems. Knowledge of LGT is to become a necessary item even for condensed matter physicists. In the first part of this paper, we present a concise review of LGT for the reader who wants to understand its basics for the first time. For illustration, we choose the Abelian Higgs model, a typical and quite useful LGT, which is the lattice version of the Ginzburg-Landau model interacting with a U(1) gauge field (vector potential). In the second part, we present an account of the recent progress in the study of ferromagnetic superconductivity (SC) as an example of application of LGT to topics in condensed matter physics. As the ferromagnetism (FM) and SC are competing orders with each other, large fluctuations are expected to take place and therefore nonperturbative methods are required for theoretical investigation. After we introduce a LGT describing the FMSC, we study its phase diagram and topological excitations (vortices of Cooper pairs) by Monte Carlo simulations.
NASA Astrophysics Data System (ADS)
Wu, Yue-Liang
2016-01-01
Treating the gravitational force on the same footing as the electroweak and strong forces, we present a quantum field theory of gravity based on spin and scaling gauge symmetries. A biframe spacetime is initiated to describe such a quantum gravity theory. The gravifield sided on both locally flat noncoordinate spacetime and globally flat Minkowski spacetime is an essential ingredient for gauging global spin and scaling symmetries. The locally flat gravifield spacetime spanned by the gravifield is associated with a noncommutative geometry characterized by a gauge-type field strength of the gravifield. A coordinate-independent and gauge-invariant action for the quantum gravity is built in the gravifield basis. In the coordinate basis, we derive equations of motion for all quantum fields including the gravitational effect and obtain basic conservation laws for all symmetries. The equation of motion for the gravifield tensor is deduced in connection directly with the total energy-momentum tensor. When the spin and scaling gauge symmetries are broken down to a background structure that possesses the global Lorentz and scaling symmetries, we obtain exact solutions by solving equations of motion for the background fields in a unitary basis. The massless graviton and massive spinon result as physical quantum degrees of freedom. The resulting Lorentz-invariant and conformally flat background gravifield spacetime is characterized by a cosmic vector with a nonzero cosmological mass scale. The evolving Universe is, in general, not isotropic in terms of conformal proper time. The conformal size of the Universe becomes singular at the cosmological horizon and turns out to be inflationary in light of cosmic proper time. A mechanism for quantum scalinon inflation is demonstrated such that it is the quantum effect that causes the breaking of global scaling symmetry and generates the inflation of the early Universe, which is ended when the evolving vacuum expectation value of the
Gauge theories on noncommutative ℂPN and Bogomol'nyi-Prasad-Sommerfield-like equations
NASA Astrophysics Data System (ADS)
Sako, Akifumi; Suzuki, Toshiya; Umetsu, Hiroshi
2015-11-01
We give the Fock representation of a noncommutative ℂPN and gauge theories on it. The Fock representation is constructed based on star products given by deformation quantization with separation of variables and operators which act on states in the Fock space are explicitly described by functions of inhomogeneous coordinates on ℂPN. Using the Fock representation, we are able to discuss the positivity of Yang-Mills type actions and the minimal action principle. Bogomol'nyi-Prasad-Sommerfield (BPS)-like equations on noncommutative ℂP1 and ℂP2 are derived from these actions. There are analogies between BPS-like equations on ℂP1 and monopole equations on ℝ3 and BPS-like equations on ℂP2 and instanton equations on ℝ8. We discuss solutions of these BPS-like equations.
The Domain Geometry and the Bubbling Phenomenon of Rank Two Gauge Theory
NASA Astrophysics Data System (ADS)
Huang, Hsin-Yuan; Zhang, Lei
2016-06-01
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.
Multi-instanton calculus in N=2 supersymmetric gauge theory. II. Coupling to matter
NASA Astrophysics Data System (ADS)
Dorey, Nicholas; Khoze, Valentin V.; Mattis, Michael P.
1996-12-01
We further discuss the N=2 superinstantons in SU(2) gauge theory, obtained from the general self-dual solutions of topological charge n constructed by Atiyah, Drinfeld, Hitchin, and Manin (ADHM). We realize the N=2 supersymmetry algebra as actions on the superinstanton moduli. This allows us to recast in concise superfield notation our previously obtained expression for the exact classical interaction between n ADHM superinstantons mediated by the adjoint Higgs bosons, and, moreover, to incorporate NF flavors of hypermultiplets. We perform explicit one- and two-instanton checks of the Seiberg-Witten prepotentials for all NF and arbitrary hypermultiplet masses. Our results for the low-energy couplings are all in precise agreement with the predictions of Seiberg and Witten except for NF=4, where we find a finite renormalization of the coupling which is absent in the proposed solution.
Gravitational energy for GR and Poincaré gauge theories: A covariant Hamiltonian approach
NASA Astrophysics Data System (ADS)
Chen, Chiang-Mei; Nester, James M.; Tung, Roh-Suan
2015-08-01
Our topic concerns a long standing puzzle: The energy of gravitating systems. More precisely we want to consider, for gravitating systems, how to best describe energy-momentum and angular momentum/center-of-mass momentum (CoMM). It is known that these quantities cannot be given by a local density. The modern understanding is that (i) they are quasi-local (associated with a closed 2-surface), (ii) they have no unique formula, (iii) they have no reference frame independent description. In the first part of this work, we review some early history, much of it not so well known, on the subject of gravitational energy in Einstein's general relativity (GR), noting especially Noether's contribution. In the second part, we review (including some new results) much of our covariant Hamiltonian formalism and apply it to Poincaré gauge theories of gravity (PG), with GR as a special case. The key point is that the Hamiltonian boundary term has two roles, it determines the quasi-local quantities, and furthermore, it determines the boundary conditions for the dynamical variables. Energy-momentum and angular momentum/CoMM are associated with the geometric symmetries under Poincaré transformations. They are best described in a local Poincaré gauge theory. The type of spacetime that naturally has this symmetry is Riemann-Cartan spacetime, with a metric compatible connection having, in general, both curvature and torsion. Thus our expression for the energy-momentum of physical systems is obtained via our covariant Hamiltonian formulation applied to the PG.
Adding flavor to the gravity dual of non-commutative gauge theories
NASA Astrophysics Data System (ADS)
Areán, Daniel; Paredes, Angel; Ramallo, Alfonso V.
2005-08-01
We study the addition of flavor degrees of freedom to the supergravity dual of the non-commutative deformation of the maximally supersymmetric gauge theories. By considering D7 flavor branes in the probe approximation and studying their fluctuations we extract the spectrum of scalar and vector mesons as a function of the non-commutativity. We find that the spectrum for very large non-commutative parameter is equal to the one in the commutative theory, while for some intermediate values of the non-commutativity some of the modes disappear from the discrete spectrum. We also study the semiclassical dynamics of rotating open strings attached to the D7-brane, which correspond to mesons with large spin. Under the effect of the non-commutativity the open strings get tilted. However, at small(large) distances they display the same Regge-like (Coulombic) behaviour as in the commutative theory. We also consider the addition of D5-flavor branes to the non-commutative deformation of the Script N = 1 supersymmetric Maldacena-Núñez background.
Wang, Juven C; Gu, Zheng-Cheng; Wen, Xiao-Gang
2015-01-23
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. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context. PMID:25658993
NASA Astrophysics Data System (ADS)
Wang, Juven C.; Gu, Zheng-Cheng; Wen, Xiao-Gang
2015-01-01
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. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4 +1 )D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.
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
NASA Astrophysics Data System (ADS)
Kürkçüoǧlu, S.; Ünal, G.
2016-05-01
We find new spontaneously generated fuzzy extra dimensions emerging from a certain deformation of N =4 supersymmetric Yang-Mills theory with cubic soft supersymmetry breaking and mass deformation terms. First, we determine a particular four-dimensional fuzzy vacuum that may be expressed in terms of a direct sum of product of two fuzzy spheres, and denote it in short as SF2 Int×SF2 Int . The direct sum structure of the vacuum is clearly revealed by a suitable splitting of the scalar fields in the model in a manner that generalizes our approach in [Phys. Rev. D 92, 025022 (2015)]. Fluctuations around this vacuum have the structure of gauge fields over SF2 Int×SF2 Int, and this enables us to conjecture the spontaneous broken model as an effective U (n ) (n
Dark matter coupling to electroweak gauge and Higgs bosons: An effective field theory approach
NASA Astrophysics Data System (ADS)
Chen, Jing-Yuan; Kolb, Edward W.; Wang, Lian-Tao
2013-12-01
If dark matter is a new species of particle produced in the early universe as a cold thermal relic (a weakly-interacting massive particle-WIMP), its present abundance, its scattering with matter in direct-detection experiments, its present-day annihilation signature in indirect-detection experiments, and its production and detection at colliders, depend crucially on the WIMP coupling to standard-model (SM) particles. It is usually assumed that the WIMP couples to the SM sector through its interactions with quarks and leptons. In this paper we explore the possibility that the WIMP coupling to the SM sector is via electroweak gauge and Higgs bosons. In the absence of an ultraviolet-complete particle-physics model, we employ effective field theory to describe the WIMP-SM coupling. We consider both scalars and Dirac fermions as possible dark-matter candidates. Starting with an exhaustive list of operators up to dimension 8, we present detailed calculation of dark-matter annihilations to all possible final states, including γγ, γZ, γh, ZZ, Zh, W+W-, hh, and ffbar, and demonstrate the correlations among them. We compute the mass scale of the effective field theory necessary to obtain the correct dark-matter mass density, and well as the resulting photon line signals.
Disorder in gauge/gravity duality, pole spectrum statistics and random matrix theory
NASA Astrophysics Data System (ADS)
Saremi, Omid
2014-05-01
In condensed-matter, level statistics has long been used to characterize the phases of a disordered system. We provide evidence within the context of a simple model that in a disordered large-N gauge theory with a gravity dual, there exist phases where the nearest neighbor spacing distribution of the unfolded pole spectra of generic two-point correlators is Poisson. This closely resembles the localized phase of the Anderson Hamiltonian. We perform two tests on our statistical hypothesis. One is based on a statistic defined in the context of random matrix theory, the so-called \\overline{\\Delta _3}, or spectral rigidity, proposed by Dyson and Mehta. The second is a χ-squared test. In our model, the results of both tests are consistent with the hypothesis that the pole spectra of two-point functions can be at least in two distinct phases; first a regular sequence and second a completely uncorrelated sequence with a Poisson nearest neighbor spacing distribution.
The Worldsheet S-Matrix of Planar N = 4 Gauge Theory (Abstract)
Beisert, N.
2007-10-03
Maximally supersymmetric Yang-Mills theory in the 't Hooft limit is apparently completely integrable. Bethe equations then enable us to compute anomalous dimensions, for example those of twist-two operators, exactly at very high perturbative orders. The Bethe ansatz in turn is based on the (worldsheet) S-matrix which is reviewed in this talk. The flavour structure of the S-matrix is completely fixed by symmetry and an overall phase is partially constrained by a crossing relation. In hep-th/0610251 we have recently proposed an expression for this phase to all perturbative orders which is consistent with presently available data. For instance, it leads to an integral equation for the high-spin limit of twist-two operators (also known as the cusp/soft anomalous dimension) at finite coupling. In fact, this result appears to be a part of the corresponding analytic answer for *every* four-dimensional gauge theory including QCD.The putatively exact phase also leads to one of the strongest tests of the AdS/CFT conjecture to date: We can now show complete agreement with dynamical results in non-interacting IIB superstrings on the AdS{sub 5}xS{sup 5} background by reexpanding the phase at strong coupling.
Quiver gauge theory of non-Abelian vortices and noncommutative instantons in higher dimensions
Popov, Alexander D.; Szabo, Richard J.
2006-01-15
We construct explicit Bogomolnyi, Prasad, Sommerfeld (BPS) and non-BPS solutions of the Yang-Mills equations on the noncommutative space R{sub {theta}}{sup 2n}xS{sup 2} which have manifest spherical symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show that the solutions imply an equivalence between instantons on R{sub {theta}}{sup 2n}xS{sup 2} and non-Abelian vortices on R{sub {theta}}{sup 2n}, which can be interpreted as a blowing-up of a chain of D0-branes on R{sub {theta}}{sup 2n} into a chain of spherical D2-branes on R{sub {theta}}{sup 2n}xS{sup 2}. The low-energy dynamics of these configurations is described by a quiver gauge theory which can be formulated in terms of new geometrical objects generalizing superconnections. This formalism enables the explicit assignment of D0-brane charges in equivariant K-theory to the instanton solutions.
NASA Astrophysics Data System (ADS)
Kataev, A. L.; Mikhailov, S. V.
2012-02-01
We propose a hypothesis on the detailed structure for the representation of the conformal symmetry breaking term in the basic Crewther relation generalized in the perturbation theory framework in QCD renormalized in the overline {MS} scheme. We establish the validity of this representation in the O(α{/s 4 }) approximation. Using the variant of the generalized Crewther relation formulated here allows finding relations between specific contributions to the QCD perturbation series coefficients for the flavor nonsinglet part of the Adler function D{/A ns } for the electron-positron annihilation in hadrons and to the perturbation series coefficients for the Bjorken sum rule S Bjp for the polarized deep-inelastic lepton-nucleon scattering. We find new relations between the α{/s 4 } coefficients of D{/A ns } and S Bjp . Satisfaction of one of them serves as an additional theoretical verification of the recent computer analytic calculations of the terms of order α{/s 4 } in the expressions for these two quantities.
Generalized Attractor Points in Gauged Supergravity
Kachru, Shamit; Kallosh, Renata; Shmakova, Marina; /KIPAC, Menlo Park /SLAC /Stanford U., Phys. Dept.
2011-08-15
The attractor mechanism governs the near-horizon geometry of extremal black holes in ungauged 4D N=2 supergravity theories and in Calabi-Yau compactifications of string theory. In this paper, we study a natural generalization of this mechanism to solutions of arbitrary 4D N=2 gauged supergravities. We define generalized attractor points as solutions of an ansatz which reduces the Einstein, gauge field, and scalar equations of motion to algebraic equations. The simplest generalized attractor geometries are characterized by non-vanishing constant anholonomy coefficients in an orthonormal frame. Basic examples include Lifshitz and Schroedinger solutions, as well as AdS and dS vacua. There is a generalized attractor potential whose critical points are the attractor points, and its extremization explains the algebraic nature of the equations governing both supersymmetric and non-supersymmetric attractors.
Infrared analysis of propagators and vertices of Yang-Mills theory in Landau and Coulomb gauge
Schleifenbaum, W.; Leder, M.; Reinhardt, H.
2006-06-15
The infrared behavior of gluon and ghost propagators, ghost-gluon vertex, and three-gluon vertex is investigated for both the covariant Landau and the noncovariant Coulomb gauge. Assuming infrared ghost dominance, we find a unique infrared exponent in the d=4 Landau gauge, while in the d=3+1 Coulomb gauge we find two different infrared exponents. We also show that a finite dressing of the ghost-gluon vertex has no influence on the infrared exponents. Finally, we determine the infrared behavior of the three-gluon vertex analytically and calculate it numerically at the symmetric point in the Coulomb gauge.
NASA Astrophysics Data System (ADS)
Banach, Zbigniew; Piekarski, Sławomir
1996-03-01
An annoying paradox which has plagued the “naive” description of density perturbations in homogeneous and isotropic cosmological models has been the gauge-dependent character of this description. The corollary of this observation is that only gauge-invariant quantities have any inherent physical meaning. Thus the present paper develops, from a new geometric point of view, a totally gauge-invariant formulation of perturbation theory applicable to the case of a general perfect fluid with two essential thermodynamic variables. Precisely speaking, the main purpose here is the systematic construction of a complete set of basic gauge-invariant variables. This set consists of 17 linearly independent, not identically vanishing quantities. It turns out that these quantities can be used to divide the infinitesimal perturbations into equivalence classes: two perturbations P and P' are said to be equivalent if their difference is equal to the Lie derivative of the background solution of Einstein's propagation equations with respect to an arbitrary vector field on the space-time manifold. In fact, the gauge-invariant perturbations, whose mathematical definition is best understood by introducing the elements of a certain quotient space, are uniquely determined from the basic variables. An additional welcome feature is that any gauge-invariant quantity can be constructed directly from the basic variables through purely algebraic and differential operations. In a companion paper, these results are used to derive the full, gauge-invariant system of equations governing the evolution of basic variables. In this sense, then, the present analysis is complete.
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
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.
Exact partition functions for the Ω-deformed {N}={2}^{ast } SU(2) gauge theory
NASA Astrophysics Data System (ADS)
Beccaria, Matteo; Macorini, Guido
2016-07-01
We study the low energy effective action of the Ω-deformed {N}={2}^{ast } SU(2) gauge theory. It depends on the deformation parameters ɛ 1, ɛ 2, the scalar field expectation value a, and the hypermultiplet mass m. We explore the plane (m/ɛ_1,ɛ_2/ɛ_1) looking for special features in the multi-instanton contributions to the prepotential, motivated by what happens in the Nekrasov-Shatashvili limit ɛ 2 → 0. We propose a simple condition on the structure of poles of the k-instanton prepotential and show that it is admissible at a finite set of points in the above plane. At these special points, the prepotential has poles at fixed positions independent on the instanton number. Besides and remarkably, both the instanton partition function and the full prepotential, including the perturbative contribution, may be given in closed form as functions of the scalar expectation value a and the modular parameter q appearing in special combinations of Eisenstein series and Dedekind η function. As a byproduct, the modular anomaly equation can be tested at all orders at these points. We discuss these special features from the point of view of the AGT correspondence and provide explicit toroidal 1-blocks in non-trivial closed form. The full list of solutions with 1, 2, 3, and 4 poles is determined and described in details.
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.
Multi-instanton calculus in {ital N}=2 supersymmetric gauge theory
Dorey, N.; Khoze, V.V.; Mattis, M.P.
1996-08-01
The Seiberg-Witten solution of {ital N}=2 supersymmetric SU(2) gauge theory may be viewed as a prediction for the infinite family of constants {l_brace}F{sub {ital n}}{r_brace} measuring the {ital n}-instanton contribution to the prepotential F. Here we examine the instanton physics directly, in particular the contribution of the general self-dual solution of topological charge {ital n} constructed by Atiyah, Drinfeld, Hitchin, and Manin (ADHM). In both the bosonic and supersymmetric cases, we determine both the large- and short-distance behavior of all the fields in this background. This allows us to construct the exact classical interaction between {ital n} ADHM (super)instantons mediated by the adjoint Higgs bosons. We calculate the one- and two-instanton contributions to the low-energy Seiberg-Witten effective action and find precise agreement with their predicted values of F{sub 1} and F{sub 2}. {copyright} {ital 1996 The American Physical Society.}
Multi-instanton calculus in {ital N}=2 supersymmetric gauge theory. II. Coupling to matter
Dorey, N.; Khoze, V.V.; Mattis, M.P.
1996-12-01
We further discuss the {ital N}=2 superinstantons in SU(2) gauge theory, obtained from the general self-dual solutions of topological charge {ital n} constructed by Atiyah, Drinfeld, Hitchin, and Manin (ADHM). We realize the {ital N}=2 supersymmetry algebra as actions on the superinstanton moduli. This allows us to recast in concise superfield notation our previously obtained expression for the exact classical interaction between {ital n} ADHM superinstantons mediated by the adjoint Higgs bosons, and, moreover, to incorporate {ital N}{sub {ital F}} flavors of hypermultiplets. We perform explicit one- and two-instanton checks of the Seiberg-Witten prepotentials for all {ital N}{sub {ital F}} and arbitrary hypermultiplet masses. Our results for the low-energy couplings are all in precise agreement with the predictions of Seiberg and Witten except for {ital N}{sub {ital F}}=4, where we find a finite renormalization of the coupling which is absent in the proposed solution. {copyright} {ital 1996 The American Physical Society.}
{N} =2 supersymmetric Janus solutions and flows: from gauged supergravity to M theory
NASA Astrophysics Data System (ADS)
Pilch, Krzysztof; Tyukov, Alexander; Warner, Nicholas P.
2016-05-01
We investigate a family of SU(3)×U(1)×U(1)-invariant holographic flows and Janus solutions obtained from gauged {N} = 8 supergravity in four dimensions. We give complete details of how to use the uplift formulae to obtain the corresponding solutions in M theory. While the flow solutions appear to be singular from the four-dimensional perspective, we find that the eleven-dimensional solutions are much better behaved and give rise to interesting new classes of compactification geometries that are smooth, up to orbifolds, in the infra-red limit. Our solutions involve new phases in which M2 branes polarize partially or even completely into M5 branes. We derive the eleven-dimensional supersymmetries and show that the eleven-dimensional equations of motion and BPS equations are indeed satisfied as a consequence of their four-dimensional counterparts. Apart from elucidating a whole new class of eleven-dimensional Janus and flow solutions, our work provides extensive and highly non-trivial tests of the recently-derived uplift formulae.
Interplay of the sign problem and the infinite volume limit: Gauge theories with a theta term
NASA Astrophysics Data System (ADS)
Cai, Yiming; Cohen, Thomas; Goldbloom-Helzner, Ari; McPeak, Brian
2016-06-01
QCD and related gauge theories have a sign problem when a θ term is included; this complicates the extraction of physical information from Euclidean-space calculations as one would do in lattice studies. The sign problem arises in this system because the partition function for configurations with fixed topological charge Q , ZQ, are summed weighted by exp (i Q θ ) to obtain the partition function for fixed θ , Z (θ ). The sign problem gets exponentially worse numerically as the space-time volume is increased. Here it is shown that, apart from the practical numerical issues associated with large volumes, there are some interesting issues of principle. A key quantity is the energy density as a function of θ , ɛ (θ )=-log (Z (θ ) )/V . This is expected to be well defined in the large four-volume limit. Similarly, one expects the energy density for a fixed topological density ɛ ˜(Q /V )=-log (ZQ )/V to be well defined in the limit of large four volumes. Intuitively, one might expect that if one had the infinite volume expression for ɛ ˜(Q /V ) to arbitrary accuracy, then one could reconstruct ɛ (θ ) by directly summing over the topological sectors of the partition function. We show here that there are circumstances where this is not the case. In particular, this occurs in regions where the curvature of ɛ (θ ) is negative.
Latent heat at the first order phase transition point of SU(3) gauge theory
NASA Astrophysics Data System (ADS)
Shirogane, Mizuki; Ejiri, Shinji; Iwami, Ryo; Kanaya, Kazuyuki; Kitazawa, Masakiyo; WHOT-QCD Collaboration
2016-07-01
We calculate the energy gap (latent heat) and pressure gap between the hot and cold phases of the SU(3) gauge theory at the first order deconfining phase transition point. We perform simulations around the phase transition point with the lattice size in the temporal direction Nt=6 , 8 and 12 and extrapolate the results to the continuum limit. We also investigate the spatial volume dependence. The energy density and pressure are evaluated by the derivative method with nonperturabative anisotropy coefficients. We adopt a multipoint reweighting method to determine the anisotropy coefficients. We confirm that the anisotropy coefficients approach the perturbative values as Nt increases. We find that the pressure gap vanishes at all values of Nt when the nonperturbative anisotropy coefficients are used. The spatial volume dependence in the latent heat is found to be small on large lattices. Performing extrapolation to the continuum limit, we obtain Δ ɛ /T4=0.75 ±0.17 and Δ (ɛ -3 p )/T4=0.623 ±0.056 .
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.
Srivastava, Y.N.; Vaughn, M.T.
1993-02-01
Work done on the following topics is summarized: (1) Coulomb potential in QED on the lattice; (2) Weyl cosmic strings and their consequences; (3) Interference between past and future events in {phi} {yields} K{bar K}; (4) Quantum effects of strong classical electromagnetic fields; (5) Application of computer algebra to calculations in supersymmetry and supergravity; (6) numerical studies of classical scalar {phi}{sup 4} field theory and related nonlinear {sigma}-models; (7) Analysis of a cubic model field theory; and, (8) Renormalization group analysis of unified gauge theories.
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
NASA Astrophysics Data System (ADS)
Xu, Hongliang; Xu, Chong-Yu; Sælthun, Nils Roar; Xu, Youpeng; Zhou, Bin; Chen, Hua
2015-06-01
Rain gauge networks are used to provide estimates of area average, spatial variability and point rainfalls at catchment scale and provide the most important input for hydrological models. Therefore, it is desired to design the optimal rain gauge networks with a minimal number of rain gauges to provide reliable data with both areal mean values and spatial-temporal variability. Based on a dense rain gauge network of 185 rain gauges in Xiangjiang River Basin, southern China, this study used an entropy theory based multi-criteria method which simultaneously considers the information derived from rainfall series, minimize the bias of areal mean rainfall as well as minimize the information overlapped by different gauges to resample the rain gauge networks with different gauge densities. The optimal networks were examined using two hydrological models: The lumped Xinanjiang Model and the distributed SWAT Model. The results indicate that the performances of the lumped model using different optimal networks are stable while the performances of the distributed model keep on improving as the number of rain gauges increases. The results reveal that the entropy theory based multi-criteria strategy provides an optimal design of rain gauge network which is of vital importance in regional hydrological study and water resources management.
NASA Astrophysics Data System (ADS)
Mirza, Behrouz; Zarei, Moslem
2010-08-01
In this paper we apply the assumption of our recent work in noncommutative scalar models to the noncommutative U(1) gauge theories. This assumption is that the noncommutative effects start to be visible continuously from a scale ΛNC and that below this scale the theory is a commutative one. Based on this assumption and using background field method and loop calculations, an effective action is derived for noncommutative U(1) gauge theory. It will be shown that the corresponding low energy effective theory is asymptotically free and that under this condition the noncommutative quadratic IR divergences will not appear. The effective theory contains higher dimensional terms, which become more important at high energies. These terms predict an elastic photon-photon scattering due to the noncommutativity of space. The coefficients of these higher dimensional terms also satisfy a positivity constraint indicating that in this theory the related diseases of superluminal signal propagating and bad analytic properties of S-matrix do not exist. In the last section, we will apply our method to the noncommutative extra dimension theories.
NASA Astrophysics Data System (ADS)
Shen, Jian Qi
2016-05-01
A gravitational gauge theory with a spin-affine connection (Lorentz connection) as a rotational gauge potential (fundamental dynamical variable) is suggested for reformulating the theory of Stephenson-Kilmister-Yang gravity, in which the Einstein field equation of gravity is a first-integral solution of a spin-connection gravitational gauge field equation. A heavy intermediate field φ that accompanies a matter field \\varphi is introduced in order to remove the conventional dimensionful gravitational coupling. Such a \\varphi -φ coupling can lead to dimensionless gravitational coupling (i.e., the gravitational constant is dimensionless) in the present gravitational gauge field theory. A low-energy effective Lagrangian density for the matter field can be obtained by integrating out the accompanying heavy field in generating functional of path integral formalism, and therefore, a dimensionful gravitational coupling coefficient (Einstein gravitational constant) emerges. Such a dimensionless coupling of gravity, where the dimensionful coupling is emergent at low energies, is considered for scalar and spinor fields, which serve as gravitating matter fields (gravitational source). Though there are higher derivatives (e.g., third- and fourth-order partial derivatives) of the scalar and spinor fields in the low-energy effective Lagrangian densities, the ordinary equations of motion of the scalar and spinor fields can also be emergent from the present gravitational gauge theory. Therefore, the Einstein gravity can be recovered from the present gravitational gauge theory. In addition to the gravitational Lagrangian of the spacetime-rotational gauge potential (i.e., spin-affine connection), the Lagrangian of a spacetime-translational gauge potential (i.e., vierbein) is also constructed. Thus, the present dimensionless gravitational gauge coupling preserves local rotational and translational gauge symmetries. Since the spin-connection gravitational gauge field equation is a
Atomic quantum simulation of U(N) and SU(N) non-Abelian lattice gauge theories.
Banerjee, D; Bögli, M; Dalmonte, M; Rico, E; Stebler, P; Wiese, U-J; Zoller, P
2013-03-22
Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at nonzero temperature or baryon density. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can address the corresponding chiral dynamics in real time. PMID:25166816
On the Infrared Behaviour of Landau Gauge Yang-Mills Theory with Differently Charged Scalar Fields
Alkofer, Reinhard; Maas, Axel; Macher, Veronika; Fister, Leonard
2011-05-23
Recently it has been argued that infrared singularities of the quark-gluon vertex of Landau gauge QCD can confine static quarks via a linear potential. It is demonstrated that the same mechanism also may confine fundamental scalar fields. This opens the possibility that within functional approaches static confinement is an universal property of the gauge sector even though it is formally represented in the functional equations of the matter sector. The colour structure of Dyson-Schwinger equations for fundamental and adjoint scalar fields is determined for the gauge groups SU(N) and G(2) exhibiting interesting cancellations purely due to colour algebra.
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.
NASA Astrophysics Data System (ADS)
Xie, Yi; Kopeikin, Sergei
2010-01-01
We construct a set of reference frames for description of the orbital and rotational motion of the Moon. We use a scalar-tensor theory of gravity depending on two parameters of the parametrized post-Newtonian (PPN) formalism and utilize the concepts of the relativistic resolutions on reference frames adopted by the International Astronomical Union in 2000. We assume that the solar system is isolated and space-time is asymptotically flat. The primary reference frame has the origin at the solar-system barycenter (SSB) and spatial axes are going to infinity. The SSB frame is not rotating with respect to distant quasars. The secondary reference frame has the origin at the Earth-Moon barycenter (EMB). The EMB frame is local with its spatial axes spreading out to the orbits of Venus and Mars and not rotating dynamically in the sense that both the Coriolis and centripetal forces acting on a free-falling test particle, moving with respect to the EMB frame, are excluded. Two other local frames, the geocentric (GRF) and the selenocentric (SRF) frames, have the origin at the center of mass of the Earth and Moon respectively. They are both introduced in order to connect the coordinate description of the lunar motion, observer on the Earth, and a retro-reflector on the Moon to the observable quantities which are the proper time and the laser-ranging distance. We solve the gravity field equations and find the metric tensor and the scalar field in all frames. We also derive the post-Newtonian coordinate transformations between the frames and analyze the residual gauge freedom of the solutions of the field equations. We discuss the gravitomagnetic effects in the barycentric equations of the motion of the Moon and argue that they are beyond the current accuracy of lunar laser ranging (LLR) observations.
Energy-momentum tensor and transformation properties of the gauge potentials in gravitation theory
NASA Astrophysics Data System (ADS)
Sukhov, Andrei M.
1991-04-01
It is shown that the transformation properties of the translational gauge potentials eαi(x), will be chosen in another way [compared with the exposition of Hehl et al., Rev. Mod. Phys. 48, 393 (1976)]. The term containing the total (symmetric) energy-momentum tensor remains in the variation of the action. This approach allows us to change the transformation properties of the gauge potentials and the conservation laws of energy momentum.
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.
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.
Unifying the PST and the auxiliary tensor field formulations of 4D self-duality
NASA Astrophysics Data System (ADS)
Ivanov, E. A.; Nurmagambetov, A. J.; Zupnik, B. M.
2014-04-01
We unify the Lorentz- and O(2) duality-covariant approach to 4D self-dual theories by Pasti, Sorokin and Tonin (PST) with the formulation involving an auxiliary tensor field. We present the basic features of the new hybrid approach, including symmetries of the relevant generalized PST action. Its salient peculiarity is the unique form of the realization of the PST gauge symmetries. The corresponding transformations do not affect the auxiliary tensor field, which guarantees the self-duality of the nonlinear actions in which the O(2) invariant interactions are constructed out of the tensor field.
NASA Astrophysics Data System (ADS)
Gazit, Snir; Randeria, Mohit; Vishwanath, Ashvin
In two space dimensions, the Z2 lattice gauge theory is known to undergo a zero temperature confinement to de-confinment quantum phase transition . In this work, we study how this transition is modified in the presence of lattice fermions which are minimally coupled to the Z2 gauge field. This may be viewed as an extreme version of the BEC-BCS transition where fermions are confined in the strong coupling phase. We investigate both a square lattice model with a large fermi surface and Dirac fermions realized on a π flux and honeycomb lattices. The models are found to be free of the numerical sign problem for all fermion density. In addition, we introduce a numerical method to stochastically incorporate the Gauss law constraint in a quantum Monte Carlo (QMC) simulation. The phase diagram as a function of the model parameters, chemical potential and temperature is determined by means of a large scale determinant QMC.
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
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.
Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy 2-sphere
Aoki, Hajime; Hirayama, Yoshiko; Iso, Satoshi
2008-07-15
We consider a gauge-Higgs system on a fuzzy 2-sphere and study the topological structure of gauge configurations, when the U(2) gauge symmetry is spontaneously broken to U(1)xU(1) by the vev of the Higgs field. The topology is classified by the index of the Dirac operator satisfying the Ginsparg-Wilson relation, which turns out to be a noncommutative analog of the topological charge introduced by 't Hooft. It can be rewritten as a form whose commutative limit becomes the winding number of the Higgs field. We also study conditions which assure the validity of the formulation, and give a generalization of the admissibility condition. Finally we explicitly calculate the topological charge of a one-parameter family of configurations.
S-duality in SU(3) Yang-Mills theory with non-abelian unbroken gauge group
NASA Astrophysics Data System (ADS)
Schroers, B. J.; Bais, F. A.
1998-12-01
It is observed that the magnetic charges of classical monopole solutions in Yang-Mills-Higgs theory with non-abelian unbroken gauge group H are in one-to-one correspondence with coherent states of a dual or magnetic group H˜. In the spirit of the Goddard-Nuyts-Olive conjecture this observation is interpreted as evidence for a hidden magnetic symmetry of Yang-Mills theory. SU(3) Yang-Mills-Higgs theory with unbroken gauge group U(2) is studied in detail. The action of the magnetic group on semi-classical states is given explicitly. Investigations of dyonic excitations show that electric and magnetic symmetry are never manifest at the same time: Non-abelian magnetic charge obstructs the realisation of electric symmetry and vice-versa. On the basis of this fact the charge sectors in the theory are classified and their fusion rules are discussed. Non-abelian electric-magnetic duality is formulated as a map between charge sectors. Coherent states obey particularly simple fusion rules, and in the set of coherent states S-duality can be formulated as an SL(2, Z) mapping between sectors which leaves the fusion rules invariant.
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.
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
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.
Final Report for "Infrared Fixed Points in Multiflavor Lattice Gauge Theory"
Meurice, Yannick; Sinclair, Donald K.
2013-09-27
The goal of the grant was to apply methods that we have developed with spin and pure gauge models to models with dynamical fermions which are considered as candidates for an alternative to the Higgs mechanism. The work on SU(3) with fundamental quarks and with sextet quarks is described.
Mass transfer based on chemical potential theory: ZnSO{sub 4}/H{sub 2}SO{sub 4}/D2EHPA
Klocker, H.; Bart, H.J.; Marr, R.; Mueller, H.
1997-10-01
The zinc sulfate/D2EHPA system is used commercially for the recovery of zinc from waste streams and secondary materials. A fundamental model based on chemical reaction kinetics and diffusional mass transfer for the extraction of zinc sulfate with di(2-ethylhexyl) phosphoric acid (D2EHPA) in n-heptane at 25 C was developed. Gradients of the chemical potential were used as the driving force for diffusion. Activity coefficients and their derivatives were calculated from the Pitzer equation in the aqueous phase, while the organic non-ideality was considered by the Hildebrand-Scott treatment. The Nerst-Planck equation was chosen for describing the diffusion of aqueous ions, paying special care to the formation of hydrogen sulfate. It was assumed that this fast ionic reaction can be described in terms of the mass action law in the bulk and film. For the multicomponent mass transfer of the organic species, the Maxwell-Stefan theory was adopted. A kinetic equation for the extraction of zinc with D2EHPA, which considers the adsorption of the D2EHPA molecules at the interface based on the Langmuir law, was suitable for the experimental data. Organic zinc concentration vs. time was obtained in a type of Lewis cell with vibrational mixing. Molar fluxes were calculated by fitting it with rational functions, which were analytically differentiated. Initial conditions of the experiments cover a wide range of the zinc (0.1 mM to 0.05 M), D2EHPA, and sulfuric acid concentration. Experimental fluxes could be well described by this model when chemical kinetics and mass transfer were considered. In particular, the resistance to mass transfer in the organic film is important.
Torsion cosmology of Poincaré gauge theory and the constraints of its parameters via SNeIa data
Ao, Xi-Chen; Li, Xin-Zhou E-mail: kychz@shnu.edu.cn
2012-02-01
Poincarè gauge theory (PGT) is an alternative gravity theory, which brings the gravity into the gauge-theoretic framework, where the Lagrangian includes both quadratic torsion and curvature terms. Recently, the cosmological models with torsion based on this theory, which explained the cosmic acceleration in a new way, have received much attention. Among these PGT cosmological models, the one with only even parity dynamical modes-SNY model, for its realistic meaning, is very attractive. In this paper, we first analyze the past-time cosmic evolution of SNY model analytically. And based on these results we fit this model to the most comprehensive SNeIa data (Union 2) and thus find the best-fit values of model parameters and initial conditions, whose related χ{sup 2} value is consistent with the one from ΛCMD at the 1σ level. Also by the χ{sup 2} estimate, we provide certain constraints on these parameters. Using these best-fit values for the Union 2 SNeIa dataset, we are able to predict the evolution of our real universe in late time. From this prediction, we know that the fate of our universe is that it would expand forever, slowly asymptotically to a halt, which is in accordance with the earlier works.
NASA Astrophysics Data System (ADS)
Edwards, Sam R.; von Smekal, Lorenz
2009-11-01
We present a precision determination of the critical coupling βc for the deconfinement transition in pure SU (2) gauge theory in 2 + 1 dimensions. This is possible from universality, by intersecting the center vortex free energy as a function of the lattice coupling β with the exactly known value of the interface free energy in the 2D Ising model at criticality. The method allows us to find critical couplings with unprecedented numerical accuracy. Results for lattices with different numbers of sites Nt along the Euclidean time direction are used to determine how β varies with temperature for a given Nt around the deconfinement transition.
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.
From toric geometry to quiver gauge theory: The equivalence of a-maximization and Z-minimization
NASA Astrophysics Data System (ADS)
Butti, A.; Zaffaroni, A.
2006-05-01
AdS/CFT predicts a precise relation between the central charge a, the scaling dimensions of some operators in the CFT on D3-branes at conical singularities and the volumes of the horizon and of certain cycles in the supergravity dual. We review how this quantitative check can be performed for all toric singularities. We discuss how these results are related to the recently discovered map between toric singularities and tilings; in particular, we discuss how to find the precise distribution of R-charges in the quiver gauge theory using dimers technology.