Bäcklund Transformations in 10D SUSY Yang-Mills Theories

NASA Astrophysics Data System (ADS)

Gervais, Jean-Loup

A Bäcklund transformation is derived for the Yang's type (super) equations previously derived (hep-th/9811108) by M. Saveliev and the author, from the ten-dimensional super-Yang-Mills field equations in an on-shell light cone gauge. It is shown to be based upon a particular gauge transformation satisfying nonlinear conditions which ensure that the equations retain the same form. These Yang's type field equations are shown to be precisely such that they automatically provide a solution of these conditions. This Bäcklund transformation is similar to the one proposed by A. Leznov for self-dual Yang-Mills in four dimensions. In the introduction a personal recollection on the birth of supersymmetry is given.

Nonperturbative finite-temperature Yang-Mills theory

NASA Astrophysics Data System (ADS)

Cyrol, Anton K.; Mitter, Mario; Pawlowski, Jan M.; Strodthoff, Nils

2018-03-01

We present nonperturbative correlation functions in Landau-gauge Yang-Mills theory at finite temperature. The results are obtained from the functional renormalisation group within a self-consistent approximation scheme. In particular, we compute the magnetic and electric components of the gluon propagator, and the three- and four-gluon vertices. We also show the ghost propagator and the ghost-gluon vertex at finite temperature. Our results for the propagators are confronted with lattice simulations and our Debye mass is compared to hard thermal loop perturbation theory.

Quantum Yang-Mills Dark Energy

NASA Astrophysics Data System (ADS)

Pasechnik, Roman

2016-02-01

In this short review, I discuss basic qualitative characteristics of quantum non-Abelian gauge dynamics in the non-stationary background of the expanding Universe in the framework of the standard Einstein--Yang--Mills formulation. A brief outlook of existing studies of cosmological Yang--Mills fields and their properties will be given. Quantum effects have a profound impact on the gauge field-driven cosmological evolution. In particular, a dynamical formation of the spatially-homogeneous and isotropic gauge field condensate may be responsible for both early and late-time acceleration, as well as for dynamical compensation of non-perturbative quantum vacua contributions to the ground state of the Universe. The main properties of such a condensate in the effective QCD theory at the flat Friedmann--Lema\\'itre--Robertson--Walker (FLRW) background will be discussed within and beyond perturbation theory. Finally, a phenomenologically consistent dark energy can be induced dynamically as a remnant of the QCD vacua compensation arising from leading-order graviton-mediated corrections to the QCD ground state.

BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.

Yangian Symmetry and Integrability of Planar N=4 Supersymmetric Yang-Mills Theory.

PubMed

Beisert, Niklas; Garus, Aleksander; Rosso, Matteo

2017-04-07

In this Letter, we establish Yangian symmetry of planar N=4 supersymmetric Yang-Mills theory. We prove that the classical equations of motion of the model close onto themselves under the action of Yangian generators. Moreover, we propose an off-shell extension of our statement, which is equivalent to the invariance of the action and prove that it is exactly satisfied. We assert that our relationship serves as a criterion for integrability in planar gauge theories by explicitly checking that it applies to the integrable Aharony-Bergman-Jafferis-Maldacena theory but not to the nonintegrable N=1 supersymmetric Yang-Mills theory.

HYM-flation: Yang-Mills cosmology with Horndeski coupling

NASA Astrophysics Data System (ADS)

Davydov, E.; Gal'tsov, D.

2016-02-01

We propose new mechanism for inflation using classical SU (2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang-Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflationary scenario, in which the Planck-scale YM-generated inflation naturally prepares the desired initial conditions for the GUT-scale Higgs inflation.

Phase transitions in Yang-Mills theories and their gravity duals

NASA Astrophysics Data System (ADS)

Marsano, Joseph Daniel

This thesis is a study of the thermal phase structure of systems that admit dual gauge theory and string theory descriptions. In a pair of examples, we explore the connection between perturbative Yang-Mills and gravitational thermodynamics which arises from the fact that these descriptions probe different corners of a single phase diagram. The structure that emerges from a detailed study of these isolated regions generally suggests a natural conjecture how they may be connected to one another within the full phase diagram. This permits the identification of interesting phenomena in the gauge and gravity regimes under a continuous change in parameters. We begin by studying the AdS5/CFT 4 system which, when the supergravity description is valid, exhibits a first order Hawking-Page phase transition as a function of temperature from a thermal gas of gravitons to a large black hole. In the perturbative Yang-Mills regime, we find that the free theory exhibits a weakly first order deconfinement transition whose precise nature at small nonzero coupling depends on the result of a nontrivial perturbative computation. It is conjectured that this deconfinement transition is continuously connected in the full phase diagram to the Hawking-Page transition at strong coupling, with the confined phase identified with the graviton gas and the deconfined phase identified with the black hole. We then turn to the study of Gregory-Laflamme (GL) black hole/black string transitions in supergravity and their realization in a setup that admits a dual description via the maximally supersymmetric Yang-Mills theory on T2. The thermodynamics of Yang-Mills theories on low dimensional tori is studied in detail revealing an intricate structure of which the GL transition at strong coupling is a small piece. We are led to conjecture that GL physics is continuously connected to deconfinement in maximally supersymmetric 0 + 1-dimensional gauged matrix quantum mechanics. This identification will then

Finite field equation of Yang--Mills theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brandt, R.A.; Wing-Chiu, N.; Yeung, W.

1980-03-01

We consider the finite local field equation -)(1+1/..cap alpha.. (1+f/sub 4/))g/sup munu/D'Alembertian-partial/sup ..mu../partial/sup ..nu../)A/sup nua/ =-(1+f/sub 3/) g/sup 2/N(A/sup c/..nu..A/sup a/..mu..A/sub ..nu..//sup c/) +xxx+(1-s)/sup 2/M/sup 2/A/sup a/..mu.., introduced by Lowenstein to rigorously describe SU(2) Yang--Mills theory, which is written in terms of normal products. We also consider the operator product expansion A/sup c/..nu..(x+xi) A/sup a/..mu..(x) A/sup b/lambda(x-xi) approx...sigma..M/sup c/ab..nu mu..lambda/sub c/'a'b'..nu..'..mu..'lambda' (xi) N(A/sup nuprimec/'A/sup muprimea/'A/sup lambdaprimeb/')(x), and using asymptotic freedom, we compute the leading behavior of the Wilson coefficients M/sup ...//sub .../(xi) with the help of a computer, and express the normal products in the field equation in terms ofmore » products of the c-number Wilson coefficients and of operator products like A/sup c/..nu..(x+xi) A/sup a/..mu..(x) A/sup b/lambda(x-xi) at separated points. Our result is -)(1+(1/..cap alpha..)(1+f/sub 4/))g/sup munu/D'Alembertian-partial/sup ..mu../partial/sup ..nu../)A/sup nua/ =-(1+f/sub 3/) g/sup 2/lim/sub xiarrow-right0/) (lnxi)/sup -0.28/2b/(A/sup c/..nu.. (x+xi) A/sup a/..mu..(x) A/sub ..nu..//sup c/(x-xi) +epsilon/sup a/bcA/sup muc/(x+xi) partial/sup ..nu../A/sup b//sub ..nu../(x)+xxx) +xxx)+(1-s)/sup 2/M/sup 2/A/sup a/..mu.., where ..beta.. (g) =-bg/sup 3/, and so (lnxi)/sup -0.28/2b/ is the leading behavior of the c-number coefficient multiplying the operator products in the field equation.« less

Glueball spectra from a matrix model of pure Yang-Mills theory

NASA Astrophysics Data System (ADS)

Acharyya, Nirmalendu; Balachandran, A. P.; Pandey, Mahul; Sanyal, Sambuddha; Vaidya, Sachindeo

2018-05-01

We present variational estimates for the low-lying energies of a simple matrix model that approximates SU(3) Yang-Mills theory on a three-sphere of radius R. By fixing the ground state energy, we obtain the (integrated) renormalization group (RG) equation for the Yang-Mills coupling g as a function of R. This RG equation allows to estimate the mass of other glueball states, which we find to be in excellent agreement with lattice simulations.

Loop quantum corrected Einstein Yang-Mills black holes

NASA Astrophysics Data System (ADS)

Protter, Mason; DeBenedictis, Andrew

2018-05-01

In this paper, we study the homogeneous interiors of black holes possessing SU(2) Yang-Mills fields subject to corrections inspired by loop quantum gravity. The systems studied possess both magnetic and induced electric Yang-Mills fields. We consider the system of equations both with and without Wilson loop corrections to the Yang-Mills potential. The structure of the Yang-Mills Hamiltonian, along with the restriction to homogeneity, allows for an anomaly-free effective quantization. In particular, we study the bounce which replaces the classical singularity and the behavior of the Yang-Mills fields in the quantum corrected interior, which possesses topology R ×S2 . Beyond the bounce, the magnitude of the Yang-Mills electric field asymptotically grows monotonically. This results in an ever-expanding R sector even though the two-sphere volume is asymptotically constant. The results are similar with and without Wilson loop corrections on the Yang-Mills potential.

Continuum strong-coupling expansion of Yang-Mills theory: quark confinement and infra-red slavery

NASA Astrophysics Data System (ADS)

Mansfield, Paul

1994-04-01

We solve Schrödinger's equation for the ground-state of four-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading-order approximation are reduced to a calculation in two-dimensional Yang-Mills theory which is known to confine. Consequently the Wilson loop in the four-dimensional theory obeys an area law to leading order and the coupling becomes infinite as the mass scale goes to zero.

The Stack of Yang-Mills Fields on Lorentzian Manifolds

NASA Astrophysics Data System (ADS)

Benini, Marco; Schenkel, Alexander; Schreiber, Urs

2018-03-01

We provide an abstract definition and an explicit construction of the stack of non-Abelian Yang-Mills fields on globally hyperbolic Lorentzian manifolds. We also formulate a stacky version of the Yang-Mills Cauchy problem and show that its well-posedness is equivalent to a whole family of parametrized PDE problems. Our work is based on the homotopy theoretical approach to stacks proposed in Hollander (Isr. J. Math. 163:93-124, 2008), which we shall extend by further constructions that are relevant for our purposes. In particular, we will clarify the concretification of mapping stacks to classifying stacks such as BG con.

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + φ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism.more » Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.« less

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

DOE PAGES

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; ...

2017-07-03

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + φ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism.more » Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.« less

Gravitational catalysis of merons in Einstein-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Canfora, Fabrizio; Oh, Seung Hun; Salgado-Rebolledo, Patricio

2017-10-01

We construct regular configurations of the Einstein-Yang-Mills theory in various dimensions. The gauge field is of meron-type: it is proportional to a pure gauge (with a suitable parameter λ determined by the field equations). The corresponding smooth gauge transformation cannot be deformed continuously to the identity. In the three-dimensional case we consider the inclusion of a Chern-Simons term into the analysis, allowing λ to be different from its usual value of 1 /2 . In four dimensions, the gravitating meron is a smooth Euclidean wormhole interpolating between different vacua of the theory. In five and higher dimensions smooth meron-like configurations can also be constructed by considering warped products of the three-sphere and lower-dimensional Einstein manifolds. In all cases merons (which on flat spaces would be singular) become regular due to the coupling with general relativity. This effect is named "gravitational catalysis of merons".

Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory

NASA Astrophysics Data System (ADS)

Kondo, Kei-Ichi; Kato, Seikou; Shibata, Akihiro; Shinohara, Toru

2015-05-01

The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the Yang-Mills theory based on change of variables extending the decomposition of the SU(N) Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the SU(N) Wilson loop operator. Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole. We show especially that magnetic monopoles in the Yang-Mills theory can be constructed in a manifestly gauge-invariant way starting from the gauge-invariant Wilson loop operator and thereby the contribution from the magnetic monopoles can be extracted from the Wilson loop in a gauge-invariant way through the non-Abelian Stokes theorem for the Wilson loop operator, which is a prerequisite for exhibiting magnetic monopole dominance for quark

Yang-Mills Theory at 60: Milestones, Landmarks and Interesting Questions

NASA Astrophysics Data System (ADS)

Chau, Ling-Lie

On the auspicious occasion of celebrating the 60th anniversary of the Yang-Mills theory, and Professor Yang's many other important contributions to physics and mathematics, I will highlight the impressive milestones and landmarks that have been established in the last 60 years, as well as some interesting questions that are worthy of answers from future researches. The paper is written (without equations) for the interest of non-scientists as well as of scientists.

Infrared propagators of Yang-Mills theory from perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tissier, Matthieu; Wschebor, Nicolas

2010-11-15

We show that the correlation functions of ghosts and gluons for the pure Yang-Mills theory in Landau gauge can be accurately reproduced for all momenta by a one-loop calculation. The key point is to use a massive extension of the Faddeev-Popov action. The agreement with lattice simulation is excellent in d=4. The one-loop calculation also reproduces all the characteristic features of the lattice simulations in d=3 and naturally explains the peculiarities of the propagators in d=2.

N = 2* Yang-Mills on the Lattice

NASA Astrophysics Data System (ADS)

Joseph, Anosh

2018-03-01

The N = 2* Yang-Mills theory in four dimensions is a non-conformal theory that appears as a mass deformation of maximally supersymmetric N = 4 Yang-Mills theory. This theory also takes part in the AdS/CFT correspondence and its gravity dual is type IIB supergravity on the Pilch-Warner background. The finite temperature properties of this theory have been studied recently in the literature. It has been argued that at large N and strong coupling this theory exhibits no thermal phase transition at any nonzero temperature. The low temperature N = 2* plasma can be compared to the QCD plasma. We provide a lattice construction of N = 2* Yang-Mills on a hypercubic lattice starting from the N = 4 gauge theory. The lattice construction is local, gauge-invariant, free from fermion doubling problem and preserves a part of the supersymmetry. This nonperturbative formulation of the theory can be used to provide a highly nontrivial check of the AdS/CFT correspondence in a non-conformal theory.

On the stability of dyons and dyonic black holes in Einstein-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Nolan, Brien C.; Winstanley, Elizabeth

2016-02-01

We investigate the stability of four-dimensional dyonic soliton and black hole solutions of {su}(2) Einstein-Yang-Mills theory in anti-de Sitter space. We prove that, in a neighbourhood of the embedded trivial (Schwarzschild-)anti-de Sitter solution, there exist non-trivial dyonic soliton and black hole solutions of the field equations which are stable under linear, spherically symmetric, perturbations of the metric and non-Abelian gauge field.

Discriminating between two reformulations of SU(3) Yang-Mills theory on a lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shibata, Akihiro; Kondo, Kei-Ichi; Shinohara, Toru

2016-01-22

In order to investigate quark confinement, we give a new reformulation of the SU (N) Yang-Mills theory on a lattice and present the results of the numerical simulations of the SU (3) Yang-Mills theory on a lattice. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the “Abelian” dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc.

Two-dimensional N = 2 Super-Yang-Mills Theory

NASA Astrophysics Data System (ADS)

August, Daniel; Wellegehausen, Björn; Wipf, Andreas

2018-03-01

Supersymmetry is one of the possible scenarios for physics beyond the standard model. The building blocks of this scenario are supersymmetric gauge theories. In our work we study the N = 1 Super-Yang-Mills (SYM) theory with gauge group SU(2) dimensionally reduced to two-dimensional N = 2 SYM theory. In our lattice formulation we break supersymmetry and chiral symmetry explicitly while preserving R symmetry. By fine tuning the bar-mass of the fermions in the Lagrangian we construct a supersymmetric continuum theory. To this aim we carefully investigate mass spectra and Ward identities, which both show a clear signal of supersymmetry restoration in the continuum limit.

Is the ground state of Yang-Mills theory Coulombic?

NASA Astrophysics Data System (ADS)

Heinzl, T.; Ilderton, A.; Langfeld, K.; Lavelle, M.; Lutz, W.; McMullan, D.

2008-08-01

We study trial states modelling the heavy quark-antiquark ground state in SU(2) Yang-Mills theory. A state describing the flux tube between quarks as a thin string of glue is found to be a poor description of the continuum ground state; the infinitesimal thickness of the string leads to UV artifacts which suppress the overlap with the ground state. Contrastingly, a state which surrounds the quarks with non-Abelian Coulomb fields is found to have a good overlap with the ground state for all charge separations. In fact, the overlap increases as the lattice regulator is removed. This opens up the possibility that the Coulomb state is the true ground state in the continuum limit.

Supersymmetric tools in Yang-Mills theories at strong coupling: The beginning of a long journey

NASA Astrophysics Data System (ADS)

Shifman, Mikhail

2018-04-01

Development of holomorphy-based methods in super-Yang-Mills theories started in the early 1980s and lead to a number of breakthrough results. I review some results in which I participated. The discovery of Seiberg’s duality and the Seiberg-Witten solution of 𝒩 = 2 Yang-Mills were the milestones in the long journey of which, I assume, much will be said in other talks. I will focus on the discovery (2003) of non-Abelian vortex strings with various degrees of supersymmetry, supported in some four-dimensional Yang-Mills theories and some intriguing implications of this discovery. One of the recent results is the observation of a soliton string in the bulk 𝒩 = 2 theory with the U(2) gauge group and four flavors, which can become critical in a certain limit. This is the case of a “reverse holography,” with a very transparent physical meaning.

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.

Spontaneously broken Yang-Mills-Einstein supergravities as double copies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik

Color/kinematics duality and the double-copy construction have proved to be systematic tools for gaining new insight into gravitational theories. Extending our earlier work, in this article we introduce new double-copy constructions for large classes of spontaneously-broken Yang-Mills-Einstein theories with adjoint Higgs elds. One gaugetheory copy entering the construction is a spontaneously-broken (super-)Yang-Mills theory, while the other copy is a bosonic Yang-Mills-scalar theory with trilinear scalar interactions that display an explicitly-broken global symmetry. We show that the kinematic numerators of these gauge theories can be made to obey color/kinematics duality by exhibiting particular additional Lie-algebraic relations. We discuss in detail explicitmore » examples with N = 2 supersymmetry, focusing on Yang-Mills-Einstein supergravity theories belonging to the generic Jordan family in four and five dimensions, and identify the map between the supergravity and double-copy elds and parameters. We also briefly discuss the application of our results to N = 4 supergravity theories. The constructions are illustrated by explicit examples of tree-level and one-loop scattering amplitudes.« less

Spontaneously broken Yang-Mills-Einstein supergravities as double copies

DOE PAGES

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; ...

2017-06-13

Color/kinematics duality and the double-copy construction have proved to be systematic tools for gaining new insight into gravitational theories. Extending our earlier work, in this article we introduce new double-copy constructions for large classes of spontaneously-broken Yang-Mills-Einstein theories with adjoint Higgs elds. One gaugetheory copy entering the construction is a spontaneously-broken (super-)Yang-Mills theory, while the other copy is a bosonic Yang-Mills-scalar theory with trilinear scalar interactions that display an explicitly-broken global symmetry. We show that the kinematic numerators of these gauge theories can be made to obey color/kinematics duality by exhibiting particular additional Lie-algebraic relations. We discuss in detail explicitmore » examples with N = 2 supersymmetry, focusing on Yang-Mills-Einstein supergravity theories belonging to the generic Jordan family in four and five dimensions, and identify the map between the supergravity and double-copy elds and parameters. We also briefly discuss the application of our results to N = 4 supergravity theories. The constructions are illustrated by explicit examples of tree-level and one-loop scattering amplitudes.« less

Callan-Symanzik equations for infrared Yang-Mills theory

NASA Astrophysics Data System (ADS)

Weber, Axel; Dall'Olio, Pietro

2017-12-01

Dyson-Schwinger equations have been successful in determining the correlation functions in Yang-Mills theory in the Landau gauge, in the infrared regime. We argue that similar results can be obtained, in a technically simpler way, with Callan-Symanzik renormalization group equations. We present generalizations of the infrared safe renormalization scheme proposed by Tissier and Wschebor in 2011, and show how the renormalization scheme dependence can be used to improve the matching to the existing lattice data for the gluon and ghost propagators.

An object oriented code for simulating supersymmetric Yang-Mills theories

NASA Astrophysics Data System (ADS)

Catterall, Simon; Joseph, Anosh

2012-06-01

We present SUSY_LATTICE - a C++ program that can be used to simulate certain classes of supersymmetric Yang-Mills (SYM) theories, including the well known N=4 SYM in four dimensions, on a flat Euclidean space-time lattice. Discretization of SYM theories is an old problem in lattice field theory. It has resisted solution until recently when new ideas drawn from orbifold constructions and topological field theories have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theories in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local, free of doublers and also possess exact gauge-invariance. In principle they form the basis for a truly non-perturbative definition of the continuum SYM theories. In the continuum limit they reproduce versions of the SYM theories formulated in terms of twisted fields, which on a flat space-time is just a change of the field variables. In this paper, we briefly review these ideas and then go on to provide the details of the C++ code. We sketch the design of the code, with particular emphasis being placed on SYM theories with N=(2,2) in two dimensions and N=4 in three and four dimensions, making one-to-one comparisons between the essential components of the SYM theories and their corresponding counterparts appearing in the simulation code. The code may be used to compute several quantities associated with the SYM theories such as the Polyakov loop, mean energy, and the width of the scalar eigenvalue distributions. Program summaryProgram title: SUSY_LATTICE Catalogue identifier: AELS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9315 No. of bytes in distributed program

Duality-symmetric supersymmetric Yang-Mills theory in three dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nishino, Hitoshi; Rajpoot, Subhash

We formulate a duality-symmetric N=1 supersymmetric Yang-Mills theory in three dimensions. Our field content is (A{sub {mu}}{sup I},{lambda}{sup I},{phi}{sup I}), where the index I is for the adjoint representation of an arbitrary gauge group G. Our Hodge duality symmetry is F{sub {mu}{nu}}{sup I}=+{epsilon}{sub {mu}{nu}}{sup {rho}D}{sub {rho}{phi}}{sup I}. Because of this relationship, the presence of two physical fields A{sub {mu}}{sup I} and {phi}{sup I} within the same N=1 supermultiplet poses no problem. We can couple this multiplet to another vector multiplet (C{sub {mu}}{sup I},{chi}{sup I};B{sub {mu}{nu}}{sup I}) with 1+1 physical degrees of freedom modulo dim G. Thanks to peculiar couplings andmore » supersymmetry, the usual problem with an extra vector field in a nontrivial representation does not arise in our system.« less

Yang-Mills theory and the ABC conjecture

NASA Astrophysics Data System (ADS)

He, Yang-Hui; Hu, Zhi; Probst, Malte; Read, James

2018-05-01

We establish a precise correspondence between the ABC Conjecture and 𝒩 = 4 super-Yang-Mills theory. This is achieved by combining three ingredients: (i) Elkies’ method of mapping ABC-triples to elliptic curves in his demonstration that ABC implies Mordell/Faltings; (ii) an explicit pair of elliptic curve and associated Belyi map given by Khadjavi-Scharaschkin; and (iii) the fact that the bipartite brane-tiling/dimer model for a gauge theory with toric moduli space is a particular dessin d’enfant in the sense of Grothendieck. We explore this correspondence for the highest quality ABC-triples as well as large samples of random triples. The conjecture itself is mapped to a statement about the fundamental domain of the toroidal compactification of the string realization of 𝒩 = 4 SYM.

Calculating the jet quenching parameter in the plasma of noncommutative Yang-Mills theory from gauge/gravity duality

NASA Astrophysics Data System (ADS)

Chakraborty, Somdeb; Roy, Shibaji

2012-02-01

A particular decoupling limit of the nonextremal (D1, D3) brane bound state system of type IIB string theory is known to give the gravity dual of space-space noncommutative Yang-Mills theory at finite temperature. We use a string probe in this background to compute the jet quenching parameter in a strongly coupled plasma of hot noncommutative Yang-Mills theory in (3+1) dimensions from gauge/gravity duality. We give expressions for the jet quenching parameter for both small and large noncommutativity. For small noncommutativity, we find that the value of the jet quenching parameter gets reduced from its commutative value. The reduction is enhanced with temperature as T7 for fixed noncommutativity and fixed ’t Hooft coupling. We also give an estimate of the correction due to noncommutativity at the present collider energies like in RHIC or in LHC and find it too small to be detected. We further generalize the results for noncommutative Yang-Mills theories in diverse dimensions.

Scattering amplitudes in $$\\mathcal{N}=2 $$ Maxwell-Einstein and Yang-Mills/Einstein supergravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiodaroli, Marco; Gunaydin, Murat; Johansson, Henrik

We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N = 2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N = 2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian andmore » Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at treelevel and one loop. Lastly, the double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes, which are naturally organized as polynomials in the gauge coupling constant.« less

Scattering amplitudes in $$\\mathcal{N}=2 $$ Maxwell-Einstein and Yang-Mills/Einstein supergravity

DOE PAGES

Chiodaroli, Marco; Gunaydin, Murat; Johansson, Henrik; ...

2015-01-15

We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N = 2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N = 2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian andmore » Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at treelevel and one loop. Lastly, the double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes, which are naturally organized as polynomials in the gauge coupling constant.« less

Pure spinor superspace action for D = 6, N = 1 super-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Cederwall, Martin

2018-05-01

A Batalin-Vilkovisky action for D = 6, N = 1 super-Yang-Mills theory, including coupling to hypermultiplets, is given. The formalism involves pure spinor superfields. The geometric properties of the D = 6, N = 1 pure spinors (which differ from Cartan pure spinors) are examined. Unlike the situation for maximally supersymmetric models, the fields and antifields (including ghosts) of the vector multiplet reside in separate superfields. The formalism provides an off-shell superspace formulation for matter hypermultiplets, which in a traditional treatment are on-shell.

Magnetic black holes and monopoles in a nonminimal Einstein-Yang-Mills theory with a cosmological constant: Exact solutions

NASA Astrophysics Data System (ADS)

Balakin, Alexander B.; Lemos, José P. S.; Zayats, Alexei E.

2016-04-01

Alternative theories of gravity and their solutions are of considerable importance since, at some fundamental level, the world can reveal new features. Indeed, it is suspected that the gravitational field might be nonminimally coupled to the other fields at scales not yet probed, bringing into the forefront nonminimally coupled theories. In this mode, we consider a nonminimal Einstein-Yang-Mills theory with a cosmological constant. Imposing spherical symmetry and staticity for the spacetime and a magnetic Wu-Yang ansatz for the Yang-Mills field, we find expressions for the solutions of the theory. Further imposing constraints on the nonminimal parameters, we find a family of exact solutions of the theory depending on five parameters—two nonminimal parameters, the cosmological constant, the magnetic charge, and the mass. These solutions represent magnetic monopoles and black holes in magnetic monopoles with de Sitter, Minkowskian, and anti-de Sitter asymptotics, depending on the sign and value of the cosmological constant Λ . We classify completely the family of solutions with respect to the number and the type of horizons and show that the spacetime solutions can have, at most, four horizons. For particular sets of the parameters, these horizons can become double, triple, and quadruple. For instance, for a positive cosmological constant Λ , there is a critical Λc for which the solution admits a quadruple horizon, evocative of the Λc that appears for a given energy density in both the Einstein static and Eddington-Lemaître dynamical universes. As an example of our classification, we analyze solutions in the Drummond-Hathrell nonminimal theory that describe nonminimal black holes. Another application is with a set of regular black holes previously treated.

Width of the confining string in Yang-Mills theory.

PubMed

Gliozzi, F; Pepe, M; Wiese, U-J

2010-06-11

We investigate the transverse fluctuations of the confining string connecting two static quarks in (2+1)D SU(2) Yang-Mills theory using Monte Carlo calculations. The exponentially suppressed signal is extracted from the large noise by a very efficient multilevel algorithm. The resulting width of the string increases logarithmically with the distance between the static quark charges. Corrections at intermediate distances due to universal higher-order terms in the effective string action are calculated analytically. They accurately fit the numerical data.

Non-Abelian Yang-Mills analogue of classical electromagnetic duality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chan, Hong-Mo; Faridani, J.; Tsun, T.S.

The classic question of non-Abelian Yang-Mills analogue to electromagnetic duality is examined here in a minimalist fashion at the strictly four-dimensional, classical field, and point charge level. A generalization of the Abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the Abelian theory. For example, there is a dual potential, but it is a two-indexed tensor {ital T}{sub {mu}{nu}} of the Freedman-Townsend-type. Though not itself functioning as such, {ital T}{sub {mu}{nu}} gives rise to a dual parallel transport {ital {tilde A}}{sub {mu}} for the phase of themore » wave function of the color magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard color (electric) charge itself is found to be a monpole of {ital {tilde A}}{sub {mu}}. At the same time, the gauge symmetry is found doubled from say SU({ital N}) to SU({ital N}){times}SU({ital N}). A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a ``universal`` principle, namely, the Wu-Yang criterion for monpoles, where interactions arise purely as a consequence of the topological definition of the monopole charge. The technique used is the loop space formulation of Polyakov.« less

Wess-Zumino and super Yang-Mills theories in D=4 integral superspace

NASA Astrophysics Data System (ADS)

Castellani, L.; Catenacci, R.; Grassi, P. A.

2018-05-01

We reconstruct the action of N = 1 , D = 4 Wess-Zumino and N = 1 , 2 , D = 4 super-Yang-Mills theories, using integral top forms on the supermanifold M^{(.4|4)} . Choosing different Picture Changing Operators, we show the equivalence of their rheonomic and superspace actions. The corresponding supergeometry and integration theory are discussed in detail. This formalism is an efficient tool for building supersymmetric models in a geometrical framework.

From SL(5, ℝ) Yang-Mills theory to induced gravity

NASA Astrophysics Data System (ADS)

Assimos, T. S.; Pereira, A. D.; Santos, T. R. S.; Sobreiro, R. F.; Tomaz, A. A.; Otoya, V. J. Vasquez

From pure Yang-Mills action for the SL(5, ℝ) group in four Euclidean dimensions we obtain a gravity theory in the first order formalism. Besides the Einstein-Hilbert term, the effective gravity has a cosmological constant term, a curvature squared term, a torsion squared term and a matter sector. To obtain such geometrodynamical theory, asymptotic freedom and the Gribov parameter (soft BRST symmetry breaking) are crucial. Particularly, Newton and cosmological constant are related to these parameters and they also run as functions of the energy scale. One-loop computations are performed and the results are interpreted.

Solutions to Yang-Mills Equations on Four-Dimensional de Sitter Space

NASA Astrophysics Data System (ADS)

Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.

2017-08-01

We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter space dS4 and construct a smooth and spatially homogeneous magnetic solution to the Yang-Mills equations. Slicing dS4 as R ×S3, via an SU(2)-equivariant ansatz, we reduce the Yang-Mills equations to ordinary matrix differential equations and further to Newtonian dynamics in a double-well potential. Its local maximum yields a Yang-Mills solution whose color-magnetic field at time τ ∈R is given by B˜a=-1/2 Ia/(R2cosh2τ ), where Ia for a =1 , 2, 3 are the SU(2) generators and R is the de Sitter radius. At any moment, this spatially homogeneous configuration has finite energy, but its action is also finite and of the value -1/2 j (j +1 )(2 j +1 )π3 in a spin-j representation. Similarly, the double-well bounce produces a family of homogeneous finite-action electric-magnetic solutions with the same energy. There is a continuum of other solutions whose energy and action extend down to zero.

Dirichlet to Neumann operator for Abelian Yang-Mills gauge fields

NASA Astrophysics Data System (ADS)

Díaz-Marín, Homero G.

We consider the Dirichlet to Neumann operator for Abelian Yang-Mills boundary conditions. The aim is constructing a complex structure for the symplectic space of boundary conditions of Euler-Lagrange solutions modulo gauge for space-time manifolds with smooth boundary. Thus we prepare a suitable scenario for geometric quantization within the reduced symplectic space of boundary conditions of Abelian gauge fields.

Non-Abelian sigma models from Yang-Mills theory compactified on a circle

NASA Astrophysics Data System (ADS)

Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.

2018-06-01

We consider SU(N) Yang-Mills theory on R 2 , 1 ×S1, where S1 is a spatial circle. In the infrared limit of a small-circle radius the Yang-Mills action reduces to the action of a sigma model on R 2 , 1 whose target space is a 2 (N - 1)-dimensional torus modulo the Weyl-group action. We argue that there is freedom in the choice of the framing of the gauge bundles, which leads to more general options. In particular, we show that this low-energy limit can give rise to a target space SU (N) ×SU (N) /ZN. The latter is the direct product of SU(N) and its Langlands dual SU (N) /ZN, and it contains the above-mentioned torus as its maximal Abelian subgroup. An analogous result is obtained for any non-Abelian gauge group.

AdS/CFT correspondence, quasinormal modes, and thermal correlators in N=4 supersymmetric Yang-Mills theory

NASA Astrophysics Data System (ADS)

Núñez, Alvaro; Starinets, Andrei O.

2003-06-01

We use the Lorentzian AdS/CFT prescription to find the poles of the retarded thermal Green’s functions of N=4 SU(N) supersymmetric Yang-Mills theory in the limit of large N and large ’t Hooft coupling. In the process, we propose a natural definition for quasinormal modes in an asymptotically AdS spacetime, with boundary conditions dictated by the AdS/CFT correspondence. The corresponding frequencies determine the dispersion laws for the quasiparticle excitations in the dual finite-temperature gauge theory. Correlation functions of operators dual to massive scalar, vector and gravitational perturbations in a five-dimensional AdS-Schwarzschild background are considered. We find asymptotic formulas for quasinormal frequencies in the massive scalar and tensor cases, and an exact expression for vector perturbations. In the long-distance, low-frequency limit we recover results of the hydrodynamic approximation to thermal Yang-Mills theory.

A Yang-Mills field on the extremal Reissner-Nordström black hole

NASA Astrophysics Data System (ADS)

Bizoń, Piotr; Kahl, Michał

2016-09-01

We consider a spherically symmetric (magnetic) SU(2) Yang-Mills field propagating on the exterior of the extremal Reissner-Nordström black hole. Taking advantage of the conformal symmetry, we reduce the problem to the study of the Yang-Mills equation in a geodesically complete spacetime with two asymptotically flat ends. We prove the existence of infinitely many static solutions (two of which are found in closed form) and determine the spectrum of their linear perturbations and quasinormal modes. Finally, using the hyperboloidal approach to the initial value problem, we describe the process of relaxation to the static endstates of evolution, both stable (for generic initial data) and unstable (for codimension-one initial data).

Yang-Mills correlators across the deconfinement phase transition

NASA Astrophysics Data System (ADS)

Reinosa, U.; Serreau, J.; Tissier, M.; Tresmontant, A.

2017-02-01

We compute the finite temperature ghost and gluon propagators of Yang-Mills theory in the Landau-DeWitt gauge. The background field that enters the definition of the latter is intimately related with the (gauge-invariant) Polyakov loop and serves as an equivalent order parameter for the deconfinement transition. We use an effective gauge-fixed description where the nonperturbative infrared dynamics of the theory is parametrized by a gluon mass which, as argued elsewhere, may originate from the Gribov ambiguity. In this scheme, one can perform consistent perturbative calculations down to infrared momenta, which have been shown to correctly describe the phase diagram of Yang-Mills theories in four dimensions as well as the zero-temperature correlators computed in lattice simulations. In this article, we provide the one-loop expressions of the finite temperature Landau-DeWitt ghost and gluon propagators for a large class of gauge groups and present explicit results for the SU(2) case. These are substantially different from those previously obtained in the Landau gauge, which corresponds to a vanishing background field. The nonanalyticity of the order parameter across the transition is directly imprinted onto the propagators in the various color modes. In the SU(2) case, this leads, for instance, to a cusp in the electric and magnetic gluon susceptibilities as well as similar signatures in the ghost sector. We mention the possibility that such distinctive features of the transition could be measured in lattice simulations in the background field gauge studied here.

SU(2) Yang-Mills solitons in R2 gravity

NASA Astrophysics Data System (ADS)

Perapechka, I.; Shnir, Ya.

2018-05-01

We construct new family of spherically symmetric regular solutions of SU (2) Yang-Mills theory coupled to pure R2 gravity. The particle-like field configurations possess non-integer non-Abelian magnetic charge. A discussion of the main properties of the solutions and their differences from the usual Bartnik-McKinnon solitons in the asymptotically flat case is presented. It is shown that there is continuous family of linearly stable non-trivial solutions in which the gauge field has no nodes.

Asymptotically flat, stable black hole solutions in Einstein-Yang-Mills-Chern-Simons theory.

PubMed

Brihaye, Yves; Radu, Eugen; Tchrakian, D H

2011-02-18

We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein-Yang-Mills-Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations.

Quantum vacua of 2d maximally supersymmetric Yang-Mills theory

NASA Astrophysics Data System (ADS)

Koloğlu, Murat

2017-11-01

We analyze the classical and quantum vacua of 2d N=(8,8) supersymmetric Yang-Mills theory with SU( N) and U( N) gauge group, describing the worldvolume interactions of N parallel D1-branes with flat transverse directions {R}^8 . We claim that the IR limit of the SU( N) theory in the superselection sector labeled M (mod N) — identified with the internal dynamics of ( M, N)-string bound states of the Type IIB string theory — is described by the symmetric orbifold N=(8,8) sigma model into ({R}^8)^{D-1}/S_D when D = gcd( M, N) > 1, and by a single massive vacuum when D = 1, generalizing the conjectures of E. Witten and others. The full worldvolume theory of the D1-branes is the U( N) theory with an additional U(1) 2-form gauge field B coming from the string theory Kalb-Ramond field. This U( N) + B theory has generalized field configurations, labeled by the Z-valued generalized electric flux and an independent {Z}_N -valued 't Hooft flux. We argue that in the quantum mechanical theory, the ( M, N)-string sector with M units of electric flux has a {Z}_N -valued discrete θ angle specified by M (mod N) dual to the 't Hooft flux. Adding the brane center-of-mass degrees of freedom to the SU( N) theory, we claim that the IR limit of the U( N) + B theory in the sector with M bound F-strings is described by the N=(8,8) sigma model into {Sym}^D({R}^8) . We provide strong evidence for these claims by computing an N=(8,8) analog of the elliptic genus of the UV gauge theories and of their conjectured IR limit sigma models, and showing they agree. Agreement is established by noting that the elliptic genera are modular-invariant Abelian (multi-periodic and meromorphic) functions, which turns out to be very restrictive.

Noncommutative Yang-Mills from equivalence of star products

NASA Astrophysics Data System (ADS)

Jurčo, B.; Schupp, P.

2000-05-01

It is shown that the transformation between ordinary and noncommutative Yang-Mills theory as formulated by Seiberg and Witten is due to the equivalence of certain star products on the D-brane world-volume.

String tensions in deformed Yang-Mills theory

NASA Astrophysics Data System (ADS)

Poppitz, Erich; Shalchian T., M. Erfan

2018-01-01

We study k-strings in deformed Yang-Mills (dYM) with SU(N) gauge group in the semiclassically calculable regime on R^3× S^1 . Their tensions Tk are computed in two ways: numerically, for 2 ≤ N ≤ 10, and via an analytic approach using a re-summed perturbative expansion. The latter serves both as a consistency check on the numerical results and as a tool to analytically study the large-N limit. We find that dYM k-string ratios Tk/T1 do not obey the well-known sine- or Casimir-scaling laws. Instead, we show that the ratios Tk/T1 are bound above by a square root of Casimir scaling, previously found to hold for stringlike solutions of the MIT Bag Model. The reason behind this similarity is that dYM dynamically realizes, in a theoretically controlled setting, the main model assumptions of the Bag Model. We also compare confining strings in dYM and in other four-dimensional theories with abelian confinement, notably Seiberg-Witten theory, and show that the unbroken Z_N center symmetry in dYM leads to different properties of k-strings in the two theories; for example, a "baryon vertex" exists in dYM but not in softly-broken Seiberg-Witten theory. Our results also indicate that, at large values of N, k-strings in dYM do not become free.

Parallel software for lattice N = 4 supersymmetric Yang-Mills theory

NASA Astrophysics Data System (ADS)

Schaich, David; DeGrand, Thomas

2015-05-01

We present new parallel software, SUSY LATTICE, for lattice studies of four-dimensional N = 4 supersymmetric Yang-Mills theory with gauge group SU(N). The lattice action is constructed to exactly preserve a single supersymmetry charge at non-zero lattice spacing, up to additional potential terms included to stabilize numerical simulations. The software evolved from the MILC code for lattice QCD, and retains a similar large-scale framework despite the different target theory. Many routines are adapted from an existing serial code (Catterall and Joseph, 2012), which SUSY LATTICE supersedes. This paper provides an overview of the new parallel software, summarizing the lattice system, describing the applications that are currently provided and explaining their basic workflow for non-experts in lattice gauge theory. We discuss the parallel performance of the code, and highlight some notable aspects of the documentation for those interested in contributing to its future development.

Cluster Adjacency Properties of Scattering Amplitudes in N =4 Supersymmetric Yang-Mills Theory

NASA Astrophysics Data System (ADS)

Drummond, James; Foster, Jack; Gürdoǧan, Ömer

2018-04-01

We conjecture a new set of analytic relations for scattering amplitudes in planar N =4 super Yang-Mills theory. They generalize the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr (4 ,n ). In terms of the symbol, they dictate which letters can appear consecutively. We study heptagon amplitudes and integrals in detail and present symbols for previously unknown integrals at two and three loops which support our conjecture.

Emerging geometry from maximally super-symmetric Yang-Mills theory

NASA Astrophysics Data System (ADS)

Vazquez, Samuel Enrique

In this thesis, we explore the emergence of space-time geometry, and string theory physics from N = 4 supersymmetric Yang-Mills (SYM) theory with gauge group U(N). This is done in the context of the anti-de-Sitter/conformal field theory correspondence (AdS/CFT). The main results of this thesis are the following. First, we study single trace perturbations around generic 1/2 BPS states of the theory. We do this in the large N limit, and at one-loop in the 't-Hooft coupling. We show how these states can be mapped to dynamical lattices with boson statistics and periodic boundary conditions. By dynamical, we mean that the total boson occupation number is not conserved in general. Then, we show how to derive an effective sigma model for these systems which coincides with the Polyakov action of a probe string on a 1/2 BPS geometry (in the fast string limit). Secondly, we study non-supersymmetric perturbations of the vacuum which give rise to bosonic lattices with open boundary conditions. We also do this in the large N limit, and at one-loop in the 't-Hooft coupling. We show that these states are dual to open strings on D3-branes known as "Giant Gravitons". These lattice systems are also dynamical, but in some special cases, we show that we get an integrable spin chain with open boundary conditions. Next, we study single trace perturbations at strong coupling. We do this by taking a "dilute gas" approximation. We derive an all-loop result for the dispersion relation of the "magnons" which coincides with previous conjectures in the literature. What is more, we derive the geometrical picture of the so-called "giant magnon" string solution of Hofman and Maldacena, directly from the field theory. Finally, we explore the question of classical integrability of open strings on D-branes. In particular, we study the case of the giant gravitons, and compare the integrable structures on both sides of the AdS/CFT correspondence.

Holography for field theory solitons

NASA Astrophysics Data System (ADS)

Domokos, Sophia K.; Royston, Andrew B.

2017-07-01

We extend a well-known D-brane construction of the AdS/dCFT correspondence to non-abelian defects. We focus on the bulk side of the correspondence and show that there exists a regime of parameters in which the low-energy description consists of two approximately decoupled sectors. The two sectors are gravity in the ambient spacetime, and a six-dimensional supersymmetric Yang-Mills theory. The Yang-Mills theory is defined on a rigid AdS4 × S 2 background and admits sixteen supersymmetries. We also consider a one-parameter deformation that gives rise to a family of Yang-Mills theories on asymptotically AdS4 × S 2 spacetimes, which are invariant under eight supersymmetries. With future holographic applications in mind, we analyze the vacuum structure and perturbative spectrum of the Yang-Mills theory on AdS4 × S 2, as well as systems of BPS equations for finite-energy solitons. Finally, we demonstrate that the classical Yang-Mills theory has a consistent truncation on the two-sphere, resulting in maximally supersymmetric Yang-Mills on AdS4.

Color Memory: A Yang-Mills Analog of Gravitational Wave Memory.

PubMed

Pate, Monica; Raclariu, Ana-Maria; Strominger, Andrew

2017-12-29

A transient color flux across null infinity in classical Yang-Mills theory is considered. It is shown that a pair of test "quarks" initially in a color singlet generically acquire net color as a result of the flux. A nonlinear formula is derived for the relative color rotation of the quarks. For a weak color flux, the formula linearizes to the Fourier transform of the soft gluon theorem. This color memory effect is the Yang-Mills analog of the gravitational memory effect.

Color Memory: A Yang-Mills Analog of Gravitational Wave Memory

NASA Astrophysics Data System (ADS)

Pate, Monica; Raclariu, Ana-Maria; Strominger, Andrew

2017-12-01

A transient color flux across null infinity in classical Yang-Mills theory is considered. It is shown that a pair of test "quarks" initially in a color singlet generically acquire net color as a result of the flux. A nonlinear formula is derived for the relative color rotation of the quarks. For a weak color flux, the formula linearizes to the Fourier transform of the soft gluon theorem. This color memory effect is the Yang-Mills analog of the gravitational memory effect.

Self-dual phase space for (3 +1 )-dimensional lattice Yang-Mills theory

NASA Astrophysics Data System (ADS)

Riello, Aldo

2018-01-01

I propose a self-dual deformation of the classical phase space of lattice Yang-Mills theory, in which both the electric and magnetic fluxes take value in the compact gauge Lie group. A local construction of the deformed phase space requires the machinery of "quasi-Hamiltonian spaces" by Alekseev et al., which is reviewed here. The results is a full-fledged finite-dimensional and gauge-invariant phase space, the self-duality properties of which are largely enhanced in (3 +1 ) spacetime dimensions. This enhancement is due to a correspondence with the moduli space of an auxiliary noncommutative flat connection living on a Riemann surface defined from the lattice itself, which in turn equips the duality between electric and magnetic fluxes with a neat geometrical interpretation in terms of a Heegaard splitting of the space manifold. Finally, I discuss the consequences of the proposed deformation on the quantization of the phase space, its quantum gravitational interpretation, as well as its relevance for the construction of (3 +1 )-dimensional topological field theories with defects.

Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions

NASA Astrophysics Data System (ADS)

de Medeiros, Paul; Figueroa-O'Farrill, José

2016-03-01

We consider bosonic supersymmetric backgrounds of ten-dimensional conformal supergravity. Up to local conformal isometry, we classify the maximally supersymmetric backgrounds, determine their conformal symmetry superalgebras and show how they arise as near-horizon geometries of certain half-BPS backgrounds or as a plane-wave limit thereof. We then show how to define Yang-Mills theory with rigid supersymmetry on any supersymmetric conformal supergravity background and, in particular, on the maximally supersymmetric backgrounds. We conclude by commenting on a striking resemblance between the supersymmetric backgrounds of ten-dimensional conformal supergravity and those of eleven-dimensional Poincaré supergravity.

Scattering of massless scalar waves by magnetically charged black holes in Einstein-Yang-Mills-Higgs theory

NASA Astrophysics Data System (ADS)

Gußmann, Alexander

2017-03-01

The existence of the classical black hole solutions of the Einstein-Yang-Mills-Higgs equations with non-Abelian Yang-Mills-Higgs hair implies that not all classical stationary magnetically charged black holes can be uniquely described by their asymptotic characteristics. In fact, in a certain domain of parameters, there exist different spherically-symmetric, non-rotating and asymptotically-flat classical black hole solutions of the Einstein-Yang-Mills-Higgs equations which have the same ADM mass and the same magnetic charge but significantly different geometries in the near-horizon regions. (These are black hole solutions which are described by a Reissner-Nordström metric on the one hand and the black hole solutions with non-Abelian Yang-Mills-Higgs hair which are described by a metric which is not of Reissner-Nordström form on the other hand). One can experimentally distinguish such black holes with the same asymptotic characteristics but different near-horizon geometries classically by probing the near-horizon regions of the black holes. We argue that one way to probe the near-horizon region of a black hole which allows one to distinguish magnetically charged black holes with the same asymptotic characteristics but different near-horizon geometries is by classical scattering of waves. Using the example of a minimally-coupled massless probe scalar field scattered by magnetically charged black holes which can be obtained as solutions of the Einstein-Yang-Mills-Higgs equations with a Higgs triplet and gauge group SU(2) in the limit of an infinite Higgs self-coupling constant we show how, in this case, the scattering cross sections differ for the magnetically charged black holes with different near-horizon geometries but the same asymptotic characteristics. We find in particular that the characteristic glory peaks in the cross sections are located at different scattering angles.

AdS charged black holes in Einstein-Yang-Mills gravity's rainbow: Thermal stability and P - V criticality

NASA Astrophysics Data System (ADS)

Hendi, Seyed Hossein; Momennia, Mehrab

2018-02-01

Motivated by the interesting non-abelian gauge field, in this paper, we look for the analytical solutions of Yang-Mills theory in the context of gravity's rainbow. Regarding the trace of quantum gravity in black hole thermodynamics, we examine the first law of thermodynamics and also thermal stability in the canonical ensemble. We show that although the rainbow functions and Yang-Mills charge modify the solutions, the first law of thermodynamics is still valid. Based on the phenomenological similarities between the adS black holes and van der Waals liquid/gas systems, we study the critical behavior of the Yang-Mills black holes in the extended phase space thermodynamics. We also investigate the effects of various parameters on thermal instability as well as critical properties by using appropriate figures.

Einstein-Yang-Mills scattering amplitudes from scattering equations

NASA Astrophysics Data System (ADS)

Cachazo, Freddy; He, Song; Yuan, Ellis Ye

2015-01-01

We present the building blocks that can be combined to produce tree-level S-matrix elements of a variety of theories with various spins mixed in arbitrary dimensions. The new formulas for the scattering of n massless particles are given by integrals over the positions of n points on a sphere restricted to satisfy the scattering equations. As applications, we obtain all single-trace amplitudes in Einstein-Yang-Mills (EYM) theory, and generalizations to include scalars. Also in EYM but extended by a B-field and a dilaton, we present all double-trace gluon amplitudes. The building blocks are made of Pfaffians and Parke-Taylor-like factors of subsets of particle labels.

Yang-Mills matrix mechanics and quantum phases

NASA Astrophysics Data System (ADS)

Pandey, Mahul; Vaidya, Sachindeo

The SU(2) Yang-Mills matrix model coupled to fundamental fermions is studied in the adiabatic limit, and quantum critical behavior is seen at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners, and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. The SU(2) Yang-Mills matrix model coupled to two Weyl fermions has three quantum phases. When coupled to a massless Dirac fermion, the number of quantum phases is four. One of these phases is the color-spin locked phase. This paper is an extended version of the lectures given by the second author (SV) at the International Workshop on Quantum Physics: Foundations and Applications, Bangalore, in February 2016, and is based on [1].

Generalization of Faddeev-Popov rules in Yang-Mills theories: N = 3,4 BRST symmetries

NASA Astrophysics Data System (ADS)

Reshetnyak, Alexander

2018-01-01

The Faddeev-Popov rules for a local and Poincaré-covariant Lagrangian quantization of a gauge theory with gauge group are generalized to the case of an invariance of the respective quantum actions, S(N), with respect to N-parametric Abelian SUSY transformations with odd-valued parameters λp, p = 1,…,N and generators sp: spsq + sqsp = 0, for N = 3, 4, implying the substitution of an N-plet of ghost fields, Cp, instead of the parameter, ξ, of infinitesimal gauge transformations: ξ = Cpλ p. The total configuration spaces of fields for a quantum theory of the same classical model coincide in the N = 3 and N = 4 symmetric cases. The superspace of N = 3 SUSY irreducible representation includes, in addition to Yang-Mills fields 𝒜μ, (3 + 1) ghost odd-valued fields Cp, B̂ and 3 even-valued Bpq for p, q = 1, 2, 3. To construct the quantum action, S(3), by adding to the classical action, S0(𝒜), of an N = 3-exact gauge-fixing term (with gauge fermion), a gauge-fixing procedure requires (1 + 3 + 3 + 1) additional fields, Φ¯(3): antighost C¯, 3 even-valued Bp, 3 odd-valued B̂pq and Nakanishi-Lautrup B fields. The action of N = 3 transformations on new fields as N = 3-irreducible representation space is realized. These transformations are the N = 3 BRST symmetry transformations for the vacuum functional, Z3(0) =∫dΦ(3)dΦ¯(3)exp{(ı/ℏ)S(3)}. The space of all fields (Φ(3),Φ¯(3)) proves to be the space of an irreducible representation of the fields Φ(4) for N = 4-parametric SUSY transformations, which contains, in addition to 𝒜μ the (4 + 6 + 4 + 1) ghost-antighost, Cr = (Cp,C¯), even-valued, Brs = -Bsr = (Bpq,Bp4 = Bp), odd-valued B̂r = (B̂,B̂pq) and B fields. The quantum action is constructed by adding to S0(𝒜) an N = 4-exact gauge-fixing term with a gauge boson, F(4). The N = 4 SUSY transformations are by N = 4 BRST transformations for the vacuum functional, Z4(0) =∫dΦ(4)exp{(ı/ℏ)S(4)}. The procedures are valid for

Gravitational matter-antimatter asymmetry and four-dimensional Yang-Mills gauge symmetry

NASA Technical Reports Server (NTRS)

Hsu, J. P.

1981-01-01

A formulation of gravity based on the maximum four-dimensional Yang-Mills gauge symmetry is studied. The theory predicts that the gravitational force inside matter (fermions) is different from that inside antimatter. This difference could lead to the cosmic separation of matter and antimatter in the evolution of the universe. Moreover, a new gravitational long-range spin-force between two fermions is predicted, in addition to the usual Newtonian force. The geometrical foundation of such a gravitational theory is the Riemann-Cartan geometry, in which there is a torsion. The results of the theory for weak fields are consistent with previous experiments.

Improved results for the mass spectrum of N = 1 supersymmetric SU(3) Yang-Mills theory

NASA Astrophysics Data System (ADS)

Ali, Sajid; Bergner, Georg; Gerber, Henning; Giudice, Pietro; Kuberski, Simon; Münster, Gernot; Montvay, István; Piemonte, Stefano; Scior, Philipp

2018-03-01

This talk summarizes the results of the DESY-Münster collaboration for N = 1 supersymmetric Yang-Mills theory with the gauge group SU(3). It is an updated status report with respect to our preliminary data presented at the last conference. In order to control the lattice artefacts we have now considered a clover improved fermion action and different values of the gauge coupling.

Phase diagram of q-deformed Yang-Mills theory on S 2 at non-zero θ-angle

NASA Astrophysics Data System (ADS)

Okuyama, Kazumi

2018-04-01

We study the phase diagram of q-deformed Yang-Mills theory on S 2 at non-zero θ-angle using the exact partition function at finite N . By evaluating the exact partition function numerically, we find evidence for the existence of a series of phase transitions at non-zero θ-angle as conjectured in [hep-th/0509004

Nonperturbative study of dynamical SUSY breaking in N =(2 ,2 ) Yang-Mills theory

NASA Astrophysics Data System (ADS)

Catterall, Simon; Jha, Raghav G.; Joseph, Anosh

2018-03-01

We examine the possibility of dynamical supersymmetry breaking in two-dimensional N =(2 ,2 ) supersymmetric Yang-Mills theory. The theory is discretized on a Euclidean spacetime lattice using a supersymmetric lattice action. We compute the vacuum energy of the theory at finite temperature and take the zero-temperature limit. Supersymmetry will be spontaneously broken in this theory if the measured ground-state energy is nonzero. By performing simulations on a range of lattices up to 96 ×96 we are able to perform a careful extrapolation to the continuum limit for a wide range of temperatures. Subsequent extrapolations to the zero-temperature limit yield an upper bound on the ground-state energy density. We find the energy density to be statistically consistent with zero in agreement with the absence of dynamical supersymmetry breaking in this theory.

Critical phenomena in the general spherically symmetric Einstein-Yang-Mills system

NASA Astrophysics Data System (ADS)

Maliborski, Maciej; Rinne, Oliver

2018-02-01

We study critical behavior in gravitational collapse of a general spherically symmetric Yang-Mills field coupled to the Einstein equations. Unlike the magnetic ansatz used in previous numerical work, the general Yang-Mills connection has two degrees of freedom in spherical symmetry. This fact changes the phenomenology of critical collapse dramatically. The magnetic sector features both type I and type II critical collapse, with universal critical solutions. In contrast, in the general system type I disappears and the critical behavior at the threshold between dispersal and black hole formation is always type II. We obtain values of the mass scaling and echoing exponents close to those observed in the magnetic sector, however we find some indications that the critical solution differs from the purely magnetic discretely self-similar attractor and exact self-similarity and universality might be lost. The additional "type III" critical phenomenon in the magnetic sector, where black holes form on both sides of the threshold but the Yang-Mills potential is in different vacuum states and there is a mass gap, also disappears in the general system. We support our dynamical numerical simulations with calculations in linear perturbation theory; for instance, we compute quasi-normal modes of the unstable attractor (the Bartnik-McKinnon soliton) in type I collapse in the magnetic sector.

Composite operator and condensate in the S U (N ) Yang-Mills theory with U (N -1 ) stability group

NASA Astrophysics Data System (ADS)

Warschinke, Matthias; Matsudo, Ryutaro; Nishino, Shogo; Shinohara, Toru; Kondo, Kei-Ichi

2018-02-01

Recently, some reformulations of the Yang-Mills theory inspired by the Cho-Faddeev-Niemi decomposition have been developed in order to understand confinement from the viewpoint of the dual superconductivity. In this paper we focus on the reformulated S U (N ) Yang-Mills theory in the minimal option with U (N -1 ) stability group. Despite existing numerical simulations on the lattice we perform the perturbative analysis to one-loop level as a first step towards the nonperturbative analytical treatment. First, we give the Feynman rules and calculate all renormalization factors to obtain the standard renormalization group functions to one-loop level in light of the renormalizability of this theory. Then we introduce a mixed gluon-ghost composite operator of mass dimension 2 and show the Bechi-Rouet-Stora-Tyutin invariance and the multiplicative renormalizability. Armed with these results, we argue the existence of the mixed gluon-ghost condensate by means of the so-called local composite operator formalism, which leads to various interesting implications for confinement as shown in preceding works.

Infrared singularities in Landau gauge Yang-Mills theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 tendmore » 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.« less

Amplitudes in the N=4 supersymmetric Yang-Mills theory from quantum geometry of momentum space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorsky, A.

We discuss multiloop maximally helicity violating amplitudes in the N=4 supersymmetric Yang-Mills theory in terms of effective gravity in the momentum space with IR regulator branes as degrees of freedom. Kinematical invariants of external particles yield the moduli spaces of complex or Kahler structures which are the playgrounds for the Kodaira-Spencer or Kahler type gravity. We suggest fermionic representation of the loop maximally helicity violating amplitudes in the N=4 supersymmetric Yang-Mills theory assuming the identification of the IR regulator branes with Kodaira-Spencer fermions in the B model and Lagrangian branes in the A model. The two-easy mass box diagram ismore » related to the correlator of fermionic currents on the spectral curve in the B model or hyperbolic volume in the A model and it plays the role of a building block in the whole picture. The Bern-Dixon-Smirnov-like ansatz has the interpretation as the semiclassical limit of a fermionic correlator. It is argued that fermionic representation implies a kind of integrability on the moduli spaces. We conjecture the interpretation of the reggeon degrees of freedom in terms of the open strings stretched between the IR regulator branes.« less

On the existence of topological dyons and dyonic black holes in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups

NASA Astrophysics Data System (ADS)

Baxter, J. Erik

2018-05-01

Here we study the global existence of "hairy" dyonic black hole and dyon solutions to four-dimensional, anti-de Sitter Einstein-Yang-Mills theories for a general simply connected and semisimple gauge group G, for the so-called topologically symmetric systems, concentrating here on the regular case. We generalise here cases in the literature which considered purely magnetic spherically symmetric solutions for a general gauge group and topological dyonic solutions for s u (N ) . We are able to establish the global existence of non-trivial solutions to all such systems, both near existing embedded solutions and as |Λ| → ∞. In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the s u (N ) case proved important to stability. We believe that these are the most general analytically proven solutions in 4D anti-de Sitter Einstein-Yang-Mills systems to date.

Running coupling from gluon and ghost propagators in the Landau gauge: Yang-Mills theories with adjoint fermions

NASA Astrophysics Data System (ADS)

Bergner, Georg; Piemonte, Stefano

2018-04-01

Non-Abelian gauge theories with fermions transforming in the adjoint representation of the gauge group (AdjQCD) are a fundamental ingredient of many models that describe the physics beyond the Standard Model. Two relevant examples are N =1 supersymmetric Yang-Mills (SYM) theory and minimal walking technicolor, which are gauge theories coupled to one adjoint Majorana and two adjoint Dirac fermions, respectively. While confinement is a property of N =1 SYM, minimal walking technicolor is expected to be infrared conformal. We study the propagators of ghost and gluon fields in the Landau gauge to compute the running coupling in the MiniMom scheme. We analyze several different ensembles of lattice Monte Carlo simulations for the SU(2) adjoint QCD with Nf=1 /2 ,1 ,3 /2 , and 2 Dirac fermions. We show how the running of the coupling changes as the number of interacting fermions is increased towards the conformal window.

The light bound states of N=1 supersymmetric SU(3) Yang-Mills theory on the lattice

NASA Astrophysics Data System (ADS)

Ali, Sajid; Bergner, Georg; Gerber, Henning; Giudice, Pietro; Montvay, Istvan; Münster, Gernot; Piemonte, Stefano; Scior, Philipp

2018-03-01

In this article we summarise our results from numerical simulations of N=1 supersymmetric Yang-Mills theory with gauge group SU(3). We use the formulation of Curci and Veneziano with clover-improved Wilson fermions. The masses of various bound states have been obtained at different values of the gluino mass and gauge coupling. Extrapolations to the limit of vanishing gluino mass indicate that the bound states form mass-degenerate supermultiplets.

Tachyonic instabilities in 2  +  1 dimensional Yang-Mills theory and its connection to number theory

NASA Astrophysics Data System (ADS)

Chamizo, Fernando; González-Arroyo, Antonio

2017-06-01

We consider the 2  +  1 dimensional Yang-Mills theory with gauge group {{SU}}(N) on a flat 2-torus under twisted boundary conditions. We study the possibility of phase transitions (tachyonic instabilities) when N and the volume vary and certain chromomagnetic flux associated to the topology of the bundle can be adjusted. Under natural assumptions about how to match the perturbative regime and the expected confinement, we prove that the absence of tachyonic instabilities is related to some problems in number theory, namely the Diophantine approximation of irreducible fractions by other fractions of smaller denominator.

Double-winding Wilson loops in SU(N) Yang-Mills theory - A criterion for testing the confinement models -

NASA Astrophysics Data System (ADS)

Matsudo, Ryutaro; Kondo, Kei-Ichi; Shibata, Akihiro

2018-03-01

We examine how the average of double-winding Wilson loops depends on the number of color N in the SU(N) Yang-Mills theory. In the case where the two loops C1 and C2 are identical, we derive the exact operator relation which relates the doublewinding Wilson loop operator in the fundamental representation to that in the higher dimensional representations depending on N. By taking the average of the relation, we find that the difference-of-areas law for the area law falloff recently claimed for N = 2 is excluded for N ⩾ 3, provided that the string tension obeys the Casimir scaling for the higher representations. In the case where the two loops are distinct, we argue that the area law follows a novel law (N - 3)A1/(N - 1) + A2 with A1 and A2(A1 < A2) being the minimal areas spanned respectively by the loops C1 and C2, which is neither sum-ofareas (A1 + A2) nor difference-of-areas (A2 - A1) law when (N ⩾ 3). Indeed, this behavior can be confirmed in the two-dimensional SU(N) Yang-Mills theory exactly.

Seiberg-Witten/Whitham Equations and Instanton Corrections in {\\mathscr{N}}=2 Supersymmetric Yang-Mills Theory

NASA Astrophysics Data System (ADS)

Dai, Jia-Liang; Fan, En-Gui

2018-05-01

We obtain the instanton correction recursion relations for the low energy effective prepotential in pure {\\mathscr{N}}=2 SU(n) supersymmetric Yang-Mills gauge theory from Whitham hierarchy and Seiberg-Witten/Whitham equations. These formulae provide us a powerful tool to calculate arbitrary order instanton corrections coefficients from the perturbative contributions of the effective prepotential in Seiberg-Witten gauge theory. We apply this idea to evaluate one- and twoorder instanton corrections coefficients explicitly in SU(n) case in detail through the dynamical scale parameter expressed in terms of Riemann’s theta-function. Supported by the National Natural Science Foundation of China under Grant No. 11271079

From decay to complete breaking: pulling the strings in SU(2) Yang-Mills theory.

PubMed

Pepe, M; Wiese, U-J

2009-05-15

We study {2Q+1} strings connecting two static charges Q in (2+1)D SU(2) Yang-Mills theory. While the fundamental {2} string between two charges Q=1/2 is unbreakable, the adjoint {3} string connecting two charges Q=1 can break. When a {4} string is stretched beyond a critical length, it decays into a {2} string by gluon pair creation. When a {5} string is stretched, it first decays into a {3} string, which eventually breaks completely. The energy of the screened charges at the ends of a string is well described by a phenomenological constituent gluon model.

Five-dimensional Yang-Mills-Einstein supergravity on orbifold spacetimes: From phenomenology to M -theory

NASA Astrophysics Data System (ADS)

McReynolds, Sean

Five-dimensional N = 2 Yang-Mills-Einstein supergravity and its couplings to hyper and tensor multiplets are considered on an orbifold spacetime of the form M4 x S1/Gamma, where Gamma is a discrete group. As is well known in such cases, supersymmetry is broken to N = 1 on the orbifold fixed planes, and chiral 4D theories can be obtained from bulk hypermultiplets (or from the coupling of fixed-plane supported fields). Five-dimensional gauge symmetries are broken by boundary conditions for the fields, which are equivalent to some set of Gamma-parity assignments in the orbifold theory, allowing for arbitrary rank reduction. Furthermore, Wilson lines looping from one boundary to the other can break bulk gauge groups, or give rise to vacuum expectation values for scalars on the boundaries, which can result in spontaneous breaking of boundary gauge groups. The broken gauge symmetries do not survive as global symmetries of the low energy theories below the compactification scale due to 4 D minimal couplings to gauge fields. Axionic fields are a generic feature, just as in any compactification of M-theory (or string theory for that matter), and we exhibit the form of this field and its role as the QCD axion, capable of resolving the strong CP problem. The main motivation for the orbifold theories here is taken to be orbifold-GUTS, wherein a unified gauge group is sought in higher dimensions while allowing the orbifold reduction to handle problems such as rapid proton decay, exotic matter, mass hierarchies, etc. To that end, we discuss the allowable minimal SU(5), SO(10) and E6 GUT theories with all fields living in five dimensions. It is argued that, within the class of homogeneous quaternionic scalar manifolds characterizing the hypermultiplet couplings in 5D, supergravity admits a restricted set of theories that yield minimal phenomenological field content. In addition, non-compact gaugings are a novel feature of supergravity theories, and in particular we consider the

Testing holography using lattice super-Yang-Mills theory on a 2-torus

NASA Astrophysics Data System (ADS)

Catterall, Simon; Jha, Raghav G.; Schaich, David; Wiseman, Toby

2018-04-01

We consider maximally supersymmetric SU (N ) Yang-Mills theory in Euclidean signature compactified on a flat two-dimensional torus with antiperiodic ("thermal") fermion boundary conditions imposed on one cycle. At large N , holography predicts that this theory describes certain black hole solutions in type IIA and IIB supergravity, and we use lattice gauge theory to test this. Unlike the one-dimensional quantum mechanics case where there is only the dimensionless temperature to vary, here we emphasize there are two more parameters which determine the shape of the flat torus. While a rectangular Euclidean torus yields a thermal interpretation, allowing for skewed tori modifies the holographic dual black hole predictions and results in another direction to test holography. Our lattice calculations are based on a supersymmetric formulation naturally adapted to a particular skewing. Using this we perform simulations up to N =16 with several lattice spacings for both skewed and rectangular tori. We observe the two expected black hole phases with their predicted behavior, with a transition between them that is consistent with the gravity prediction based on the Gregory-Laflamme transition.

An instability of hyperbolic space under the Yang-Mills flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gegenberg, Jack; Day, Andrew C.; Liu, Haitao

2014-04-15

We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated Riemannian geometry is one of constant curvature. We analytically solve the linearized flow equations for a large class of perturbations to the fixed point corresponding to hyperbolic 3-space. These can be expressed as a linear superposition of distinct modes, some of which are exponentially growing along the flow. The growing modes imply the divergence ofmore » the (gauge invariant) perturbative torsion for a wide class of initial data, indicating an instability of the background geometry that we confirm with numeric simulations in the partially compactified case. There are stable modes with zero torsion, but all the unstable modes are torsion-full. This leads us to speculate that the instability is induced by the torsion degrees of freedom present in the Yang-Mills flow.« less

Adventures in Topological Field Theory

NASA Astrophysics Data System (ADS)

Horne, James H.

1990-01-01

This thesis consists of 5 parts. In part I, the topological Yang-Mills theory and the topological sigma model are presented in a superspace formulation. This greatly simplifies the field content of the theories, and makes the Q-invariance more obvious. The Feynman rules for the topological Yang -Mills theory are derived. We calculate the one-loop beta-functions of the topological sigma model in superspace. The lattice version of these theories is presented. The self-duality constraints of both models lead to spectrum doubling. In part II, we show that conformally invariant gravity in three dimensions is equivalent to the Yang-Mills gauge theory of the conformal group in three dimensions, with a Chern-Simons action. This means that conformal gravity is finite and exactly soluble. In part III, we derive the skein relations for the fundamental representations of SO(N), Sp(2n), Su(m| n), and OSp(m| 2n). These relations can be used recursively to calculate the expectation values of Wilson lines in three-dimensional Chern-Simons gauge theory with these gauge groups. A combination of braiding and tying of Wilson lines completely describes the skein relations. In part IV, we show that the k = 1 two dimensional gravity amplitudes at genus 3 agree precisely with the results from intersection theory on moduli space. Predictions for the genus 4 intersection numbers follow from the two dimensional gravity theory. In part V, we discuss the partition function in two dimensional gravity. For the one matrix model at genus 2, we use the partition function to derive a recursion relation. We show that the k = 1 amplitudes completely determine the partition function at arbitrary genus. We present a conjecture for the partition function for the arbitrary topological field theory coupled to topological gravity.

Integrability in dipole-deformed \\boldsymbol{N=4} super Yang-Mills

NASA Astrophysics Data System (ADS)

Guica, Monica; Levkovich Maslyuk, Fedor; Zarembo, Konstantin

2017-09-01

We study the null dipole deformation of N=4 super Yang-Mills theory, which is an example of a potentially solvable ‘dipole CFT’: a theory that is non-local along a null direction, has non-relativistic conformal invariance along the remaining ones, and is holographically dual to a Schrödinger space-time. We initiate the field-theoretical study of the spectrum in this model by using integrability inherited from the parent theory. The dipole deformation corresponds to a nondiagonal Drinfeld-Reshetikhin twist in the spin chain picture, which renders the traditional Bethe ansatz inapplicable from the very beginning. We use instead the Baxter equation supplemented with nontrivial asymptotics, which gives the full 1-loop spectrum in the sl(2) sector. We show that anomalous dimensions of long gauge theory operators perfectly match the string theory prediction, providing a quantitative test of Schrödinger holography. Dedicated to the memory of Petr Petrovich Kulish.

The universal character of Zwanziger's horizon function in Euclidean Yang-Mills theories

NASA Astrophysics Data System (ADS)

Capri, M. A. L.; Dudal, D.; Guimaraes, M. S.; Pereira, A. D.; Mintz, B. W.; Palhares, L. F.; Sorella, S. P.

2018-06-01

In light of the recently established BRST invariant formulation of the Gribov-Zwanziger theory, we show that Zwanziger's horizon function displays a universal character. More precisely, the correlation functions of local BRST invariant operators evaluated with the Yang-Mills action supplemented with a BRST invariant version of the Zwanziger's horizon function and quantized in an arbitrary class of covariant, color invariant and renormalizable gauges which reduce to the Landau gauge when all gauge parameters are set to zero, have a unique, gauge parameters independent result, corresponding to that of the Landau gauge when the restriction to the Gribov region Ω in the latter gauge is imposed. As such, thanks to the BRST invariance, the cut-off at the Gribov region Ω acquires a gauge independent meaning in the class of the physical correlators.

New perspectives on an old problem: The bending of light in Yang-Mills gravity

NASA Astrophysics Data System (ADS)

Cottrell, Kazuo Ota; Hsu, Jong-Ping

Yang-Mills gravity with electromagnetism predicts, in the geometric optics limit, a value for the deflection of light by the sun which agrees closely with the reanalysis of Eddington's 1919 optical measurements done in 1979. Einstein's General Theory of Relativity, on the other hand, agrees very closely with measurements of the deflection of electromagnetic waves made in the range of radio frequencies. Since both General Relativity and Yang-Mills gravity with electromagnetism in the geometric optics limit make predictions for the optical region which fall within experimental uncertainty, it becomes important to consider the possibility of the existence of a frequency dependence in the measurement results for the deflection of light, in order to determine which theory more closely describes nature...

Finite-action solutions of Yang-Mills equations on de Sitter dS4 and anti-de Sitter AdS4 spaces

NASA Astrophysics Data System (ADS)

Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.

2017-11-01

We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter dS4 and anti-de Sitter AdS4 spaces and construct various solutions to the Yang-Mills equations. On de Sitter space we reduce the Yang-Mills equations via an SU(2)-equivariant ansatz to Newtonian mechanics of a particle moving in R^3 under the influence of a quartic potential. Then we describe magnetic and electric-magnetic solutions, both Abelian and non-Abelian, all having finite energy and finite action. A similar reduction on anti-de Sitter space also yields Yang-Mills solutions with finite energy and action. We propose a lower bound for the action on both backgrounds. Employing another metric on AdS4, the SU(2) Yang-Mills equations are reduced to an analytic continuation of the above particle mechanics from R^3 to R^{2,1} . We discuss analytical solutions to these equations, which produce infinite-action configurations. After a Euclidean continuation of dS4 and AdS4 we also present self-dual (instanton-type) Yang-Mills solutions on these backgrounds.

Tests of conformal field theory at the Yang-Lee singularity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wydro, Tomasz; McCabe, John F.

2009-12-14

This paper studies the Yang-Lee edge singularity of 2-dimensional (2D) Ising model based on a quantum spin chain and transfer matrix measurements on the cylinder. Based on finite-size scaling, the low-lying excitation spectrum is found at the Yang-Lee edge singularity. Based on transfer matrix techniques, the single structure constant is evaluated at the Yang-Lee edge singularity. The results of both types of measurements are found to be fully consistent with the predictions for the (A{sub 4}, A{sub 1}) minimal conformal field theory, which was previously identified with this critical point.

A note on local BRST cohomology of Yang-Mills type theories with free Abelian factors

NASA Astrophysics Data System (ADS)

Barnich, Glenn; Boulanger, Nicolas

2018-05-01

We extend previous work on antifield dependent local Becchi-Rouet-Stora-Tyutin (BRST) cohomology for matter coupled gauge theories of Yang-Mills type to the case of gauge groups that involve free Abelian factors. More precisely, we first investigate in a model independent way how the dynamics enters the computation of the cohomology for a general class of Lagrangians in general spacetime dimensions. We then discuss explicit solutions in the case of specific models. Our analysis has implications for the structure of characteristic cohomology and for consistent deformations of the classical models, as well as for divergences/counterterms and for gauge anomalies that may appear during perturbative quantization.

Higher spin gravitational couplings: Ghosts in the Yang-Mills detour complex

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gover, A. R.; Hallowell, K.; Waldron, A.

2007-01-15

Gravitational interactions of higher spin fields are generically plagued by inconsistencies. There exists however, a simple framework that couples higher spins to a broad class of gravitational backgrounds (including Ricci flat and Einstein) consistently at the classical level. The model is the simplest example of a Yang-Mills detour complex and has broad mathematical applications, especially to conformal geometry. Even the simplest version of the theory, which couples gravitons, vectors and scalar fields in a flat background is rather rich, providing an explicit setting for detailed analysis of ghost excitations. Its asymptotic scattering states consist of a physical massless graviton, scalar,more » and massive vector along with a degenerate pair of zero norm photon excitations. Coherent states of the unstable sector do have positive norms, but their evolution is no longer unitary and amplitudes grow with time. The class of models proposed is extremely general and of considerable interest for ghost condensation and invariant theory.« less

S-Duality, Deconstruction and Confinement for a Marginal Deformation of N=4 SUSY Yang-Mills

NASA Astrophysics Data System (ADS)

Dorey, Nick

2004-08-01

We study an exactly marginal deformation of Script N = 4 SUSY Yang-Mills with gauge group U(N) using field theory and string theory methods. The classical theory has a Higgs branch for rational values of the deformation parameter. We argue that the quantum theory also has an S-dual confining branch which cannot be seen classically. The low-energy effective theory on these branches is a six-dimensional non-commutative gauge theory with sixteen supercharges. Confinement of magnetic and electric charges, on the Higgs and confining branches respectively, occurs due to the formation of BPS-saturated strings in the low energy theory. The results also suggest a new way of deconstructing Little String Theory as a large-N limit of a confining gauge theory in four dimensions.

Perturbative tests for a large-N reduced model of {N} = {4} super Yang-Mills theory

NASA Astrophysics Data System (ADS)

Ishiki, Goro; Shimasaki, Shinji; Tsuchiya, Asato

2011-11-01

We study a non-perturbative formulation of {N} = {4} super Yang-Mills theory (SYM) on R × S 3 in the planar limit proposed in arXiv:0807.2352. This formulation is based on the large- N reduction, and the theory can be described as a particular large- N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S 3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.

Yang-Mills gauge conditions from Witten's open string field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Feng Haidong; Siegel, Warren

2007-02-15

We construct the Zinn-Justin-Batalin-Vilkovisky action for tachyons and gauge bosons from Witten's 3-string vertex of the bosonic open string without gauge fixing. Through canonical transformations, we find the off-shell, local, gauge-covariant action up to 3-point terms, satisfying the usual field theory gauge transformations. Perturbatively, it can be extended to higher-point terms. It also gives a new gauge condition in field theory which corresponds to the Feynman-Siegel gauge on the world-sheet.

Constructing the tree-level Yang-Mills S-matrix using complex factorization

NASA Astrophysics Data System (ADS)

Schuster, Philip C.; Toro, Natalia

2009-06-01

A remarkable connection between BCFW recursion relations and constraints on the S-matrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of four-particle amplitudes generates non-trivial (but familiar) constraints on three-particle coupling constants — these include gauge invariance, the equivalence principle, and the lack of non-trivial couplings for spins > 2. These constraints can also be derived with weaker assumptions, by demanding the existence of four-point amplitudes that factorize properly in all unitarity limits with complex momenta. From this starting point, we show that the BCFW prescription can be interpreted as an algorithm for fully constructing a tree-level S-matrix, and that complex factorization of general BCFW amplitudes follows from the factorization of four-particle amplitudes. The allowed set of BCFW deformations is identified, formulated entirely as a statement on the three-particle sector, and using only complex factorization as a guide. Consequently, our analysis based on the physical consistency of the S-matrix is entirely independent of field theory. We analyze the case of pure Yang-Mills, and outline a proof for gravity. For Yang-Mills, we also show that the well-known scaling behavior of BCFW-deformed amplitudes at large z is a simple consequence of factorization. For gravity, factorization in certain channels requires asymptotic behavior ~ 1/z2.

Existence of topological hairy dyons and dyonic black holes in anti-de Sitter su(N) Einstein-Yang-Mills theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baxter, J. Erik, E-mail: e.baxter@shu.ac.uk

We investigate dyonic black hole and dyon solutions of four-dimensional su(N) Einstein-Yang-Mills theory with a negative cosmological constant. We derive a set of field equations in this case, and prove the existence of non-trivial solutions to these equations for any integer N, with 2N − 2 gauge degrees of freedom. We do this by showing that solutions exist locally at infinity, and at the event horizon for black holes and the origin for solitons. We then prove that we can patch these solutions together regularly into global solutions that can be integrated arbitrarily far into the asymptotic regime. Our mainmore » result is to show that dyonic solutions exist in open sets in the parameter space, and hence that we can find non-trivial dyonic solutions in a number of regimes whose magnetic gauge fields have no zeros, which is likely important to the stability of the solutions.« less

Doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group

NASA Astrophysics Data System (ADS)

Caspar, S.; Mesterházy, D.; Olesen, T. Z.; Vlasii, N. D.; Wiese, U.-J.

2016-11-01

We construct doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group G in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov-Bohm phase, which is manifested in the doubled theory in terms of a nontrivial ground-state degeneracy on a single cross. We discuss several examples of these doubled theories with different gauge groups including the cyclic group Z(k) ⊂ U(1) , the symmetric group S3 ⊂ O(2) , the binary dihedral (or quaternion) group D¯2 ⊂ SU(2) , and the finite group Δ(27) ⊂ SU(3) . In each case the spectrum of the single-cross electric Hamiltonian is determined exactly. We examine the nature of the low-lying excited states in the full Hilbert space, and emphasize the role of the center symmetry for the confinement of charges. Whether the investigated doubled models admit a non-Abelian topological state which allows for fault-tolerant quantum computation will be addressed in a future publication.

Hadamard States for the Linearized Yang-Mills Equation on Curved Spacetime

NASA Astrophysics Data System (ADS)

Gérard, C.; Wrochna, M.

2015-07-01

We construct Hadamard states for the Yang-Mills equation linearized around a smooth, space-compact background solution. We assume the spacetime is globally hyperbolic and its Cauchy surface is compact or equal . We first consider the case when the spacetime is ultra-static, but the background solution depends on time. By methods of pseudodifferential calculus we construct a parametrix for the associated vectorial Klein-Gordon equation. We then obtain Hadamard two-point functions in the gauge theory, acting on Cauchy data. A key role is played by classes of pseudodifferential operators that contain microlocal or spectral type low-energy cutoffs. The general problem is reduced to the ultra-static spacetime case using an extension of the deformation argument of Fulling, Narcowich and Wald. As an aside, we derive a correspondence between Hadamard states and parametrices for the Cauchy problem in ordinary quantum field theory.

Non-Perturbative Yang-Mills from Supersymmetry and Strings, Or, in the Jungles of Strong Coupling

NASA Astrophysics Data System (ADS)

Shifman, M.

2005-12-01

I summarize some recent developments in the issue of planar equivalence between supersymmetric Yang-Mills theory and its orbifold/orientifold daughters. This talk is based on works carried out in collaboration with Adi Armoni, Sasha Gorsky and Gabriele Veneziano.

Non-Perturbative Yang--Mills from Supersymmetry and Strings, or, in the Jungles of Strong Coupling

NASA Astrophysics Data System (ADS)

Shifman, M.

2005-12-01

I summarize some recent developments in the issue of planar equivalence between supersymmetric Yang--Mills theory and its orbifold/orientifold daughters. This talk is based on works carried out in collaboration with Adi Armoni, Sasha Gorsky and Gabriele Veneziano.

Non-Perturbative Yang-Mills from Supersymmetry and Strings, or, in the Jungles of Strong Coupling

NASA Astrophysics Data System (ADS)

Shifman, M.

2006-06-01

I summarize some recent developments in the issue of planar equivalence between supersymmetric Yang-Mills theory and its orbifold/orientifold daughters. This talk is based on works carried out in collaboration with Adi Armoni, Sasha Gorsky and Gabriele Veneziano.

Perturbative tests for a large-N reduced model of mathcal{N} = {4} super Yang-Mills theory

NASA Astrophysics Data System (ADS)

Ishiki, Goro; Shimasaki, Shinji; Tsuchiya, Asato

2012-02-01

We study a non-perturbative formulation of mathcal{N} = {4} super Yang-Mills theory (SYM) on R × S 3 in the planar limit proposed in arXiv:0807.2352. This formulation is based on the large- N reduction, and the theory can be described as a particular large- N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S 3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.

On the stability of soliton and hairy black hole solutions of 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant

NASA Astrophysics Data System (ADS)

Baxter, J. Erik; Winstanley, Elizabeth

2016-02-01

We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant Λ. These solutions are described by N - 1 magnetic gauge field functions ωj. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any N, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions ωj have no zeros and satisfy a set of N - 1 inequalities. In the gravitational sector, we prove that there are solutions which have no instabilities in a neighbourhood of stable embedded 𝔰𝔲(2) solutions, provided the magnitude of the cosmological constant |" separators=" Λ | is sufficiently large.

Instantons in Lifshitz field theories

NASA Astrophysics Data System (ADS)

Fujimori, Toshiaki; Nitta, Muneto

2015-10-01

BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4 + 1 dimensions, for which we take the Chern-Simons term as the superpotential.

Black p-branes versus black holes in non-asymptotically flat Einstein-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Habib Mazharimousavi, S.; Halilsoy, M.

2016-09-01

We present a class of non-asymptotically flat (NAF) charged black p-branes (BpB) with p-compact dimensions in higher-dimensional Einstein-Yang-Mills theory. Asymptotically the NAF structure manifests itself as an anti-de sitter spacetime. We determine the total mass/energy enclosed in a thin shell located outside the event horizon. By comparing the entropies of BpB with those of black holes in the same dimensions we derive transition criteria between the two types of black objects. Given certain conditions satisfied, our analysis shows that BpB can be considered excited states of black holes. An event horizon r+ versus charge square Q2 plot for the BpB reveals such a transition where r+ is related to the horizon radius rh of the black hole (BH) both with the common charge Q.

FLRW Cosmology from Yang-Mills Gravity

NASA Astrophysics Data System (ADS)

Katz, Daniel

2013-04-01

We extend to basic cosmology the subject of Yang-Mills gravity - a theory of gravity based on local translational gauge invariance in flat spacetime. It has been shown that this particular gauge invariance leads to tensor factors in the macroscopic limit of the equations of motion of particles which plays the same role as the metric tensor of General Relativity. The assumption that this ``effective metric" tensor takes on the standard FLRW form is our starting point. Equations analogous to the Friedman equations are derived and then solved in closed form for the three special cases of a universe dominated by 1) matter, 2) radiation, and 3) dark energy. We find that the solutions for the scale factor are similar to, but distinct from, those found in the corresponding GR based treatment.

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.

Austerity and Geometric Structure of Field Theories

NASA Astrophysics Data System (ADS)

Kheyfets, Arkady

The relation between the austerity idea and the geometric structure of the three basic field theories- -electrodynamics, Yang-Mills theory, and general relativity --is studied. The idea of austerity was originally suggested by J. A. Wheeler in an attempt to formulate the laws of physics in such a way that they would come into being only within "the gates of time" extending from big bang to big crunch, rather than exist from everlasting to everlasting. One of the most significant manifestations of the austerity idea in field theories is thought to be expressed by the boundary of a boundary principle (BBP). The BBP says that almost all content of the field theories can be deduced from the topological identity (PAR-DIFF)(CCIRC)(PAR -DIFF) = 0 used twice, at the 1-2-3-dimensional level (providing the homgeneous field equations), and at the 2-3-4-dimensional level (providing the conservation laws for the source currents). There are some difficulties in this line of thought due to the apparent lack of universality in application of the BBP to the three basic modern field theories--electrodynamics, Yang-Mills theory, and general relativity. This dissertation: (a) analyses the difficulties by means of algebraic topology, integration theory and modern differential geometry based on the concepts of principal bundles and Ehresmann connections; (b) extends the BBP to the unified Kaluza-Klein theory; (c) reformulates the inhomogeneous field equations and the BBP in terms of E. Cartan moment of rotation, in the way universal for all the three theories and compatible with the original austerity idea; (d) underlines the important role of the soldering structure on spacetime, and indicates that the future development of the austerity idea would involve the generalized theories, including the soldering form as a dynamical variable rather than as a background structure.

The Analytic Structure of Scattering Amplitudes in N = 4 Super-Yang-Mills Theory

NASA Astrophysics Data System (ADS)

Litsey, Sean Christopher

We begin the dissertation in Chapter 1 with a discussion of tree-level amplitudes in Yang-. Mills theories. The DDM and BCJ decompositions of the amplitudes are described and. related to one another by the introduction of a transformation matrix. This is related to the. Kleiss-Kuijf and BCJ amplitude identities, and we conjecture a connection to the existence. of a BCJ representation via a condition on the generalized inverse of that matrix. Under. two widely-believed assumptions, this relationship is proved. Switching gears somewhat, we introduce the RSVW formulation of the amplitude, and the extension of BCJ-like features to residues of the RSVW integrand is proposed. Using the previously proven connection of BCJ representations to the generalized inverse condition, this extension is validated, including a version of gravitational double copy. The remainder of the dissertation involves an analysis of the analytic properties of loop. amplitudes in N = 4 super-Yang-Mills theory. Chapter 2 contains a review of the planar case, including an exposition of dual variables and momentum twistors, dual conformal symmetry, and their implications for the amplitude. After defining the integrand and on-shell diagrams, we explain the crucial properties that the amplitude has no poles at infinite momentum and that its leading singularities are dual-conformally-invariant cross ratios, and can therefore be normalized to unity. We define the concept of a dlog form, and show that it is a feature of the planar integrand as well. This leads to the definition of a pure integrand basis. The proceeding setup is connected to the amplituhedron formulation, and we put forward the hypothesis that the amplitude is determined by zero conditions. Chapter 3 contains the primary computations of the dissertation. This chapter treats. amplitudes in fully nonplanar N = 4 super-Yang-Mills, analyzing the conjecture that they. follow the pattern of having no poles at infinity, can be written in dlog

Covariant open bosonic string field theory on multiple D-branes in the proper-time gauge

NASA Astrophysics Data System (ADS)

Lee, Taejin

2017-12-01

We construct a covariant open bosonic string field theory on multiple D-branes, which reduces to a non-Abelian group Yang-Mills gauge theory in the zero-slope limit. Making use of the first quantized open bosonic string in the proper time gauge, we convert the string amplitudes given by the Polyakov path integrals on string world sheets into those of the second quantized theory. The world sheet diagrams generated by the constructed open string field theory are planar in contrast to those of the Witten's cubic string field theory. However, the constructed string field theory is yet equivalent to the Witten's cubic string field theory. Having obtained planar diagrams, we may adopt the light-cone string field theory technique to calculate the multi-string scattering amplitudes with an arbitrary number of external strings. We examine in detail the three-string vertex diagram and the effective four-string vertex diagrams generated perturbatively by the three-string vertex at tree level. In the zero-slope limit, the string scattering amplitudes are identified precisely as those of non-Abelian Yang-Mills gauge theory if the external states are chosen to be massless vector particles.

Nonminimal Wu-Yang wormhole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balakin, A. B.; Zayats, A. E.; Sushkov, S. V.

2007-04-15

We discuss exact solutions of a three-parameter nonminimal Einstein-Yang-Mills model, which describe the wormholes of a new type. These wormholes are considered to be supported by the SU(2)-symmetric Yang-Mills field, nonminimally coupled to gravity, the Wu-Yang ansatz for the gauge field being used. We distinguish between regular solutions, describing traversable nonminimal Wu-Yang wormholes, and black wormholes possessing one or two event horizons. The relation between the asymptotic mass of the regular traversable Wu-Yang wormhole and its throat radius is analyzed.

Vacuum structure and string tension in Yang-Mills dimeron ensembles

NASA Astrophysics Data System (ADS)

Zimmermann, Falk; Forkel, Hilmar; Müller-Preußker, Michael

2012-11-01

We numerically simulate ensembles of SU(2) Yang-Mills dimeron solutions with a statistical weight determined by the classical action and perform a comprehensive analysis of their properties as a function of the bare coupling. In particular, we examine the extent to which these ensembles and their classical gauge interactions capture topological and confinement properties of the Yang-Mills vacuum. This also allows us to put the classic picture of meron-induced quark confinement, with the confinement-deconfinement transition triggered by dimeron dissociation, to stringent tests. In the first part of our analysis we study spacial, topological-charge and color correlations at the level of both the dimerons and their meron constituents. At small to moderate couplings, the dependence of the interactions between the dimerons on their relative color orientations is found to generate a strong attraction (repulsion) between nearest neighbors of opposite (equal) topological charge. Hence, the emerging short- to mid-range order in the gauge-field configurations screens topological charges. With increasing coupling this order weakens rapidly, however, in part because the dimerons gradually dissociate into their less localized meron constituents. Monitoring confinement properties by evaluating Wilson-loop expectation values, we find the growing disorder due to the long-range tails of these progressively liberated merons to generate a finite and (with the coupling) increasing string tension. The short-distance behavior of the static quark-antiquark potential, on the other hand, is dominated by small, “instantonlike” dimerons. String tension, action density and topological susceptibility of the dimeron ensembles in the physical coupling region turn out to be of the order of standard values. Hence, the above results demonstrate without reliance on weak-coupling or low-density approximations that the dissociating dimeron component in the Yang-Mills vacuum can indeed produce a

On the global existence of hairy black holes and solitons in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups

NASA Astrophysics Data System (ADS)

Baxter, J. Erik

2016-10-01

We investigate the existence of black hole and soliton solutions to four dimensional, anti-de Sitter (adS), Einstein-Yang-Mills theories with general semisimple connected and simply connected gauge groups, concentrating on the so-called regular case. We here generalise results for the asymptotically flat case, and compare our system with similar results from the well-researched adS {mathfrak {su}}(N) system. We find the analysis differs from the asymptotically flat case in some important ways: the biggest difference is that for Λ <0, solutions are much less constrained as r→ infty , making it possible to prove the existence of global solutions to the field equations in some neighbourhood of existing trivial solutions, and in the limit of |Λ |→ infty . In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the {mathfrak {su}}(N) case proved important to stability.

On non-primitively divergent vertices of Yang-Mills theory

NASA Astrophysics Data System (ADS)

Huber, Markus Q.

2017-11-01

Two correlation functions of Yang-Mills beyond the primitively divergent ones, the two-ghost-two-gluon and the four-ghost vertices, are calculated and their influence on lower vertices is examined. Their full (transverse) tensor structure is taken into account. As input, a solution of the full two-point equations - including two-loop terms - is used that respects the resummed perturbative ultraviolet behavior. A clear hierarchy is found with regard to the color structure that reduces the number of relevant dressing functions. The impact of the two-ghost-two-gluon vertex on the three-gluon vertex is negligible, which is explained by the fact that all non-small dressing functions drop out due to their color factors. Only in the ghost-gluon vertex a small net effect below 2% is seen. The four-ghost vertex is found to be extremely small in general. Since these two four-point functions do not enter into the propagator equations, these findings establish their small overall effect on lower correlation functions.

Yang-Baxter σ -models, conformal twists, and noncommutative Yang-Mills theory

NASA Astrophysics Data System (ADS)

Araujo, T.; Bakhmatov, I.; Colgáin, E. Ó.; Sakamoto, J.; Sheikh-Jabbari, M. M.; Yoshida, K.

2017-05-01

The Yang-Baxter σ -model is a systematic way to generate integrable deformations of AdS5×S5 . We recast the deformations as seen by open strings, where the metric is undeformed AdS5×S5 with constant string coupling, and all information about the deformation is encoded in the noncommutative (NC) parameter Θ . We identify the deformations of AdS5 as twists of the conformal algebra, thus explaining the noncommutativity. We show that the unimodularity condition on r -matrices for supergravity solutions translates into Θ being divergence-free. Integrability of the σ -model for unimodular r -matrices implies the existence and planar integrability of the dual NC gauge theory.

Matrix models for 5d super Yang-Mills

NASA Astrophysics Data System (ADS)

Minahan, Joseph A.

2017-11-01

In this contribution to the issue on localization in gauge theories we investigate the matrix models derived from localizing N=1 super Yang-Mills on S 5. We consider the large-N limit and attempt to solve the matrix model by a saddle-point approximation. In general it is not possible to find an analytic solution, but at the weak and the strong limits of the ’t Hooft coupling there are dramatic simplifications that allows us to extract most of the interesting information. At weak coupling we show that the matrix model is close to the Gaussian matrix model and that the free-energy scales as N 2. At strong coupling we show that if the theory contains one adjoint hypermultiplet then the free-energy scales as N 3. We also find the expectation value of a supersymmetric Wilson loop that wraps the equator. We demonstrate how to extract the effective couplings and reproduce results of Seiberg. Finally, we compare to results for the six-dimensional (2,0) theory derived using the AdS/CFT correspondence. We show that by choosing the hypermultiplet mass such that the supersymmetry is enhanced to N=2 , the Wilson loop result matches the analogous calculation using AdS/CFT. The free-energies differ by a rational fraction. This is a contribution to the review issue ‘Localization techniques in quantum field theories’ (ed Pestun and Zabzine) which contains 17 chapters available at [1].

Dyons and dyonic black holes in su (N ) Einstein-Yang-Mills theory in anti-de Sitter spacetime

NASA Astrophysics Data System (ADS)

Shepherd, Ben L.; Winstanley, Elizabeth

2016-03-01

We present new spherically symmetric, dyonic soliton and black hole solutions of the su (N ) Einstein-Yang-Mills equations in four-dimensional asymptotically anti-de Sitter spacetime. The gauge field has nontrivial electric and magnetic components and is described by N -1 magnetic gauge field functions and N -1 electric gauge field functions. We explore the phase space of solutions in detail for su (2 ) and su (3 ) gauge groups. Combinations of the electric gauge field functions are monotonic and have no zeros; in general the magnetic gauge field functions may have zeros. The phase space of solutions is extremely rich, and we find solutions in which the magnetic gauge field functions have more than fifty zeros. Of particular interest are solutions for which the magnetic gauge field functions have no zeros, which exist when the negative cosmological constant has sufficiently large magnitude. We conjecture that at least some of these nodeless solutions may be stable under linear, spherically symmetric, perturbations.

Some exact solutions of (2+1)-dimensional Yang-Mills equations with the Chern-Simons term

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oh, C. H.; Sia, L. C.; Teh, R.

1989-07-15

Two /ital Ansa/$/ital uml/---/ital tze/ for the gauge field potential are given so that the(2+1)-dimensional Yang-Mills equations with the Chern-Simons termcan be solved in terms of the modified Bessel functions and the ellipticfunction respectively.

Supersymmetric electric-magnetic duality in D =3 +3 and D =5 +5 dimensions as foundation of self-dual supersymmetric Yang-Mills theory

NASA Astrophysics Data System (ADS)

Nishino, Hitoshi; Rajpoot, Subhash

2016-05-01

We present electric-magnetic (EM)-duality formulations for non-Abelian gauge groups with N =1 supersymmetry in D =3 +3 and 5 +5 space-time dimensions. We show that these systems generate self-dual N =1 supersymmetric Yang-Mills (SDSYM) theory in D =2 +2 . For a N =2 supersymmetric EM-dual system in D =3 +3 , we have the Yang-Mills multiplet (Aμ I,λA I) and a Hodge-dual multiplet (Bμν ρ I,χA I) , with an auxiliary tensors Cμν ρ σ I and Kμ ν. Here, I is the adjoint index, while A is for the doublet of S p (1 ). The EM-duality conditions are Fμν I=(1 /4 !)ɛμν ρ σ τ λGρσ τ λ I with its superpartner duality condition λA I=-χA I . Upon appropriate dimensional reduction, this system generates SDSYM in D =2 +2 . This system is further generalized to D =5 +5 with the EM-duality condition Fμν I=(1 /8 !)ɛμν ρ1⋯ρ8Gρ1⋯ρ8 I with its superpartner condition λI=-χI . Upon appropriate dimensional reduction, this theory also generates SDSYM in D =2 +2 . As long as we maintain Lorentz covariance, D =5 +5 dimensions seems to be the maximal space-time dimensions that generate SDSYM in D =2 +2 . Namely, EM-dual system in D =5 +5 serves as the Master Theory of all supersymmetric integrable models in dimensions 1 ≤D ≤3 .

Step scaling and the Yang-Mills gradient flow

NASA Astrophysics Data System (ADS)

Lüscher, Martin

2014-06-01

The use of the Yang-Mills gradient flow in step-scaling studies of lattice QCD is expected to lead to results of unprecedented precision. Step scaling is usually based on the Schrödinger functional, where time ranges over an interval [0 , T] and all fields satisfy Dirichlet boundary conditions at time 0 and T. In these calculations, potentially important sources of systematic errors are boundary lattice effects and the infamous topology-freezing problem. The latter is here shown to be absent if Neumann instead of Dirichlet boundary conditions are imposed on the gauge field at time 0. Moreover, the expectation values of gauge-invariant local fields at positive flow time (and of other well localized observables) that reside in the center of the space-time volume are found to be largely insensitive to the boundary lattice effects.

Retrieving Storm Electric Fields from Aircraft Field Mill Data. Part 1; Theory

NASA Technical Reports Server (NTRS)

Koshak, W. J.

2006-01-01

It is shown that the problem of retrieving storm electric fields from an aircraft instrumented with several electric field mill sensors can be expressed in terms of a standard Lagrange multiplier optimization problem. The method naturally removes aircraft charge from the retrieval process without having to use a high voltage stinger and linearly combined mill data values. It allows a variety of user-supplied physical constraints (the so-called side constraints in the theory of Lagrange multipliers) and also helps improve absolute calibration. Additionally, this paper introduces an alternate way of performing the absolute calibration of an aircraft that has some benefits over conventional analyses. It is accomplished by using the time derivatives of mill and pitch data for a pitch down maneuver performed at high (greater than 1 km) altitude. In Part II of this study, the above methods are tested and then applied to complete a full calibration of a Citation aircraft.

Retrieving Storm Electric Fields From Aircraft Field Mill Data. Part I: Theory

NASA Technical Reports Server (NTRS)

Koshak, W. J.

2005-01-01

It is shown that the problem of retrieving storm electric fields from an aircraft instrumented with several electric field mill sensors can be expressed in terms of a standard Lagrange multiplier optimization problem. The method naturally removes aircraft charge from the retrieval process without having to use a high voltage stinger and linearly combined mill data values. It also allows a variety of user-supplied physical constraints (the so-called side constraints in the theory of Lagrange multipliers). Additionally, this paper introduces a novel way of performing the absolute calibration of an aircraft that has several benefits over conventional analyses. In the new approach, absolute calibration is completed by inspecting the time derivatives of mill and pitch data for a pitch down maneuver performed at high (greater than 1 km) altitude. In Part II of this study, the above methods are tested and then applied to complete a full calibration of a Citation aircraft.

Dualities and Topological Field Theories from Twisted Geometries

NASA Astrophysics Data System (ADS)

Markov, Ruza

I will present three studies of string theory on twisted geometries. In the first calculation included in this dissertation we use gauge/gravity duality to study the Coulomb branch of an unusual type of nonlocal field theory, called Puff Field Theory. On the gravity side, this theory is given in terms of D3-branes in type IIB string theory with a geometric twist. While the field theory description, available in the IR limit, is a deformation of Yang-Mills gauge theory by an order seven operator which we here compute. In the rest of this dissertation we explore N = 4 super Yang-Mills (SYM) theory compactied on a circle with S-duality and R-symmetry twists that preserve N = 6 supersymmetry in 2 + 1D. It was shown that abelian theory on a flat manifold gives Chern-Simons theory in the low-energy limit and here we are interested in the non-abelian counterpart. To that end, we introduce external static supersymmetric quark and anti-quark sources into the theory and calculate the Witten Index of the resulting Hilbert space of ground states on a two-torus. Using these results we compute the action of simple Wilson loops on the Hilbert space of ground states without sources. In some cases we find disagreement between our results for the Wilson loop eigenvalues and previous conjectures about a connection with Chern-Simons theory. The last result discussed in this dissertation demonstrates a connection between gravitational Chern-Simons theory and N = 4 four-dimensional SYM theory compactified on a circle twisted by S-duality where the remaining three-manifold is not flat starting with the explicit geometric realization of S-duality in terms of (2, 0) theory.

Galilean field theories and conformal structure

NASA Astrophysics Data System (ADS)

Bagchi, Arjun; Chakrabortty, Joydeep; Mehra, Aditya

2018-04-01

We perform a detailed analysis of Galilean field theories, starting with free theories and then interacting theories. We consider non-relativistic versions of massless scalar and Dirac field theories before we go on to review our previous construction of Galilean Electrodynamics and Galilean Yang-Mills theory. We show that in all these cases, the field theories exhibit non-relativistic conformal structure (in appropriate dimensions). The surprising aspect of the analysis is that the non-relativistic conformal structure exhibited by these theories, unlike relativistic conformal invariance, becomes infinite dimensional even in spacetime dimensions greater than two. We then couple matter with Galilean gauge theories and show that there is a myriad of different sectors that arise in the non-relativistic limit from the parent relativistic theories. In every case, if the parent relativistic theory exhibited conformal invariance, we find an infinitely enhanced Galilean conformal invariance in the non-relativistic case. This leads us to suggest that infinite enhancement of symmetries in the non-relativistic limit is a generic feature of conformal field theories in any dimension.

Strolling along gauge theory vacua

NASA Astrophysics Data System (ADS)

Seraj, Ali; Van den Bleeken, Dieter

2017-08-01

We consider classical, pure Yang-Mills theory in a box. We show how a set of static electric fields that solve the theory in an adiabatic limit correspond to geodesic motion on the space of vacua, equipped with a particular Riemannian metric that we identify. The vacua are generated by spontaneously broken global gauge symmetries, leading to an infinite number of conserved momenta of the geodesic motion. We show that these correspond to the soft multipole charges of Yang-Mills theory.

A noncompact Weyl-Einstein-Yang-Mills model: A semiclassical quantum gravity

NASA Astrophysics Data System (ADS)

Dengiz, Suat

2017-08-01

We construct and study perturbative unitarity (i.e., ghost and tachyon analysis) of a 3 + 1-dimensional noncompact Weyl-Einstein-Yang-Mills model. The model describes a local noncompact Weyl's scale plus SU(N) phase invariant Higgs-like field,conformally coupled to a generic Weyl-invariant dynamical background. Here, the Higgs-like sector generates the Weyl's conformal invariance of system. The action does not admit any dimensionful parameter and genuine presence of de Sitter vacuum spontaneously breaks the noncompact gauge symmetry in an analogous manner to the Standard Model Higgs mechanism. As to flat spacetime, the dimensionful parameter is generated within the dimensional transmutation in quantum field theories, and thus the symmetry is radiatively broken through the one-loop Effective Coleman-Weinberg potential. We show that the mere expectation of reducing to Einstein's gravity in the broken phases forbids anti-de Sitter space to be its stable vacua. The model is unitary in de Sitter and flat vacua around which a massless graviton, N2 - 1 massless scalar bosons, N massless Dirac fermions, N2 - 1 Proca-type massive Abelian and non-Abelian vector bosons are generically propagated.

Exact equivalence of the D=4 gauged Wess-Zumino-Witten term and the D=5 Yang-Mills Chern-Simons term

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hill, Christopher T.

We derive the full Wess-Zumino-Witten term of a gauged chiral Lagrangian in D=4 by starting from a pure Yang-Mills theory of gauged quark flavor in a flat, compactified D=5. The theory is compactified such that there exists a B{sub 5} zero mode, and supplemented with quarks that are 'chirally delocalized' with q{sub L} (q{sub R}) on the left (right) boundary (brane). The theory then necessarily contains a Chern-Simons term (anomaly flux) to cancel the fermionic anomalies on the boundaries. The constituent quark mass represents chiral symmetry breaking and is a bilocal operator in D=5 of the form: q{sub L}Wq{sub R}+h.c,more » where W is the Wilson line spanning the bulk, 0{<=}x{sup 5}{<=}R, and is interpreted as a chiral meson field, W=exp(2i{pi}-tilde/f{sub {pi}}), where f{sub {pi}}{approx}1/R. The quarks are integrated out, yielding a Dirac determinant which takes the form of a 'boundary term' (anomaly flux return), and is equivalent to Bardeen's counterterm that connects consistent and covariant anomalies. The Wess-Zumino-Witten term then emerges straightforwardly, from the Yang-Mills Chern-Simons term, plus boundary term. The method is systematic and allows generalization of the Wess-Zumino-Witten term to theories of extra dimensions, and to express it in alternative and more compact forms. We give a novel form appropriate to the case of (unintegrated) massless fermions.« less

Classical phase space and Hadamard states in the BRST formalism for gauge field theories on curved spacetime

NASA Astrophysics Data System (ADS)

Wrochna, Michał; Zahn, Jochen

We investigate linearized gauge theories on globally hyperbolic spacetimes in the BRST formalism. A consistent definition of the classical phase space and of its Cauchy surface analogue is proposed. We prove that it is isomorphic to the phase space in the ‘subsidiary condition’ approach of Hack and Schenkel in the case of Maxwell, Yang-Mills, and Rarita-Schwinger fields. Defining Hadamard states in the BRST formalism in a standard way, their existence in the Maxwell and Yang-Mills case is concluded from known results in the subsidiary condition (or Gupta-Bleuler) formalism. Within our framework, we also formulate criteria for non-degeneracy of the phase space in terms of BRST cohomology and discuss special cases. These include an example in the Yang-Mills case, where degeneracy is not related to a non-trivial topology of the Cauchy surface.

Yang-Mills condensate as dark energy: A nonperturbative approach

NASA Astrophysics Data System (ADS)

Donà, Pietro; Marcianò, Antonino; Zhang, Yang; Antolini, Claudia

2016-02-01

Models based on the Yang-Mills condensate (YMC) have been advocated for in the literature and claimed as successful candidates for explaining dark energy. Several variations on this simple idea have been considered, the most promising of which are reviewed here. Nevertheless, the previously attained results relied heavily on the perturbative approach to the analysis of the effective Yang-Mills action, which is only adequate in the asymptotically free limit, and were extended into a regime, the infrared limit, in which confinement is expected. We show that if a minimum of the effective Lagrangian in θ =-Fμν aFa μ ν/2 exists, a YMC forms that drives the Universe toward an accelerated de Sitter phase. The details of the models depend weakly on the specific form of the effective Yang-Mills Lagrangian. Using nonperturbative techniques mutated from the functional renormalization-group procedure, we finally show that the minimum in θ of the effective Lagrangian exists. Thus, a YMC can actually take place. The nonperturbative model has properties similar to the ones in the perturbative model. In the early stage of the Universe, the YMC equation of state has an evolution that resembles the radiation component, i.e., wy→1 /3 . However, in the late stage, wy naturally runs to the critical state with wy=-1 , and the Universe transitions from a matter-dominated into a dark energy dominated stage only at latest time, at a redshift whose value depends on the initial conditions that are chosen while solving the dynamical system.

Localization of effective actions in open superstring field theory

NASA Astrophysics Data System (ADS)

Maccaferri, Carlo; Merlano, Alberto

2018-03-01

We consider the construction of the algebraic part of D-branes tree-level effective action from Berkovits open superstring field theory. Applying this construction to the quartic potential of massless fields carrying a specific worldsheet charge, we show that the full contribution to the potential localizes at the boundary of moduli space, reducing to elementary two-point functions. As examples of this general mechanism, we show how the Yang-Mills quartic potential and the instanton effective action of a Dp/D( p - 4) system are reproduced.

Radiation-like scalar field and gauge fields in cosmology for a theory with dynamical time

NASA Astrophysics Data System (ADS)

Benisty, David; Guendelman, E. I.

2016-09-01

Cosmological solutions with a scalar field behaving as radiation are obtained, in the context of gravitational theory with dynamical time. The solution requires the spacial curvature of the universe k, to be zero, unlike the standard radiation solutions, which do not impose any constraint on the spatial curvature of the universe. This is because only such k = 0 radiation solutions pose a homothetic Killing vector. This kind of theory can be used to generalize electromagnetism and other gauge theories, in curved spacetime, and there are no deviations from standard gauge field equation (like Maxwell equations) in the case there exist a conformal Killing vector. But there could be departures from Maxwell and Yang-Mills equations, for more general spacetimes.

5D Super Yang-Mills on Y p, q Sasaki-Einstein Manifolds

NASA Astrophysics Data System (ADS)

Qiu, Jian; Zabzine, Maxim

2015-01-01

On any simply connected Sasaki-Einstein five dimensional manifold one can construct a super Yang-Mills theory which preserves at least two supersymmetries. We study the special case of toric Sasaki-Einstein manifolds known as Y p, q manifolds. We use the localisation technique to compute the full perturbative part of the partition function. The full equivariant result is expressed in terms of a certain special function which appears to be a curious generalisation of the triple sine function. As an application of our general result we study the large N behaviour for the case of single hypermultiplet in adjoint representation and we derive the N 3-behaviour in this case.

FLRW Cosmology from Yang-Mills Gravity with Translational Gauge Symmetry

NASA Astrophysics Data System (ADS)

Katz, Daniel

2013-03-01

We extend to basic cosmology the subject of Yang-Mills gravity — a theory of gravity based on local translational gauge invariance in flat space-time. It has been shown that this particular gauge invariance leads to tensor factors in the macroscopic limit of the equations of motion of particles which plays the same role as the metric tensor of general relativity (GR). The assumption that this "effective metric" tensor takes on the standard FLRW form is our starting point. Equations analogous to the Friedmann equations are derived and then solved in closed form for the three special cases of a universe dominated by (1) matter, (2) radiation and (3) dark energy. We find that the solutions for the scale factor are similar to, but distinct from, those found in the corresponding GR based treatment.

String theory, gauge theory and quantum gravity. Proceedings. Trieste Spring School and Workshop on String Theory, Gauge Theory and Quantum Gravity, Trieste (Italy), 11 - 22 Apr 1994.

NASA Astrophysics Data System (ADS)

1995-04-01

The following topics were dealt with: string theory, gauge theory, quantum gravity, quantum geometry, black hole physics and information loss, second quantisation of the Wilson loop, 2D Yang-Mills theory, topological field theories, equivariant cohomology, superstring theory and fermion masses, supergravity, topological gravity, waves in string cosmology, superstring theories, 4D space-time.

Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence.

PubMed

Ryu, Shinsei; Takayanagi, Tadashi

2006-05-12

A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We argue that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal agrees perfectly with the entanglement entropy in 2D CFT when applied to AdS(3). We also compare the entropy computed in AdS(5)XS(5) with that of the free N=4 super Yang-Mills theory.

BPS Z{sub N} string tensions, sine law and Casimir scaling, and integrable field theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kneipp, Marco A. C.; International Centre for Theoretical Physics

We consider a Yang-Mills-Higgs theory with spontaneous symmetry breaking of the gauge group G{yields}U(1){sup r}{yields}C{sub G}, with C{sub G} being the center of G. We study two vacua solutions of the theory which produce this symmetry breaking. We show that for one of these vacua, the theory in the Coulomb phase has the mass spectrum of particles and monopoles which is exactly the same as the mass spectrum of particles and solitons of two-dimensional affine Toda field theory, for suitable coupling constants. That result holds also for N=4 super Yang-Mills theories. On the other hand, in the Higgs phase, wemore » show that for each of the two vacua the ratio of the tensions of the BPS Z{sub N} strings satisfy either the Casimir scaling or the sine law scaling for G=SU(N). These results are extended to other gauge groups: for the Casimir scaling, the ratios of the tensions are equal to the ratios of the quadratic Casimir constant of specific representations; for the sine law scaling, the tensions are proportional to the components of the left Perron-Frobenius eigenvector of Cartan matrix K{sub ij} and the ratios of tensions are equal to the ratios of the soliton masses of affine Toda field theories.« less

BOOK REVIEW: Path Integrals in Field Theory: An Introduction

NASA Astrophysics Data System (ADS)

Ryder, Lewis

2004-06-01

In the 1960s Feynman was known to particle physicists as one of the people who solved the major problems of quantum electrodynamics, his contribution famously introducing what are now called Feynman diagrams. To other physicists he gained a reputation as the author of the Feynman Lectures on Physics; in addition some people were aware of his work on the path integral formulation of quantum theory, and a very few knew about his work on gravitation and Yang--Mills theories, which made use of path integral methods. Forty years later the scene is rather different. Many of the problems of high energy physics are solved; and the standard model incorporates Feynman's path integral method as a way of proving the renormalisability of the gauge (Yang--Mills) theories involved. Gravitation is proving a much harder nut to crack, but here also questions of renormalisability are couched in path-integral language. What is more, theoretical studies of condensed matter physics now also appeal to this technique for quantisation, so the path integral method is becoming part of the standard apparatus of theoretical physics. Chapters on it appear in a number of recent books, and a few books have appeared devoted to this topic alone; the book under review is a very recent one. Path integral techniques have the advantage of enormous conceptual appeal and the great disadvantage of mathematical complexity, this being partly the result of messy integrals but more fundamentally due to the notions of functional differentiation and integration which are involved in the method. All in all this subject is not such an easy ride. Mosel's book, described as an introduction, is aimed at graduate students and research workers in particle physics. It assumes a background knowledge of quantum mechanics, both non-relativistic and relativistic. After three chapters on the path integral formulation of non-relativistic quantum mechanics there are eight chapters on scalar and spinor field theory, followed

Regge meets collinear in strongly-coupled N=4 super Yang-Mills

NASA Astrophysics Data System (ADS)

Sprenger, Martin

2017-01-01

We revisit the calculation of the six-gluon remainder function in planar N=4 super Yang-Mills theory from the strong coupling TBA in the multi-Regge limit and identify an infinite set of kinematically subleading terms. These new terms can be compared to the strong coupling limit of the finite-coupling expressions for the impact factor and the BFKL eigenvalue proposed by Basso et al. in [1], which were obtained from an analytic continuation of the Wilson loop OPE. After comparing the results order by order in those subleading terms, we show that it is possible to precisely map both formalisms onto each other. A similar calculation can be carried out for the seven-gluon amplitude, the result of which shows that the central emission vertex does not become trivial at strong coupling.

Gluon dynamics, center symmetry, and the deconfinement phase transition in SU(3) pure Yang-Mills theory

NASA Astrophysics Data System (ADS)

Silva, P. J.; Oliveira, O.

2016-06-01

The correlations between the modulus of the Polyakov loop, its phase θ , and the Landau gauge gluon propagator at finite temperature are investigated in connection with the center symmetry for pure Yang-Mills SU(3) theory. In the deconfined phase, where the center symmetry is spontaneously broken, the phase of the Polyakov loop per configuration is close to θ =0 , ±2 π /3 . We find that the gluon propagator form factors associated with θ ≈0 differ quantitatively and qualitatively from those associated to θ ≈±2 π /3 . This difference between the form factors is a property of the deconfined phase and a sign of the spontaneous breaking of the center symmetry. Furthermore, given that this difference vanishes in the confined phase, it can be used as an order parameter associated to the deconfinement transition. For simulations near the critical temperature Tc, the difference between the propagators associated to θ ≈0 and θ ≈±2 π /3 allows one to classify the configurations as belonging to the confined or deconfined phase. This establishes a selection procedure which has a measurable impact on the gluon form factors. Our results also show that the absence of the selection procedure can be erroneously interpreted as lattice artifacts.

Hydrodynamics of the Polyakov line in SU(N c) Yang-Mills

DOE PAGES

Liu, Yizhuang; Warchoł, Piotr; Zahed, Ismail

2015-12-08

We discuss a hydrodynamical description of the eigenvalues of the Polyakov line at large but finite N c for Yang-Mills theory in even and odd space-time dimensions. The hydro-static solutions for the eigenvalue densities are shown to interpolate between a uniform distribution in the confined phase and a localized distribution in the de-confined phase. The resulting critical temperatures are in overall agreement with those measured on the lattice over a broad range of N c, and are consistent with the string model results at N c = ∞. The stochastic relaxation of the eigenvalues of the Polyakov line out ofmore » equilibrium is captured by a hydrodynamical instanton. An estimate of the probability of formation of a Z(N c)bubble using a piece-wise sound wave is suggested.« less

Abelian Toda field theories on the noncommutative plane

NASA Astrophysics Data System (ADS)

Cabrera-Carnero, Iraida

2005-10-01

Generalizations of GL(n) abelian Toda and GL with tilde above(n) abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by algebra-valued gauge potentials dependent on the fields. This condition can be expressed as noncommutative Leznov-Saveliev equations which make possible to define the noncommutative generalizations as systems of second order differential equations, with an infinite chain of conserved currents. The actions corresponding to these field theories are also provided. The special cases of GL(2) Liouville and GL with tilde above(2) sinh/sine-Gordon are explicitly studied. It is also shown that from the noncommutative (anti-)self-dual Yang-Mills equations in four dimensions it is possible to obtain by dimensional reduction the equations of motion of the two-dimensional models constructed. This fact supports the validity of the noncommutative version of the Ward conjecture. The relation of our proposal to previous versions of some specific Toda field theories reported in the literature is presented as well.

Austerity and geometric structure of field theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kheyfets, A.

The relation between the austerity idea and the geometric structure of the three basic field theories - electrodynamics, Yang-Mills theory, and general relativity - is studied. One of the most significant manifestations of the austerity idea in field theories is thought to be expressed by the boundary of a boundary principle (BBP). The BBP says that almost all content of the field theories can be deduced from the topological identity of delta dot produced with delta = 0 used twice, at the 1-2-3-dimensional level (providing the homogeneous field equations), and at the 2-3-4-dimensional level (providing the conservation laws for themore » source currents). There are some difficulties in this line of thought due to the apparent lack of universality in application of the BBP to the three basic modern field theories above. This dissertation: (a) analyzes the difficulties by means of algebraic topology, integration theory, and modern differential geometry based on the concepts of principal bundles and Ehresmann connections: (b) extends the BBP to the unified Kaluza-Klein theory; (c) reformulates the inhomogeneous field equations and the BBP in terms of E. Cartan moment of rotation, in the way universal for the three theories and compatible with the original austerity idea; and (d) underlines the important role of the soldering structure on spacetime, and indicates that the future development of the austerity idea would involve the generalized theories.« less

Experiments on Frequency Dependence of the Deflection of Light in Yang-Mills Gravity

NASA Astrophysics Data System (ADS)

Hao, Yun; Zhu, Yiyi; Hsu, Jong-Ping

2018-01-01

In Yang-Mills gravity based on flat space-time, the eikonal equation for a light ray is derived from the modified Maxwell's wave equations in the geometric-optics limit. One obtains a Hamilton-Jacobi type equation, GLµv∂µΨ∂vΨ = 0 with an effective Riemannian metric tensor GLµv. According to Yang-Mills gravity, light rays (and macroscopic objects) move as if they were in an effective curved space-time with a metric tensor. The deflection angle of a light ray by the sun is about 1.53″ for experiments with optical frequencies ≈ 1014Hz. It is roughly 12% smaller than the usual value 1.75″. However, the experimental data in the past 100 years for the deflection of light by the sun in optical frequencies have uncertainties of (10-20)% due to large systematic errors. If one does not take the geometric-optics limit, one has the equation, GLµv[∂µΨ∂vΨcosΨ+ (∂µ∂vΨ)sinΨ] = 0, which suggests that the deflection angle could be frequency-dependent, according to Yang-Mills gravity. Nowadays, one has very accurate data in the radio frequencies ≈ 109Hz with uncertainties less than 0.1%. Thus, one can test this suggestion by using frequencies ≈ 1012 Hz, which could have a small uncertainty 0.1% due to the absence of systematic errors in the very long baseline interferometry.

The large N limit of superconformal field theories and supergravity

NASA Astrophysics Data System (ADS)

Maldacena, Juan

1999-07-01

We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near horizon geometry for large N. The enhanced supersymmetries of the near horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). The 't Hooft limit of 3+1N=4 super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes is dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five non-compact dimensions.

How nonperturbative is the infrared regime of Landau gauge Yang-Mills correlators?

NASA Astrophysics Data System (ADS)

Reinosa, U.; Serreau, J.; Tissier, M.; Wschebor, N.

2017-07-01

We study the Landau gauge correlators of Yang-Mills fields for infrared Euclidean momenta in the context of a massive extension of the Faddeev-Popov Lagrangian which, we argue, underlies a variety of continuum approaches. Standard (perturbative) renormalization group techniques with a specific, infrared-safe renormalization scheme produce so-called decoupling and scaling solutions for the ghost and gluon propagators, which correspond to nontrivial infrared fixed points. The decoupling fixed point is infrared stable and weakly coupled, while the scaling fixed point is unstable and generically strongly coupled except for low dimensions d →2 . Under the assumption that such a scaling fixed point exists beyond one-loop order, we find that the corresponding ghost and gluon scaling exponents are, respectively, 2 αF=2 -d and 2 αG=d at all orders of perturbation theory in the present renormalization scheme. We discuss the relation between the ghost wave function renormalization, the gluon screening mass, the scale of spectral positivity violation, and the gluon mass parameter. We also show that this scaling solution does not realize the standard Becchi-Rouet-Stora-Tyutin symmetry of the Faddeev-Popov Lagrangian. Finally, we discuss our findings in relation to the results of nonperturbative continuum methods.

Exact Cosmological Models with Yang–Mills Fields on Lyra Manifold

NASA Astrophysics Data System (ADS)

Shchigolev, V. K.; Bezbatko, D. N.

2018-04-01

The present study deals with the Friedmann-Robertson-Walker cosmological models with Yang-Mills (YM) fields in Lyra geometry. The energy-momentum tensor of the YM fields for our models is obtained with the help of an exact solution to the YM equations with minimal coupling to gravity. Two specific exact solutions of the model are obtained regarding the effective equation of state and the exponential law of expansion. The physical and geometric behavior of the model is also discussed.

Wave fluctuations in the system with some Yang-Mills condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prokhorov, G., E-mail: zhoraprox@yandex.ru; Pasechnik, R., E-mail: Roman.Pasechnik@thep.lu.se; Vereshkov, G., E-mail: gveresh@gmail.com

2016-12-15

Self-consistent dynamics of non-homogeneous fluctuations and homogeneous and isotropic condensate of Yang–Mills fields was investigated in zero, linear and quasilinear approximations over the wave modes in the framework of N = 4 supersymmetric model in Hamilton gauge in quasiclassical theory. The models with SU(2), SU(3) and SU(4) gauge groups were considered. Particle production effect and effect of generation of longitudinal oscillations were obtained.

Aspects of Superconformal Field Theories

NASA Astrophysics Data System (ADS)

Gadde, Abhijit

Recently, a lot of progress has been made towards understanding the strongly coupled supersymmetric quantum gauge theories. The problem of strong coupling for SU(N) gauge theories can be formulated in two separate regimes of interest, one at finite N and the other at large N in 't Hooft limit. In the first case electric/magnetic duality also called S-duality and in the second, AdS/CFT duality map the strongly coupled problem to a weakly coupled one. Both of the dualities have been well understood in the maximally supersymmetric 4 d gauge theory, the N = 4 super Yang-Mills. In this thesis, as a natural next step, we focus on the strong coupling behavior in N = 2 supersymmetric gauge theories.

The boundary of a boundary principle in field theories and the issue of austerity of the laws of physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kheyfets, A.; Miller, W.A.

The boundary of a boundary principle has been suggested by J. A. Wheeler as a realization of the austerity idea in field theories. This principle is described in three basic field theories---electrodynamics, Yang--Mills theory, and general relativity. It is demonstrated that it supplies a unified geometric interpretation of the source current in each of the three theories in terms of a generalized E. Cartan moment of rotation. The extent to which the boundary of a boundary principle represents the austerity principle is discussed. It is concluded that it works in a way analogous to thermodynamic relations and it is arguedmore » that deeper principles might be needed to comprehend the nature of austerity.« less

Chiral higher spin theories and self-duality

NASA Astrophysics Data System (ADS)

Ponomarev, Dmitry

2017-12-01

We study recently proposed chiral higher spin theories — cubic theories of interacting massless higher spin fields in four-dimensional flat space. We show that they are naturally associated with gauge algebras, which manifest themselves in several related ways. Firstly, the chiral higher spin equations of motion can be reformulated as the self-dual Yang-Mills equations with the associated gauge algebras instead of the usual colour gauge algebra. We also demonstrate that the chiral higher spin field equations, similarly to the self-dual Yang-Mills equations, feature an infinite algebra of hidden symmetries, which ensures their integrability. Secondly, we show that off-shell amplitudes in chiral higher spin theories satisfy the generalised BCJ relations with the usual colour structure constants replaced by the structure constants of higher spin gauge algebras. We also propose generalised double copy procedures featuring higher spin theory amplitudes. Finally, using the light-cone deformation procedure we prove that the structure of the Lagrangian that leads to all these properties is universal and follows from Lorentz invariance.

The boundary of a boundary principle in field theories and the issue of austerity of the laws of physics

NASA Astrophysics Data System (ADS)

Kheyfets, Arkady; Miller, Warner A.

1991-11-01

The boundary of a boundary principle has been suggested by J. A. Wheeler as a realization of the austerity idea in field theories. This principle is described in three basic field theories—electrodynamics, Yang-Mills theory, and general relativity. It is demonstrated that it supplies a unified geometric interpretation of the source current in each of the three theories in terms of a generalized E. Cartan moment of rotation. The extent to which the boundary of a boundary principle represents the austerity principle is discussed. It is concluded that it works in a way analogous to thermodynamic relations and it is argued that deeper principles might be needed to comprehend the nature of austerity.

Topics in Higher-Derivative Supergravity and N = 2 Yang-Mills Theories

NASA Astrophysics Data System (ADS)

Hindawi, Ahmed Abdel-Ati

1997-09-01

In Part I of the thesis we discuss higher-derivative theories of gravity. We start by discussing the field content of quadratic higher-derivative gravity, together with a new example of a massless spin-two field consistently coupled to gravity. The full quadratic gravity theory is shown to be equivalent to a canonical second-order theory of a massive scalar field, a massive spin-two symmetric tensor field and gravity. It is shown that flat-space is the only stable vacuum, and that the spin-two field around it is always ghost-like. We give a procedure for exhibiting the new propagating degrees of freedom in a generic higher-derivative gravity, at the full non-linear level. We show that around any vacuum the elementary excitations remain the massless graviton, a massive scalar field and a massive ghost-like spin-two field. In Part II of the thesis we extend our investigations to the realm of supergravity. We consider the general form of quadratic (1, 1) supergravity in two dimensions. It is demonstrated that the theory possesses stable vacua with vanishing cosmological constant which spontaneously break supersymmetry. We then consider higher-derivative N=1 supergravity in four dimensions. We construct two classes of higher-derivative supergravity theories. They are found to be equivalent to Einstein supergravity coupled to one or two chiral superfields and have a rich vacuum structure. It is demonstrated that theories of the second class can possess a stable vacuum with vanishing cosmological constant that spontaneously breaks supersymmetry. We then proceed to show how spontaneous supersymmetry breaking in the vacuum state of higher-derivative supergravity is transmitted, as explicit soft supersymmetry-breaking terms, to the effective Lagrangian of the standard electroweak model. In Part III we use central charge superspace to give a geometrical construction of the N=2 Abelian vector-tensor multiplet consisting, under N=1 supersymmetry, of one vector and one linear

Quark-antiquark potential in defect conformal field theory

NASA Astrophysics Data System (ADS)

Preti, Michelangelo; Trancanelli, Diego; Vescovi, Edoardo

2017-10-01

We consider antiparallel Wilson lines in N = 4 super Yang-Mills in the presence of a codimension-1 defect. We compute the Wilson lines' expectation value both at weak coupling, in the gauge theory, and at strong coupling, by finding the string configurations which are dual to this operator. These configurations display a Gross-Ooguri transition between a connected, U-shaped string phase and a phase in which the string breaks into two disconnected surfaces. We analyze in detail the critical configurations separating the two phases and compare the string result with the gauge theory one in a certain double scaling limit.

Nonlocal symmetries and Bäcklund transformations for the self-dual Yang-Mills system

NASA Astrophysics Data System (ADS)

Papachristou, C. J.; Harrison, B. Kent

1988-01-01

The observation is made that generalized evolutionary isovectors of the self-dual Yang-Mills equation, obtained by ``verticalization'' of the geometrical isovectors derived in a previous paper [J. Math. Phys. 28, 1261 (1987)], generate Bäcklund transformations for the self-dual system. In particular, new Bäcklund transformations are obtained by ``verticalizing'' the generators of point transformations on the solution manifold. A geometric ansatz for the derivation of such (generally nonlocal) symmetries is proposed.

Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q})

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roche, Ph., E-mail: philippe.roche@univ-montp2.fr

We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.

Retrieving Storm Electric Fields From Aircraft Field Mill Data. Part 2; Applications

NASA Technical Reports Server (NTRS)

Koshak, W. J.; Mach, D. M.; Christian, H. J.; Stewart, M. F.; Bateman, M. G.

2005-01-01

The Lagrange multiplier theory and "pitch down method" developed in Part I of this study are applied to complete the calibration of a Citation aircraft that is instrumented with six field mill sensors. When side constraints related to average fields are used, the method performs well in computer simulations. For mill measurement errors of 1 V/m and a 5 V/m error in the mean fair weather field function, the 3-D storm electric field is retrieved to within an error of about 12%. A side constraint that involves estimating the detailed structure of the fair weather field was also tested using computer simulations. For mill measurement errors of 1 V/m, the method retrieves the 3-D storm field to within an error of about 8% if the fair weather field estimate is typically within 1 V/m of the true fair weather field. Using this side constraint and data from fair weather field maneuvers taken on 29 June 2001, the Citation aircraft was calibrated. The resulting calibration matrix was then used to retrieve storm electric fields during a Citation flight on 2 June 2001. The storm field results are encouraging and agree favorably with the results obtained from earlier calibration analyses that were based on iterative techniques.

Linear-response time-dependent density-functional theory with pairing fields.

PubMed

Peng, Degao; van Aggelen, Helen; Yang, Yang; Yang, Weitao

2014-05-14

Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013), Y. Yang, H. van Aggelen, S. N. Steinmann, D. Peng, and W. Yang, J. Chem. Phys. 139, 174110 (2013); D. Peng, S. N. Steinmann, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 104112 (2013)] and N ± 2 excitation energies [Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013)]. So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functional theory with pairing fields with both adiabatic and frequency-dependent kernels. This theory is related to the density-functional theory and time-dependent density-functional theory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing field for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justifies the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.

Classical r matrix of the su(2 vertical bar 2) super Yang-Mills spin chain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Torrielli, Alessandro

2007-05-15

In this note we straightforwardly derive and make use of the quantum R matrix for the su(2 vertical bar 2) super Yang-Mills spin chain in the manifest su(1 vertical bar 2)-invariant formulation, which solves the standard quantum Yang-Baxter equation, in order to obtain the correspondent (undressed) classical r matrix from the first order expansion in the 'deformation' parameter 2{pi}/{radical}({lambda}) and check that this last solves the standard classical Yang-Baxter equation. We analyze its bialgebra structure, its dependence on the spectral parameters, and its pole structure. We notice that it still preserves an su(1 vertical bar 2) subalgebra, thereby admitting anmore » expression in terms of a combination of projectors, which spans only a subspace of su(1 vertical bar 2)xsu(1 vertical bar 2). We study the residue at its simple pole at the origin and comment on the applicability of the classical Belavin-Drinfeld type of analysis.« less

Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dixon, Lance J.; /SLAC; Drummond, James M.

2012-02-15

We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parametersmore » uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.« less

Cluster-enriched Yang-Baxter equation from SUSY gauge theories

NASA Astrophysics Data System (ADS)

Yamazaki, Masahito

2018-04-01

We propose a new generalization of the Yang-Baxter equation, where the R-matrix depends on cluster y-variables in addition to the spectral parameters. We point out that we can construct solutions to this new equation from the recently found correspondence between Yang-Baxter equations and supersymmetric gauge theories. The S^2 partition function of a certain 2d N=(2,2) quiver gauge theory gives an R-matrix, whereas its FI parameters can be identified with the cluster y-variables.

Towards an M5-brane model I: A 6d superconformal field theory

NASA Astrophysics Data System (ADS)

Sämann, Christian; Schmidt, Lennart

2018-04-01

We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the string Lie 2-algebra as a gauge structure, which we motivated in previous work. The kinematical data contains a connection on a categorified principal bundle, which is the appropriate mathematical description of the parallel transport of self-dual strings. Our action can be written down for each of the simply laced Dynkin diagrams, and each case reduces to a four-dimensional supersymmetric Yang-Mills theory with corresponding gauge Lie algebra. Our action also reduces nicely to an M2-brane model which is a deformation of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model. While this action is certainly not the desired M5-brane model, we regard it as a key stepping stone towards a potential construction of the (2, 0)-theory.

Einstein-Yang-Mills-Dirac systems from the discretized Kaluza-Klein theory

NASA Astrophysics Data System (ADS)

Wali, Kameshwar; Viet, Nguyen Ali

2017-01-01

A unified theory of the non-Abelian gauge interactions with gravity in the framework of a discretized Kaluza-Klein theory is constructed with a modified Dirac operator and wedge product. All the couplings of chiral spinors to the non-Abelian gauge fields emerge naturally as components of the coupling of the chiral spinors in the generalized gravity together with some new interactions. In particular, the currently prevailing gravity-QCD quark and gravity-electroweak-quark and lepton models are shown to follow as special cases of the general framework.

Nonabelian Bundle Gerbes, Their Differential Geometry and Gauge Theory

NASA Astrophysics Data System (ADS)

Aschieri, Paolo; Cantini, Luigi; Jurčo, Branislav

2005-03-01

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent formalism and in local coordinates. These are the gauge fields needed for the construction of Yang-Mills theories with 2-form gauge potential.

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.

Retrieving Storm Electric Fields from Aircrfaft Field Mill Data: Part II: Applications

NASA Technical Reports Server (NTRS)

Koshak, William; Mach, D. M.; Christian H. J.; Stewart, M. F.; Bateman M. G.

2006-01-01

The Lagrange multiplier theory developed in Part I of this study is applied to complete a relative calibration of a Citation aircraft that is instrumented with six field mill sensors. When side constraints related to average fields are used, the Lagrange multiplier method performs well in computer simulations. For mill measurement errors of 1 V m(sup -1) and a 5 V m(sup -1) error in the mean fair-weather field function, the 3D storm electric field is retrieved to within an error of about 12%. A side constraint that involves estimating the detailed structure of the fair-weather field was also tested using computer simulations. For mill measurement errors of 1 V m(sup -l), the method retrieves the 3D storm field to within an error of about 8% if the fair-weather field estimate is typically within 1 V m(sup -1) of the true fair-weather field. Using this type of side constraint and data from fair-weather field maneuvers taken on 29 June 2001, the Citation aircraft was calibrated. Absolute calibration was completed using the pitch down method developed in Part I, and conventional analyses. The resulting calibration matrices were then used to retrieve storm electric fields during a Citation flight on 2 June 2001. The storm field results are encouraging and agree favorably in many respects with results derived from earlier (iterative) techniques of calibration.

Rotationally Vibrating Electric-Field Mill

NASA Technical Reports Server (NTRS)

Kirkham, Harold

2008-01-01

A proposed instrument for measuring a static electric field would be based partly on a conventional rotating-split-cylinder or rotating-split-sphere electric-field mill. However, the design of the proposed instrument would overcome the difficulty, encountered in conventional rotational field mills, of transferring measurement signals and power via either electrical or fiber-optic rotary couplings that must be aligned and installed in conjunction with rotary bearings. Instead of being made to rotate in one direction at a steady speed as in a conventional rotational field mill, a split-cylinder or split-sphere electrode assembly in the proposed instrument would be set into rotational vibration like that of a metronome. The rotational vibration, synchronized with appropriate rapid electronic switching of electrical connections between electric-current-measuring circuitry and the split-cylinder or split-sphere electrodes, would result in an electrical measurement effect equivalent to that of a conventional rotational field mill. A version of the proposed instrument is described.

Holographic Tools for Probing the Dynamics of Strongly Coupled Field Theories

NASA Astrophysics Data System (ADS)

Fuini, John F.

Since it was conjectured almost 20 years ago, AdS/CFT duality, or holography, has enabled steady progress in understanding certain gauge theories in the strongly coupled limit. In this thesis we examine various aspects of holography and holographic techniques, as well as particular applications to the dynamics of strongly coupled plasmas. We discuss the energy loss of general probe defects in generic holographic plasmas and the lifetime of quasinormal modes of sufficiently short-wavelength in a strongly coupled N = 4 Super Yang-Mills (SYM) plasma. We then perform a thorough investigation of the far-from-equilibrium dynamics of the SYM plasma, focusing on how the presence of large magnetic fields or chemical potentials affect the timescale of equilibration. Finally we discuss some non-relativistic directions by finding a covariant construction of Lagrangians for spinor fields in generic Newton-Cartan backgrounds via a non-relativistic reduction, which may assist in the construction of non-relativistic versions of holography.

Solitons and black holes in non-Abelian Einstein-Born-Infeld theory

NASA Astrophysics Data System (ADS)

Dyadichev, V. V.; Gal'tsov, D. V.

2000-08-01

Recently it was shown that the Born-Infeld modification of the quadratic Yang-Mills action gives rise to classical particle-like solutions in the flat space which have a striking similarity with the Bartnik-McKinnon solutions obtained within the gravity coupled Yang-Mills theory. We show that both families of solutions are continuously related within the framework of the Einstein-Born-Infeld theory via interpolating sequences of parameters. We also investigate an internal structure of the associated black holes and find that the Born-Infeld non-linearity changes drastically the black hole interior typical for the usual quadratic Yang-Mills theory. In the latter case a generic solution exhibits violent metric oscillations near the singularity. In the Born-Infeld case the generic interior solution is smooth, the metric tends to the standard Schwarzschild type singularity, and we did not observe internal horizons. Smoothing of the `violent' EYM singularity may be interpreted as a result of non-gravitational quantum effects.

Classical BV Theories on Manifolds with Boundary

NASA Astrophysics Data System (ADS)

Cattaneo, Alberto S.; Mnev, Pavel; Reshetikhin, Nicolai

2014-12-01

In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV construction on the boundary and we develop its extension to strata of higher codimension in the case of manifolds with corners. We present several examples including electrodynamics, Yang-Mills theory and topological field theories coming from the AKSZ construction, in particular, the Chern-Simons theory, the BF theory, and the Poisson sigma model. This paper is the first step towards developing the perturbative quantization of such theories on manifolds with boundary in a way consistent with gluing.

Quantum spectral curve of the N=6 supersymmetric Chern-Simons theory.

PubMed

Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto

2014-07-11

Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N=6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.

Improved actions and asymptotic scaling in lattice Yang-Mills theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Langfeld, Kurt

2007-11-01

Improved actions in SU(2) and SU(3) lattice gauge theories are investigated with an emphasis on asymptotic scaling. A new scheme for tadpole improvement is proposed. The standard but heuristic tadpole improvement emerges from a mean field approximation from the new approach. Scaling is investigated by means of the large distance static quark potential. Both the generic and the new tadpole scheme yield significant improvements on asymptotic scaling when compared with loop improved actions. A study of the rotational symmetry breaking terms, however, reveals that only the new improvement scheme efficiently eliminates the leading irrelevant term from the action.

The lattice and quantized Yang–Mills theory

DOE PAGES

Creutz, Michael

2015-11-30

Quantized Yang–Mills fields lie at the heart of our understanding of the strong nuclear force. To understand the theory at low energies, we must work in the strong coupling regime. The primary technique for this is the lattice. While basically an ultraviolet regulator, the lattice avoids the use of a perturbative expansion. In this paper, I discuss the historical circumstances that drove us to this approach, which has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles.

An almost trivial gauge theory in the limit of infinite gauge coupling constant.

NASA Astrophysics Data System (ADS)

Kaptanoglu, S.

A local SU(2) gauge theory with one multiplet of scalars in the adjoint representation is considered. In the limit of infinite gauge coupling constant Yang-Mills fields become auxiliary and the action possesses a larger invariance than the usual gauge invariance; hence, the system develops a richer structure of constraints. The constraint analysis is carried out.

Yang-Mills instantons in Kähler spaces with one holomorphic isometry

NASA Astrophysics Data System (ADS)

Chimento, Samuele; Ortín, Tomás; Ruipérez, Alejandro

2018-03-01

We consider self-dual Yang-Mills instantons in 4-dimensional Kähler spaces with one holomorphic isometry and show that they satisfy a generalization of the Bogomol'nyi equation for magnetic monopoles on certain 3-dimensional metrics. We then search for solutions of this equation in 3-dimensional metrics foliated by 2-dimensional spheres, hyperboloids or planes in the case in which the gauge group coincides with the isometry group of the metric (SO(3), SO (1 , 2) and ISO(2), respectively). Using a generalized hedgehog ansatz the Bogomol'nyi equations reduce to a simple differential equation in the radial variable which admits a universal solution and, in some cases, a particular one, from which one finally recovers instanton solutions in the original Kähler space. We work out completely a few explicit examples for some Kähler spaces of interest.

Twistor theory at fifty: from contour integrals to twistor strings

NASA Astrophysics Data System (ADS)

Atiyah, Michael; Dunajski, Maciej; Mason, Lionel J.

2017-10-01

We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space-time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold-the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics-anti-self-duality equations on Yang-Mills or conformal curvature-can be encoded into twistor cohomology. These twistor correspondences yield explicit examples of Yang-Mills and gravitational instantons, which we review. They also underlie the twistor approach to integrability: the solitonic systems arise as symmetry reductions of anti-self-dual (ASD) Yang-Mills equations, and Einstein-Weyl dispersionless systems are reductions of ASD conformal equations. We then review the holomorphic string theories in twistor and ambitwistor spaces, and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes. Finally, we discuss the Newtonian limit of twistor theory and its possible role in Penrose's proposal for a role of gravity in quantum collapse of a wave function.

Twistor theory at fifty: from contour integrals to twistor strings.

PubMed

Atiyah, Michael; Dunajski, Maciej; Mason, Lionel J

2017-10-01

We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space-time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold-the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics-anti-self-duality equations on Yang-Mills or conformal curvature-can be encoded into twistor cohomology. These twistor correspondences yield explicit examples of Yang-Mills and gravitational instantons, which we review. They also underlie the twistor approach to integrability: the solitonic systems arise as symmetry reductions of anti-self-dual (ASD) Yang-Mills equations, and Einstein-Weyl dispersionless systems are reductions of ASD conformal equations. We then review the holomorphic string theories in twistor and ambitwistor spaces, and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes. Finally, we discuss the Newtonian limit of twistor theory and its possible role in Penrose's proposal for a role of gravity in quantum collapse of a wave function.

Reformulations of Yang–Mills theories with space–time tensor fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Zhi-Qiang, E-mail: gzhqedu@gmail.com

2016-01-15

We provide the reformulations of Yang–Mills theories in terms of gauge invariant metric-like variables in three and four dimensions. The reformulations are used to analyze the dimension two gluon condensate and give gauge invariant descriptions of gluon polarization. In three dimensions, we obtain a non-zero dimension two gluon condensate by one loop computation, whose value is similar to the square of photon mass in the Schwinger model. In four dimensions, we obtain a Lagrangian with the dual property, which shares the similar but different property with the dual superconductor scenario. We also make discussions on the effectiveness of one loopmore » approximation.« less

Analytic Solution to the Problem of Aircraft Electric Field Mill Calibration

NASA Technical Reports Server (NTRS)

Koshak, William

2003-01-01

It is by no means a simple task to retrieve storm electric fields from an aircraft instrumented with electric field mill sensors. The presence of the aircraft distorts the ambient field in a complicated way. Before retrievals of the storm field can be made, the field mill measurement system must be "calibrated". In other words, a relationship between impressed (i.e., ambient) electric field and mill output must be established. If this relationship can be determined, it is mathematically inverted so that ambient field can be inferred from the mill outputs. Previous studies have primarily focused on linear theories where the relationship between ambient field and mill output is described by a "calibration matrix" M. Each element of the matrix describes how a particular component of the ambient field is enhanced by the aircraft. For example the product M(sub ix), E(sub x), is the contribution of the E(sub x) field to the i(th) mill output. Similarly, net aircraft charge (described by a "charge field component" E(sub q)) contributes an amount M(sub iq)E(sub q) to the output of the i(th) sensor. The central difficulty in obtaining M stems from the fact that the impressed field (E(sub x), E(sub y), E(sub z), E(sub q) is not known but is instead estimated. Typically, the aircraft is flown through a series of roll and pitch maneuvers in fair weather, and the values of the fair weather field and aircraft charge are estimated at each point along the aircraft trajectory. These initial estimates are often highly inadequate, but several investigators have improved the estimates by implementing various (ad hoc) iterative methods. Unfortunately, none of the iterative methods guarantee absolute convergence to correct values (i.e., absolute convergence to correct values has not been rigorously proven). In this work, the mathematical problem is solved directly by analytic means. For m mills installed on an arbitrary aircraft, it is shown that it is possible to solve for a single 2m

Loops in AdS from conformal field theory

DOE PAGES

Aharony, Ofer; Alday, Luis F.; Bissi, Agnese; ...

2017-07-10

We propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely unexplored, mostly due to technical difficulties in direct calculations. We revisit this problem, and the dual 1=N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1=N 2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for nite values of the spin. Our second approach involves Mellin space. We show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case ofmore » $$\\phi$$ 4 theory in AdS, our crossing solution reproduces a previous computation of the one-loop bubble diagram. We can go further, deriving the four-point scalar triangle diagram in AdS, which had never been computed. In the process, we show how to analytically derive anomalous dimensions from Mellin amplitudes with an in nite series of poles, and discuss applications to more complicated cases such as the N = 4 super-Yang-Mills theory.« less

Loops in AdS from conformal field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aharony, Ofer; Alday, Luis F.; Bissi, Agnese

We propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely unexplored, mostly due to technical difficulties in direct calculations. We revisit this problem, and the dual 1=N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1=N 2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for nite values of the spin. Our second approach involves Mellin space. We show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case ofmore » $$\\phi$$ 4 theory in AdS, our crossing solution reproduces a previous computation of the one-loop bubble diagram. We can go further, deriving the four-point scalar triangle diagram in AdS, which had never been computed. In the process, we show how to analytically derive anomalous dimensions from Mellin amplitudes with an in nite series of poles, and discuss applications to more complicated cases such as the N = 4 super-Yang-Mills theory.« less

Loops in AdS from conformal field theory

NASA Astrophysics Data System (ADS)

Aharony, Ofer; Alday, Luis F.; Bissi, Agnese; Perlmutter, Eric

2017-07-01

We propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely unexplored, mostly due to technical difficulties in direct calculations. We revisit this problem, and the dual 1 /N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1 /N 2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. Our second approach involves Mellin space. We show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of ϕ 4 theory in AdS, our crossing solution reproduces a previous computation of the one-loop bubble diagram. We can go further, deriving the four-point scalar triangle diagram in AdS, which had never been computed. In the process, we show how to analytically derive anomalous dimensions from Mellin amplitudes with an infinite series of poles, and discuss applications to more complicated cases such as the N = 4 super-Yang-Mills theory.

Perturbative quantum gravity as a double copy of gauge theory.

PubMed

Bern, Zvi; Carrasco, John Joseph M; Johansson, Henrik

2010-08-06

In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.

[Talk about nomenclature of twelve meridians from quantitative yin-yang theory].

PubMed

Zhao, Xi-xin; Wang, Xue-xia; Zhao, Zhao; Ran, Peng-fei; Lü, Xiao-rui

2009-03-01

Based on leads provided by Neijing and other literature, analyze origins of the three-yin and the three-yang and the their respective contents of yin and yang, indicating the principle that the order of yang-qi from more to less is Yang ming, Tai yang, Shao yang, and the order of yin-qi is Tai yin, Shao yin, Jue yin. According to the location of five (six) zang-organs, respective yin-qi content is defined, and according to the principle of more yin-qi matches more, and less yin-qi matches less, five (six) zang-organs match each other. The zang-organs above the diaphragm joints with The Hand-Channels and the zang-organs below the diaphragm with The Foot-Channels, completing the nomenclature of twelve meridians. The names of the six yang-channels correspond to the yin-channels of the exterior-interior relationship, the yin-channels link with hands (feet), and the yang-channels also link with hands (feet), and the amount of yin-qi of the zang-organs corresponding to the yin-channels and the amount of yang-qi of the fu-organs corresponding to yang-channels are in a state of balance. Based on this principle, nomenclature of six channels are completed. Emphasize that the nomenclature of twelve meridians contains profound TCM theories, especially, TCM, by yin-yang, three-yin and three- yang, illustrates living phenomena from the whole to the system and organ level in human body, and the scientific principle "yin-yang can be unlimitedly divided" and its significance, which must guide the studies on living phenomena with modern life sciences from the whole to the molecular level.

Holographic complexity and noncommutative gauge theory

NASA Astrophysics Data System (ADS)

Couch, Josiah; Eccles, Stefan; Fischler, Willy; Xiao, Ming-Lei

2018-03-01

We study the holographic complexity of noncommutative field theories. The four-dimensional N=4 noncommutative super Yang-Mills theory with Moyal algebra along two of the spatial directions has a well known holographic dual as a type IIB supergravity theory with a stack of D3 branes and non-trivial NS-NS B fields. We start from this example and find that the late time holographic complexity growth rate, based on the "complexity equals action" conjecture, experiences an enhancement when the non-commutativity is turned on. This enhancement saturates a new limit which is exactly 1/4 larger than the commutative value. We then attempt to give a quantum mechanics explanation of the enhancement. Finite time behavior of the complexity growth rate is also studied. Inspired by the non-trivial result, we move on to more general setup in string theory where we have a stack of D p branes and also turn on the B field. Multiple noncommutative directions are considered in higher p cases.

Higher-Loop Amplitude Monodromy Relations in String and Gauge Theory.

PubMed

Tourkine, Piotr; Vanhove, Pierre

2016-11-18

The monodromy relations in string theory provide a powerful and elegant formalism to understand some of the deepest properties of tree-level field theory amplitudes, like the color-kinematics duality. This duality has been instrumental in tremendous progress on the computations of loop amplitudes in quantum field theory, but a higher-loop generalization of the monodromy construction was lacking. In this Letter, we extend the monodromy relations to higher loops in open string theory. Our construction, based on a contour deformation argument of the open string diagram integrands, leads to new identities that relate planar and nonplanar topologies in string theory. We write one and two-loop monodromy formulas explicitly at any multiplicity. In the field theory limit, at one-loop we obtain identities that reproduce known results. At two loops, we check our formulas by unitarity in the case of the four-point N=4 super-Yang-Mills amplitude.

Duality and integrability: Electromagnetism, linearized gravity, and massless higher spin gauge fields as bi-Hamiltonian systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barnich, Glenn; Troessaert, Cedric

2009-04-15

In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of bi-Hamiltonian evolution equations in the standard way. The result can be extended to linearized Yang-Mills theory, linearized gravity, and massless higher spin gauge fields.

Gauge and integrable theories in loop spaces

NASA Astrophysics Data System (ADS)

Ferreira, L. A.; Luchini, G.

2012-05-01

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1+1) dimensions, Chern-Simons theories in (2+1) dimensions, and non-abelian gauge theories in (2+1) and (3+1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3+1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations.

Classical field configurations and infrared slavery

NASA Astrophysics Data System (ADS)

Swanson, Mark S.

1987-09-01

The problem of determining the energy of two spinor particles interacting through massless-particle exchange is analyzed using the path-integral method. A form for the long-range interaction energy is obtained by analyzing an abridged vertex derived from the parent theory. This abridged vertex describes the radiation of zero-momentum particles by pointlike sources. A path-integral formalism for calculating the energy of the radiation field associated with this abridged vertex is developed and applications are made to determine the energy necessary for adiabatic separation of two sources in quantum electrodynamics and for an SU(2) Yang-Mills theory. The latter theory is shown to be consistent with confinement via infrared slavery.

Action principle for overdetermined systems of nonlinear field equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nissimov, E.; Pacheva, S.; Solomon, S.

1989-01-01

The authors propose a general scheme for constructing an action principle for arbitrary consistent overdetermined systems of nonlinear field equations. The principal tool is the BFV-BRST formalism. There is no need for star-product nor Chern-Simons forms. The main application of this general construction is the derivation of a superspace action in terms of unconstrained superfields for the D = 10N = 1 Super-Yang-Mills theory. The latter contains cubic as well as quartic interactions.

On the two-loop divergences of the 2-point hypermultiplet supergraphs for 6D, N = (1 , 1) SYM theory

NASA Astrophysics Data System (ADS)

Buchbinder, I. L.; Ivanov, E. A.; Merzlikin, B. S.; Stepanyantz, K. V.

2018-03-01

We consider 6D, N = (1 , 1) supersymmetric Yang-Mills theory formulated in N = (1 , 0) harmonic superspace and analyze the structure of the two-loop divergences in the hypermultiplet sector. Using the N = (1 , 0) superfield background field method we study the two-point supergraphs with the hypermultiplet legs and prove that their total contribution to the divergent part of effective action vanishes off shell.

Adiabatic regularization for gauge fields and the conformal anomaly

NASA Astrophysics Data System (ADS)

Chu, Chong-Sun; Koyama, Yoji

2017-03-01

Adiabatic regularization for quantum field theory in conformally flat spacetime is known for scalar and Dirac fermion fields. In this paper, we complete the construction by establishing the adiabatic regularization scheme for the gauge field. We show that the adiabatic expansion for the mode functions and the adiabatic vacuum can be defined in a similar way using Wentzel-Kramers-Brillouin-type (WKB-type) solutions as the scalar fields. As an application of the adiabatic method, we compute the trace of the energy momentum tensor and reproduce the known result for the conformal anomaly obtained by the other regularization methods. The availability of the adiabatic expansion scheme for the gauge field allows one to study various renormalized physical quantities of theories coupled to (non-Abelian) gauge fields in conformally flat spacetime, such as conformal supersymmetric Yang Mills, inflation, and cosmology.

The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

2000-09-01

We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.

Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rinaldi, Massimiliano, E-mail: massimiliano.rinaldi@unitn.it

We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to mattermore » domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.« less

Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations

NASA Astrophysics Data System (ADS)

Rinaldi, Massimiliano

2015-10-01

We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to matter domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.

Exact supersymmetry on the lattice

NASA Astrophysics Data System (ADS)

Ghadab, Sofiane

We describe a new approach of putting supersymmetric theories on the lattice. The basic idea is to discretize a twisted formulation of the (extended) supersymmetric theory. One can think about the twisting as an exotic change of variables that modifies the quantum numbers of the original fields. It exposes a scalar nilpotent supercharge which one can be preserved exactly on the lattice. We give explicit examples from sigma models and Yang-Mills theories. For the former, we show how to deform the theory by the addition of potential terms which preserve the supersymmmetry and play the role of Wilson terms, thus preventing the appearance of doublers. For the Yang-Mills theories however, one can show that their twisted versions can be rewritten in terms of two real Kahler-Dirac fields whose components transform into each other under the twisted supersymmetry. Once written in this geometrical language, one can ensure that the model does not exhibit spectrum doubling if one maps the component tensor fields to appropriate geometrical structures in the lattice. Numerical study of the O(3) sigma models and U(2) and SU(2) Yang-Mills theories for the case N = D = 2 indicates that no additional fine tuning is needed to recover the continuum supersymmetric models.

Conical twist fields and null polygonal Wilson loops

NASA Astrophysics Data System (ADS)

Castro-Alvaredo, Olalla A.; Doyon, Benjamin; Fioravanti, Davide

2018-06-01

Using an extension of the concept of twist field in QFT to space-time (external) symmetries, we study conical twist fields in two-dimensional integrable QFT. These create conical singularities of arbitrary excess angle. We show that, upon appropriate identification between the excess angle and the number of sheets, they have the same conformal dimension as branch-point twist fields commonly used to represent partition functions on Riemann surfaces, and that both fields have closely related form factors. However, we show that conical twist fields are truly different from branch-point twist fields. They generate different operator product expansions (short distance expansions) and form factor expansions (large distance expansions). In fact, we verify in free field theories, by re-summing form factors, that the conical twist fields operator product expansions are correctly reproduced. We propose that conical twist fields are the correct fields in order to understand null polygonal Wilson loops/gluon scattering amplitudes of planar maximally supersymmetric Yang-Mills theory.

Chern-Simons theory and S-duality

NASA Astrophysics Data System (ADS)

Dimofte, Tudor; Gukov, Sergei

2013-05-01

We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become related to objects and operations in dual 2d, 3d, and 4d theories. For example, the space of flat SL(2 , {C} ) connections on M is identified with the space of supersymmetric vacua in a dual 3d gauge theory. The hidden symmetry [InlineMediaObject not available: see fulltext.] of SL(2) Chern-Simons theory can be identified as the S-duality transformation of {N}=4 super-Yang-Mills theory (obtained by compactifying the five-brane theory on a torus); whereas the mapping class group action in Chern-Simons theory on a three-manifold M with boundary C is realized as S-duality in 4d {N}=2 super-Yang-Mills theory associated with the Riemann surface C. We illustrate these symmetries by considering simple examples of 3-manifolds that include knot complements and punctured torus bundles, on the one hand, and mapping cylinders associated with mapping class group transformations, on the other. A generalization of mapping class group actions further allows us to study the transformations between several distinguished coordinate systems on the phase space of Chern-Simons theory, the SL(2) Hitchin moduli space.

Periodic arrays of M2-branes

NASA Astrophysics Data System (ADS)

Jeon, Imtak; Lambert, Neil; Richmond, Paul

2012-11-01

We consider periodic arrays of M2-branes in the ABJM model in the spirit of a circle compactification to D2-branes in type IIA string theory. The result is a curious formulation of three-dimensional maximally supersymmetric Yang-Mills theory in terms of fermions, seven transverse scalars, a non-dynamical gauge field and an additional scalar `dual gluon'. Upon further T-duality on a transverse torus we obtain a non-manifest- Lorentz-invariant description of five-dimensional maximally supersymmetric Yang-Mills. Here the additional scalar field can be thought of as the components of a two-form along the torus. This action can be viewed as an M-theory description of M5-branes on {{{T}}^3}.

Tensor modes in pure natural inflation

NASA Astrophysics Data System (ADS)

Nomura, Yasunori; Yamazaki, Masahito

2018-05-01

We study tensor modes in pure natural inflation [1], a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang-Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang-Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the θ-angle dependence of the vacuum energy.

The large-N Yang-Mills S matrix is ultraviolet finite, but the large-N QCD S matrix is only renormalizable

NASA Astrophysics Data System (ADS)

Bochicchio, Marco

2017-03-01

Yang-Mills (YM) theory and QCD are known to be renormalizable, but not ultraviolet (UV) finite, order by order, in perturbation theory. It is a fundamental question whether YM theory or QCD is UV finite, or only renormalizable, order by order, in the large-N 't Hooft or Veneziano expansions. We demonstrate that the renormalization group (RG) and asymptotic freedom imply that in 't Hooft large-N expansion the S matrix in YM theory is UV finite, while in both 't Hooft and Veneziano large-N expansions, the S matrix in confining massless QCD is renormalizable but not UV finite. By the same argument, the large-N N =1 supersymmetry (SUSY) YM S matrix is UV finite as well. Besides, we demonstrate that, in both 't Hooft and Veneziano large-N expansions, the correlators of local gauge-invariant operators, as opposed to the S matrix, are renormalizable but, in general, not UV finite, either in YM theory and N =1 SUSY YM theory or a fortiori in massless QCD. Moreover, we compute explicitly the counterterms that arise from renormalizing the 't Hooft and Veneziano expansions by deriving in confining massless QCD-like theories a low-energy theorem of the Novikov-Shifman-Vainshtein-Zakharov type that relates the log derivative with respect to the gauge coupling of a k -point correlator, or the log derivative with respect to the RG-invariant scale, to a (k +1 )-point correlator with the insertion of Tr F2 at zero momentum. Finally, we argue that similar results hold in the large-N limit of a vast class of confining massive QCD-like theories, provided a renormalization scheme exists—as, for example, MS ¯ —in which the beta function is not dependent on the masses. Specifically, in both 't Hooft and Veneziano large-N expansions, the S matrix in confining massive QCD and massive N =1 SUSY QCD is renormalizable but not UV finite.

Nonrelativistic Yang-Mills theory for a naturally light Higgs boson

NASA Astrophysics Data System (ADS)

Berthier, Laure; Grosvenor, Kevin T.; Yan, Ziqi

2017-11-01

We continue the study of the nonrelativistic short-distance completions of a naturally light Higgs, focusing on the interplay between the gauge symmetries and the polynomial shift symmetries. We investigate the naturalness of nonrelativistic scalar quantum electrodynamics with a dynamical critical exponent z =3 by computing leading power law divergences to the scalar propagator in this theory. We find that power law divergences exhibit a more refined structure in theories that lack boost symmetries. Finally, in this toy model, we show that it is possible to preserve a fairly large hierarchy between the scalar mass and the high-energy naturalness scale across 7 orders of magnitude, while accommodating a gauge coupling of order 0.1.

Recursive Techniques for Computing Gluon Scattering in Anti-de-Sitter Space

NASA Astrophysics Data System (ADS)

Shyaka, Claude; Kharel, Savan

2016-03-01

The anti-de Sitter/conformal field theory correspondence is a relationship between two kinds of physical theories. On one side of the duality are special type of quantum (conformal) field theories known as the Yang-Mills theory. These quantum field theories are known to be equivalent to theories of gravity in Anti-de Sitter (AdS) space. The physical observables in the theory are the correlation functions that live in the boundary of AdS space. In general correlation functions are computed using configuration space and the expressions are extremely complicated. Using momentum basis and recursive techniques developed by Raju, we extend tree level correlation functions for four and five-point correlation functions in Yang-Mills theory in Anti-de Sitter space. In addition, we show that for certain external helicity, the correlation functions have simple analytic structure. Finally, we discuss how one can generalize these results to n-point functions. Hendrix college odyssey Grant.

Poisson sigma models, reduction and nonlinear gauge theories

NASA Astrophysics Data System (ADS)

Signori, Daniele

This dissertation comprises two main lines of research. Firstly, we study non-linear gauge theories for principal bundles, where the structure group is replaced by a Lie groupoid. We follow the approach of Moerdijk-Mrcun and establish its relation with the existing physics literature. In particular, we derive a new formula for the gauge transformation which closely resembles and generalizes the classical formulas found in Yang Mills gauge theories. Secondly, we give a field theoretic interpretation of the of the BRST (Becchi-Rouet-Stora-Tyutin) and BFV (Batalin-Fradkin-Vilkovisky) methods for the reduction of coisotropic submanifolds of Poisson manifolds. The generalized Poisson sigma models that we define are related to the quantization deformation problems of coisotropic submanifolds using homotopical algebras.

Beauty and physics: 13 important contributions of Chen Ning Yang

NASA Astrophysics Data System (ADS)

Shi, Yu

2014-06-01

In 2012, Chen Ning Yang received a 90th birthday gift in the form of a black cube inscribed with his 13 most important contributions, which cover four major areas of physics: statistical mechanics, condensed matter physics, particle physics and field theory. We briefly describe these 13 contributions and make general comments about Yang's distinctive style as a trailblazing leader in research.

The Status of Children in John Stuart Mill's Theory of Liberty.

ERIC Educational Resources Information Center

Habibi, D. A.

1983-01-01

John Stuart Mill viewed children in a more favorable light than is generally believed. Mill wished to protect children from society's bad influences long enough for their individual personalities and talents to develop. Complexities that arise in applying a liberal theory to the education of the immature are discussed. (PP)

The dyon spectra of finite gauge theories

NASA Astrophysics Data System (ADS)

Ferrari, Frank

1997-02-01

It is shown that all the ( p, q) dyon bound states exist and are unique in N = 4 and N = 2 with four massless flavor supersymmetric SU(2) Yang-Mills theories, where p and q are any relatively prime integers. The proof can be understood in the context of field theory alone, and does not rely on any duality assumption. We also give a general physical argument showing that these theories should have at least an exact Γ(2) duality symmetry, and then deduce in particular the existence of the (2 p,2 q) vector multiplets in the Nf = 4 theory. The corresponding massive theories are studied in parallel, and it is shown that though in these cases the spectrum is no longer self-dual at a given point on the moduli space, it is still in perfect agreement with an exact S duality. We also discuss the interplay between our results and both the semiclassical quantization and the heterotic-type II string-string duality conjecture.

Abundant stable gauge field hair for black holes in anti-de Sitter space.

PubMed

Baxter, J E; Helbling, Marc; Winstanley, Elizabeth

2008-01-11

We present new hairy black hole solutions of SU(N) Einstein-Yang-Mills (EYM) theory in asymptotically anti-de Sitter (AdS) space. These black holes are described by N+1 independent parameters and have N-1 independent gauge field degrees of freedom. Solutions in which all gauge field functions have no zeros exist for all N, and for a sufficiently large (and negative) cosmological constant. At least some of these solutions are shown to be stable under classical, linear, spherically symmetric perturbations. Therefore there is no upper bound on the amount of stable gauge field hair with which a black hole in AdS can be endowed.

Plasmon mass scale and quantum fluctuations of classical fields on a real time lattice

NASA Astrophysics Data System (ADS)

Kurkela, Aleksi; Lappi, Tuomas; Peuron, Jarkko

2018-03-01

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Above the Debye scale the classical Yang-Mills (CYM) theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determining the plasmon mass of the system using 3 different methods. Then we argue that one needs a numerical calculation of a system of classical gauge fields and small linearized fluctuations, which correspond to quantum fluctuations, in a way that keeps the separation between the two manifest. We demonstrate and test an implementation of an algorithm with the linearized fluctuation showing that the linearization indeed works and that the Gauss's law is conserved.

Renormalized Polyakov loop in the deconfined phase of SU(N) gauge theory and gauge-string duality.

PubMed

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.

Causal hydrodynamics of gauge theory plasmas from AdS/CFT duality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Natsuume, Makoto; Okamura, Takashi; Department of Physics, Kwansei Gakuin University, Sanda, Hyogo, 669-1337

2008-03-15

We study causal hydrodynamics (Israel-Stewart theory) of gauge theory plasmas from the AdS/CFT duality. Causal hydrodynamics requires new transport coefficients (relaxation times) and we compute them for a number of supersymmetric gauge theories including the N=4 super Yang-Mills theory. However, the relaxation times obtained from the 'shear mode' do not agree with the ones from the 'sound mode', which implies that the Israel-Stewart theory is not a sufficient framework to describe the gauge theory plasmas.

Dark energy fingerprints in the nonminimal Wu-Yang wormhole structure

NASA Astrophysics Data System (ADS)

Balakin, Alexander B.; Zayats, Alexei E.

2014-08-01

We discuss new exact solutions to nonminimally extended Einstein-Yang-Mills equations describing spherically symmetric static wormholes supported by the gauge field of the Wu-Yang type in a dark energy environment. We focus on the analysis of three types of exact solutions to the gravitational field equations. Solutions of the first type relate to the model, in which the dark energy is anisotropic; i.e., the radial and tangential pressures do not coincide. Solutions of the second type correspond to the isotropic pressure tensor; in particular, we discuss the exact solution, for which the dark energy is characterized by the equation of state for a string gas. Solutions of the third type describe the dark energy model with constant pressure and energy density. For the solutions of the third type, we consider in detail the problem of horizons and find constraints for the parameters of nonminimal coupling and for the constitutive parameters of the dark energy equation of state, which guarantee that the nonminimal wormholes are traversable.

Interacting vector fields in relativity without relativity

NASA Astrophysics Data System (ADS)

Anderson, Edward; Barbour, Julian

2002-06-01

Barbour, Foster and Ó Murchadha have recently developed a new framework, called here the 3-space approach, for the formulation of classical bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime are presupposed. Both arise as emergent features of the world from geodesic-type dynamics on a space of three-dimensional metric-matter configurations. In fact gravity, the universal light-cone and Abelian gauge theory minimally coupled to gravity all arise naturally through a single common mechanism. It yields relativity - and more - without presupposing relativity. This paper completes the recovery of the presently known bosonic sector within the 3-space approach. We show, for a rather general ansatz, that 3-vector fields can interact among themselves only as Yang-Mills fields minimally coupled to gravity.

2D Kac-Moody symmetry of 4D Yang-Mills theory

DOE PAGES

He, Temple; Mitra, Prahar; Strominger, Andrew

2016-10-25

Scattering amplitudes of any four-dimensional theory with nonabelian gauge group G may be recast as two-dimensional correlation functions on the asymptotic twosphere at null in nity. The soft gluon theorem is shown, for massless theories at the semiclassical level, to be the Ward identity of a holomorphic two-dimensional G-Kac-Moody symmetry acting on these correlation functions. Holomorphic Kac-Moody current insertions are positive helicity soft gluon insertions. Furthermore, the Kac-Moody transformations are a CPT invariant subgroup of gauge transformations which act nontrivially at null in nity and comprise the four-dimensional asymptotic symmetry group.

Two-Loop Gell-Mann Function for General Renormalizable N = 1 Supersymmetric Theory, Regularized by Higher Derivatives

NASA Astrophysics Data System (ADS)

Shevtsova, Ekaterina

2011-10-01

For the general renormalizable N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives, a two-loop β-function is calculated. It is shown that all integrals, needed for its obtaining are integrals of total derivatives.

Structure of UV divergences in maximally supersymmetric gauge theories

NASA Astrophysics Data System (ADS)

Kazakov, D. I.; Borlakov, A. T.; Tolkachev, D. M.; Vlasenko, D. E.

2018-06-01

We consider the UV divergences up to sub-subleading order for the four-point on-shell scattering amplitudes in D =8 supersymmetric Yang-Mills theory in the planar limit. We trace how the leading, subleading, etc divergences appear in all orders of perturbation theory. The structure of these divergences is typical for any local quantum field theory independently on renormalizability. We show how the generalized renormalization group equations allow one to evaluate the leading, subleading, etc. contributions in all orders of perturbation theory starting from one-, two-, etc. loop diagrams respectively. We focus then on subtraction scheme dependence of the results and show that in full analogy with renormalizable theories the scheme dependence can be absorbed into the redefinition of the couplings. The only difference is that the role of the couplings play dimensionless combinations like g2s2 or g2t2, where s and t are the Mandelstam variables.

On SYM theory and all order bulk singularity structures of BPS strings in type II theory

NASA Astrophysics Data System (ADS)

Hatefi, Ehsan

2018-06-01

The complete forms of the S-matrix elements of a transverse scalar field, two world volume gauge fields, and a Potential Cn-1 Ramond-Ramond (RR) form field are investigated. In order to find an infinite number of t , s , (t + s + u)-channel bulk singularity structures of this particular mixed open-closed amplitude, we employ all the conformal field theory techniques to , exploring all the entire correlation functions and all order α‧ contact interactions to these supersymmetric Yang-Mills (SYM) couplings. Singularity and contact term comparisons with the other symmetric analysis, and are also carried out in detail. Various couplings from pull-Back of branes, Myers terms and several generalized Bianchi identities should be taken into account to be able to reconstruct all order α‧ bulk singularities of type IIB (IIA) superstring theory. Finally, we make a comment on how to derive without any ambiguity all order α‧ contact terms of this S-matrix which carry momentum of RR in transverse directions.

Bootstrapping non-commutative gauge theories from L∞ algebras

NASA Astrophysics Data System (ADS)

Blumenhagen, Ralph; Brunner, Ilka; Kupriyanov, Vladislav; Lüst, Dieter

2018-05-01

Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L∞ algebra, that governs not only the action of the symmetries but also the dynamics of the theory. Our approach is well motivated from string theory. We recall that such field theories arise in the context of branes in WZW models and briefly comment on its appearance for integrable deformations of AdS5 sigma models. For the SU(2) WZW model, we show that the earlier proposed matrix valued gauge theory on the fuzzy 2-sphere can be bootstrapped via an L∞ algebra. We then apply this approach to the construction of non-commutative Chern-Simons and Yang-Mills theories on flat and curved backgrounds with non-constant NC-structure. More concretely, up to the second order, we demonstrate how derivative and curvature corrections to the equations of motion can be bootstrapped in an algebraic way from the L∞ algebra. The appearance of a non-trivial A∞ algebra is discussed, as well.

Revisiting the phase transition of AdS-Maxwell-power-Yang-Mills black holes via AdS/CFT tools

NASA Astrophysics Data System (ADS)

El Moumni, H.

2018-01-01

In the present work we investigate the Van der Waals-like phase transition of AdS black hole solution in the Einstein-Maxwell-power-Yang-Mills gravity (EMPYM) via different approaches. After reconsidering this phase structure in the entropy-thermal plane, we recall the nonlocal observables such as holographic entanglement entropy and two point correlation function to show that the both observables exhibit a Van der Waals-like behavior as the case of the thermal entropy. By checking the Maxwell's equal area law and calculating the critical exponent for different values of charge C and nonlinearity parameter q we confirm that the first and the second order phases persist in the holographic framework. Also the validity of the Maxwell law is governed by the proximity to the critical point.

Hidden simplicity of gauge theory amplitudes

NASA Astrophysics Data System (ADS)

Drummond, J. M.

2010-11-01

These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight the hidden symmetries which appear. Using the Britto, Cachzo, Feng and Witten (BCFW) recursion relations we solve the tree-level S-matrix in \\ {N}=4 super Yang-Mills theory and describe how it produces a sum of invariants of a large symmetry algebra. We review amplitudes in the planar theory beyond tree level, describing the connection between amplitudes and Wilson loops, and discuss the implications of the hidden symmetries.

Inverse bootstrapping conformal field theories

NASA Astrophysics Data System (ADS)

Li, Wenliang

2018-01-01

We propose a novel approach to study conformal field theories (CFTs) in general dimensions. In the conformal bootstrap program, one usually searches for consistent CFT data that satisfy crossing symmetry. In the new method, we reverse the logic and interpret manifestly crossing-symmetric functions as generating functions of conformal data. Physical CFTs can be obtained by scanning the space of crossing-symmetric functions. By truncating the fusion rules, we are able to concentrate on the low-lying operators and derive some approximate relations for their conformal data. It turns out that the free scalar theory, the 2d minimal model CFTs, the ϕ 4 Wilson-Fisher CFT, the Lee-Yang CFTs and the Ising CFTs are consistent with the universal relations from the minimal fusion rule ϕ 1 × ϕ 1 = I + ϕ 2 + T , where ϕ 1 , ϕ 2 are scalar operators, I is the identity operator and T is the stress tensor.

Noncommutative Wilson lines in higher-spin theory and correlation functions of conserved currents for free conformal fields

NASA Astrophysics Data System (ADS)

Bonezzi, Roberto; Boulanger, Nicolas; De Filippi, David; Sundell, Per

2017-11-01

We first prove that, in Vasiliev’s theory, the zero-form charges studied in Sezgin E and Sundell P 2011 (arXiv:1103.2360 [hep-th]) and Colombo N and Sundell P 20 (arXiv:1208.3880 [hep-th]) are twisted open Wilson lines in the noncommutative Z space. This is shown by mapping Vasiliev’s higher-spin model on noncommutative Yang-Mills theory. We then prove that, prior to Bose-symmetrising, the cyclically-symmetric higher-spin invariants given by the leading order of these n-point zero-form charges are equal to corresponding cyclically-invariant building blocks of n-point correlation functions of bilinear operators in free conformal field theories (CFT) in three dimensions. On the higher spin gravity side, our computation reproduces the results of Didenko V and Skvortsov E 2013 J. High Energy Phys. JHEP04(2013)158 using an alternative method amenable to the computation of subleading corrections obtained by perturbation theory in normal order. On the free CFT side, our proof involves the explicit computation of the separate cyclic building blocks of the correlation functions of n conserved currents in arbitrary dimension d>2 using polarization vectors, which is an original result. It is shown to agree, for d=3 , with the results obtained in Gelfond O A and Vasiliev M A 2013 Nucl. Phys. B 876 871-917 in various dimensions and where polarization spinors were used.

One-loop tests of supersymmetric gauge theories on spheres

DOE PAGES

Minahan, Joseph A.; Naseer, Usman

2017-07-14

Here, we show that a recently conjectured form for perturbative supersymmetric partition functions on spheres of general dimension d is consistent with the at space limit of 6-dimensional N = 1 super Yang-Mills. We also show that the partition functions for N = 1 8- and 9-dimensional theories are consistent with their known at space limits.

A Low Noise, Microprocessor-Controlled, Internally Digitizing Rotating-Vane Electric Field Mill for Airborne Platforms

NASA Technical Reports Server (NTRS)

Bateman, M. G.; Stewart, M. F.; Blakeslee, R. J.; Podgorny, s. J.; Christian, H. J.; Mach, D. M.; Bailey, J. C.; Daskar, D.

2006-01-01

This paper reports on a new generation of aircraft-based rotating-vane style electric field mills designed and built at NASA's Marshall Spaceflight Center. The mills have individual microprocessors that digitize the electric field signal at the mill and respond to commands from the data system computer. The mills are very sensitive (1 V/m per bit), have a wide dynamic range (115 dB), and are very low noise (+/-1 LSB). Mounted on an aircraft, these mills can measure fields from +/-1 V/m to +/-500 kV/m. Once-per-second commanding from the data collection computer to each mill allows for precise timing and synchronization. The mills can also be commanded to execute a self-calibration in flight, which is done periodically to monitor the status and health of each mill.

A test of the AdS/CFT duality on the Coulomb branch

NASA Astrophysics Data System (ADS)

Costa, M. S.

2000-06-01

We consider the /N=4 /SU(N) Super Yang Mills theory on the Coulomb branch with gauge symmetry broken to S(U(N1)×U(N2)). By integrating the W particles, the effective action near the IR SU(Ni) conformal fixed points is seen to be a deformation of the Super Yang Mills theory by a non-renormalized, irrelevant, dimension 8 operator. The correction to the two-point function of the dilaton field dual operator near the IR is related to a three-point function of chiral primary operators at the conformal fixed points and agrees with the classical gravity prediction, including the numerical factor.

Liberty, Authority, and Character Cultivation: John Stuart Mill's Revised Liberal Theories.

ERIC Educational Resources Information Center

Kim, Ki Su

1988-01-01

The article examines educational changes recommended by Mill in his liberal political theories to point out some of the attempts of liberals to adjust themselves to changing historical circumstances. (CB)

An /N=2 gauge theory and its supergravity dual

NASA Astrophysics Data System (ADS)

Brandhuber, A.; Sfetsos, K.

2000-09-01

We study flows on the scalar manifold of /N=8 gauged supergravity in five dimensions which are dual to certain mass deformations of /N=4 super Yang-Mills theory. In particular, we consider a perturbation of the gauge theory by a mass term for the adjoint hyper-multiplet, giving rise to an /N=2 theory. The exact solution of the 5-dim gauged supergravity equations of motion is found and the metric is uplifted to a ten-dimensional background of type-IIB supergravity. Using these geometric data and the AdS/CFT correspondence we analyze the spectra of certain operators as well as Wilson loops on the dual gauge theory side. The physical flows are parametrized by a single non-positive constant and describe part of the Coulomb branch of the /N=2 theory at strong coupling. We also propose a general criterion to distinguish between `physical' and `unphysical' curvature singularities. Applying it in many backgrounds arising within the AdS/CFT correspondence we find results that are in complete agreement with field theory expectations.

Computing Critical Properties with Yang-Yang Anomalies

NASA Astrophysics Data System (ADS)

Orkoulas, Gerassimos; Cerdeirina, Claudio; Fisher, Michael

2017-01-01

Computation of the thermodynamics of fluids in the critical region is a challenging task owing to divergence of the correlation length and lack of particle-hole symmetries found in Ising or lattice-gas models. In addition, analysis of experiments and simulations reveals a Yang-Yang (YY) anomaly which entails sharing of the specific heat singularity between the pressure and the chemical potential. The size of the YY anomaly is measured by the YY ratio Rμ =C μ /CV of the amplitudes of C μ = - T d2 μ /dT2 and of the total specific heat CV. A ``complete scaling'' theory, in which the pressure mixes into the scaling fields, accounts for the YY anomaly. In Phys. Rev. Lett. 116, 040601 (2016), compressible cell gas (CCG) models which exhibit YY and singular diameter anomalies, have been advanced for near-critical fluids. In such models, the individual cell volumes are allowed to fluctuate. The thermodynamics of CCGs can be computed through mapping onto the Ising model via the seldom-used great grand canonical ensemble. The computations indicate that local free volume fluctuations are the origins of the YY effects. Furthermore, local energy-volume coupling (to model water) is another crucial factor underlying the phenomena.

Kaluza-Klein theories as a tool to find new gauge symmetries

NASA Astrophysics Data System (ADS)

Dolan, L.

Non-abelian Kaluza-Klein theories are studied with respect to using the invariances of multi-dimensional general relativity to investigate hidden symmetry, such as Kac-Mody Lie algebras, of the four-dimensional Yang-Mills theory. Several properties of the affine transformations on the self-dual set are identified and are used to motivate the Kaluza-Klein analysis. In this context, a system of differential equations is derived for new symmetry transformations which may be extendable to the full gauge theory.

Tsallis’ quantum q-fields

NASA Astrophysics Data System (ADS)

Plastino, A.; Rocca, M. C.

2018-05-01

We generalize several well known quantum equations to a Tsallis’ q-scenario, and provide a quantum version of some classical fields associated with them in the recent literature. We refer to the q-Schródinger, q-Klein-Gordon, q-Dirac, and q-Proca equations advanced in, respectively, Phys. Rev. Lett. 106, 140601 (2011), EPL 118, 61004 (2017) and references therein. We also introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and non-Abelian instances. We show how to define the q-quantum field theories corresponding to the above equations, introduce the pertinent actions, and obtain equations of motion via the minimum action principle. These q-fields are meaningful at very high energies (TeV scale) for q = 1.15, high energies (GeV scale) for q = 1.001, and low energies (MeV scale) for q = 1.000001 [Nucl. Phys. A 955 (2016) 16 and references therein]. (See the ALICE experiment at the LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields’ logarithms.

Tunneling in quantum cosmology and holographic SYM theory

NASA Astrophysics Data System (ADS)

Ghoroku, Kazuo; Nakano, Yoshimasa; Tachibana, Motoi; Toyoda, Fumihiko

2018-03-01

We study the time evolution of the early Universe, which is developed by a cosmological constant Λ4 and supersymmetric Yang-Mills (SYM) fields in the Friedmann-Robertson-Walker space-time. The renormalized vacuum expectation value of the energy-momentum tensor of the SYM theory is obtained in a holographic way. It includes a radiation of the SYM field, parametrized as C . The evolution is controlled by this radiation C and the cosmological constant Λ4. For positive Λ4, an inflationary solution is obtained at late time. When C is added, the quantum mechanical situation at early time is fairly changed. Here we perform the early time analysis in terms of two different approaches, (i) the Wheeler-DeWitt equation and (ii) Lorentzian path integral with the Picard-Lefschetz method by introducing an effective action. The results of two methods are compared.

Remarks on a New Possible Discretization Scheme for Gauge Theories

NASA Astrophysics Data System (ADS)

Magnot, Jean-Pierre

2018-03-01

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.

Remarks on a New Possible Discretization Scheme for Gauge Theories

NASA Astrophysics Data System (ADS)

Magnot, Jean-Pierre

2018-07-01

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.

4D and 2D superconformal index with surface operator

NASA Astrophysics Data System (ADS)

Nakayama, Yu

2011-08-01

We study the superconformal index of the mathcal{N} = 4 super-Yang-Milles theory on S 3 × S 1 with the half BPS superconformal surface operator (defect) inserted at the great circle of S 3. The half BPS superconformal surface operators preserve the same supersymmetry as well as the symmetry of the chemical potential used in the definition of the superconformal index, so the structure and the parameterization of the superconformal index remain unaffected by the presence of the surface operator. On the surface defect, a two-dimensional (4, 4) superconformal field theory resides, and the four-dimensional super-conformal index may be regarded as a superconformal index of the two-dimensional (4, 4) superconformal field theory coupled with the four-dimensional bulk system. We construct the matrix model that computes the superconformal index with the surface operator when it couples with the bulk mathcal{N} = 4 super-Yang-Milles theory through the defect hypermultiplets on it.

Ghost-gluon vertex in the presence of the Gribov horizon

NASA Astrophysics Data System (ADS)

Mintz, B. W.; Palhares, L. F.; Sorella, S. P.; Pereira, A. D.

2018-02-01

We consider Yang-Mills theories quantized in the Landau gauge in the presence of the Gribov horizon via the refined Gribov-Zwanziger (RGZ) framework. As the restriction of the gauge path integral to the Gribov region is taken into account, the resulting gauge field propagators display a nontrivial infrared behavior, being very close to the ones observed in lattice gauge field theory simulations. In this work, we explore a higher correlation function in the refined Gribov-Zwanziger theory: the ghost-gluon interaction vertex, at one-loop level. We show explicit compatibility with kinematical constraints, as required by the Ward identities of the theory, and obtain analytical expressions in the limit of vanishing gluon momentum. We find that the RGZ results are nontrivial in the infrared regime, being compatible with lattice Yang-Mills simulations in both SU(2) and SU(3), as well as with solutions from Schwinger-Dyson equations in different truncation schemes, Functional Renormalization Group analysis, and the renormalization group-improved Curci-Ferrari model.

Cartan gravity, matter fields, and the gauge principle

NASA Astrophysics Data System (ADS)

Westman, Hans F.; Zlosnik, Tom G.

2013-07-01

Gravity is commonly thought of as one of the four force fields in nature. However, in standard formulations its mathematical structure is rather different from the Yang-Mills fields of particle physics that govern the electromagnetic, weak, and strong interactions. This paper explores this dissonance with particular focus on how gravity couples to matter from the perspective of the Cartan-geometric formulation of gravity. There the gravitational field is represented by a pair of variables: (1) a 'contact vector' VA which is geometrically visualized as the contact point between the spacetime manifold and a model spacetime being 'rolled' on top of it, and (2) a gauge connection AμAB, here taken to be valued in the Lie algebra of SO(2,3) or SO(1,4), which mathematically determines how much the model spacetime is rotated when rolled. By insisting on two principles, the gauge principle and polynomial simplicity, we shall show how one can reformulate matter field actions in a way that is harmonious with Cartan's geometric construction. This yields a formulation of all matter fields in terms of first order partial differential equations. We show in detail how the standard second order formulation can be recovered. In particular, the Hodge dual, which characterizes the structure of bosonic field equations, pops up automatically. Furthermore, the energy-momentum and spin-density three-forms are naturally combined into a single object here denoted the spin-energy-momentum three-form. Finally, we highlight a peculiarity in the mathematical structure of our first-order formulation of Yang-Mills fields. This suggests a way to unify a U(1) gauge field with gravity into a SO(1,5)-valued gauge field using a natural generalization of Cartan geometry in which the larger symmetry group is spontaneously broken down to SO(1,3)×U(1). The coupling of this unified theory to matter fields and possible extensions to non-Abelian gauge fields are left as open questions.

Particular transcendent solution of the Ernst system generalized on n fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leaute, B.; Marcilhacy, G.

A particular solution, a function of a particular form of the fifth Painleve transcendent, of the Ernst system generalized to n fields is determined, which characterizes both the stationary axially symmetric fields, the solution of the Einstein (n-1) Maxwell equations, and one class of axially symmetric static self-dual SU(n+1) Yang--Mills fields.

{{SO(d,1)}}-Invariant Yang-Baxter Operators and the dS/CFT Correspondence

NASA Astrophysics Data System (ADS)

Hollands, Stefan; Lechner, Gandalf

2018-01-01

We propose a model for the dS/CFT correspondence. The model is constructed in terms of a "Yang-Baxter operator" R for unitary representations of the de Sitter group {SO(d,1)}. This R-operator is shown to satisfy the Yang-Baxter equation, unitarity, as well as certain analyticity relations, including in particular a crossing symmetry. With the aid of this operator we construct: (a) a chiral (light-ray) conformal quantum field theory whose internal degrees of freedom transform under the given unitary representation of {SO(d,1)}. By analogy with the O( N) non-linear sigma model, this chiral CFT can be viewed as propagating in a de Sitter spacetime. (b) A (non-unitary) Euclidean conformal quantum field theory on R}^{d-1, where SO( d, 1) now acts by conformal transformations in (Euclidean) spacetime. These two theories can be viewed as dual to each other if we interpret R}^{d-1 as conformal infinity of de Sitter spacetime. Our constructions use semi-local generator fields defined in terms of R and abstract methods from operator algebras.

Rotating hairy black holes.

PubMed

Kleihaus, B; Kunz, J

2001-04-23

We construct stationary black-hole solutions in SU(2) Einstein-Yang-Mills theory which carry angular momentum and electric charge. Possessing nontrivial non-Abelian magnetic fields outside their regular event horizon, they represent nonperturbative rotating hairy black holes.

Notes on wall crossing and instanton in compactified gauge theory with matter

NASA Astrophysics Data System (ADS)

Chen, Heng-Yu; Petunin, Kirill

2010-10-01

We study the quantum effects on the Coulomb branch of mathcal{N} = 2 SU(2) super-symmetric Yang-Mills with fundamental matters compactified on {mathbb{R}^3} × {S^1} , and extract the explicit perturbative and leading non-perturbative corrections to the moduli space metric predicted from the recent work of Gaiotto, Moore and Neitzke on wall-crossing [1]. We verify the predicted metric by computing the leading weak coupling instanton contribution to the four fermion correlation using standard field theory techniques, and demonstrate perfect agreement. We also demonstrate how previously known three dimensional quantities can be recovered in appropriate small radius limit, and provide a simple geometric picture from brane construction.

All conjugate-maximal-helicity-violating amplitudes from topological open string theory in twistor space.

PubMed

Roiban, Radu; Volovich, Anastasia

2004-09-24

It has recently been proposed that the D-instanton expansion of the open topological B model on P(3|4) is equivalent to the perturbative expansion of the maximally supersymmetric Yang-Mills theory in four dimensions. In this letter we show how to construct the gauge theory results for all n-point conjugate-maximal-helicity-violating amplitudes by computing the integral over the moduli space of curves of degree n-3 in P(3|4), providing strong support to the string theory construction.

Spinning particle and gauge theories as integrability conditions

NASA Astrophysics Data System (ADS)

Eisenberg, Yeshayahu

1992-02-01

Starting from a new four dimensional spinning point particle we obtain new representations of the standard four dimensional gauge field equations in terms of a generalized space (Minkowski + light cone). In terms of this new formulation we define linear systems whose integrability conditions imply the massive Dirac-Maxwell and the Yang-Mills equations. Research supported by the Rothschild Fellowship.

Event-by-Event Anisotropic Flow in Heavy-ion Collisions from Combined Yang-Mills and Viscous Fluid Dynamics

NASA Astrophysics Data System (ADS)

Gale, Charles; Jeon, Sangyong; Schenke, Björn; Tribedy, Prithwish; Venugopalan, Raju

2013-01-01

Anisotropic flow coefficients v1-v5 in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time Glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The Glasma dynamics, as realized in the impact parameter dependent Glasma (IP-Glasma) model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic subnucleon scale color charge fluctuations; the preequilibrium flow of matter is then matched to the music algorithm describing viscous hydrodynamic flow and particle production at freeze-out. The IP-Glasma+MUSIC model describes well both transverse momentum dependent and integrated vn data measured at the Large Hadron Collider and the Relativistic Heavy Ion Collider. The model also reproduces the event-by-event distributions of v2, v3 and v4 measured by the ATLAS Collaboration. The implications of our results for better understanding of the dynamics of the Glasma and for the extraction of transport properties of the quark-gluon plasma are outlined.

Statistical effects in large N supersymmetric gauge theories

NASA Astrophysics Data System (ADS)

Czech, Bartlomiej Stanislaw

This thesis discusses statistical simplifications arising in supersymmetric gauge theories in the limit of large rank. Applications involve the physics of black holes and the problem of predicting the low energy effective theory from a landscape of string vacua. The first part of this work uses the AdS/CFT correspondence to explain properties of black holes. We establish that in the large charge sector of toric quiver gauge theories there exists a typical state whose structure is closely mimicked by almost all other states. Then, working in the settings of the half-BPS sector of N = 4 super-Yang-Mills theory, we show that in the dual gravity theory semiclassical observations cannot distinguish a pair of geometries corresponding to two generic heavy states. Finally, we argue on general grounds that these conclusions are exponentially enhanced in quantum cosmological settings. The results establish that one may consistently account for the entropy of a black hole with heavy states in the dual field theory and suggest that the usual properties of black holes arise as artifacts of imposing a semiclassical description on a quantum system. In the second half we develop new tools to determine the infrared behavior of quiver gauge theories in a certain class. We apply the dynamical results to a toy model of the landscape of effective field theories defined at some high energy scale, and derive firm statistical predictions for the low energy effective theory.

Topological resolution of gauge theory singularities

NASA Astrophysics Data System (ADS)

Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

2013-08-01

Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.

Materials Processing in Magnetic Fields

NASA Astrophysics Data System (ADS)

Schneider-Muntau, Hans J.; Wada, Hitoshi

The latest in lattice QCD -- Quark-gluon plasma physics -- String theory and exact results in quantum field theory -- The status of local supersymmetry.Supersymmetry in nuclei -- Inflation, dark matter, dark energy -- How many dimensions are really compactified? -- Horizons -- Neutrino oscillations physics -- Fundamental constants and their possible time dependence.Highlights from BNL. new phenomena at RHIC -- Highlights from BABAR -- Diffraction studied with a hard scale at HERA -- The large hadron collider: a status report -- Status of non-LHC experiments at CERN -- Highlights from Gran Sass.Fast automatic systems for nuclear emulsion scanning: technique and experiments -- Probing the QGP with charm at ALICE-LHC -- magnetic screening length in hot QCD -- Non-supersymmetric deformation of the Klebanov-Strassler model and the related plane wave theory -- Holographic renormalization made simple: an example -- The kamLAND impact on neutrino oscillations -- Particle identification with the ALIC TOF detector at very high multiplicity -- Superpotentials of N = 1 SUSY gauge theories -- Measurement of the proton structure function F2 in QED compton scattering at HERA -- Yang-Mills effective action at high temperature -- The time of flight (TOF) system of the ALICE experiment -- Almost product manifolds as the low energy geometry of Dirichlet Brane.

BOOK REVIEW: Quantum Field Theory in a Nutshell (2nd edn) Quantum Field Theory in a Nutshell (2nd edn)

NASA Astrophysics Data System (ADS)

Peskin, Michael E.

2011-04-01

and topology, and applications to condensed matter systems including the Peierls instability and the quantum Hall fluid. It is a large amount of territory to cover in a single volume. Few derivations are more than one page long. Those that fit in that space are very smooth, but others are too abbreviated to be fully comprehensible. The prose that accompanies the derivations, though, is always enticing. Zee misses no opportunity to point out that an argument he gives opens the door to some deeper subject that he encourages the reader to explore. I do warn students that it is easy to learn from this book how to talk quantum field theory without understanding it. To avoid this pitfall, it is important (as Zee emphasizes) to fill in the steps of his arguments with hard calculation. One topic from which Zee does not restrain himself is the quantum theory of gravity. In the first hundred pages we find a `concise introduction to curved spacetime' that includes a very pretty derivation of the Christoffel symbol from the geodesic equation. Toward the end of the book, there is a set of chapters devoted to the quantization of the gravitational field. The structure of the graviton propagator is worked out carefully. The van Dam-Veltman discontinuity between massless and massive spin 2 exchange is explained clearly. But after this Zee runs out of steam in presenting fully worked arguments. Still, there is room for more prose on connections to the great mysteries of the subject: the ultraviolet behavior, the cosmological constant, and the unification of forces. A new chapter added to the second edition discusses `Is Einstein Gravity The Square Of Yang-Mills Theory?' and suggests an affirmative answer, based on brand-new developments in perturbative quantum field theory. Quantum field theory is a large subject that still has not reached its definitive form. As such, there is room for many textbooks of complementary character. Zee states frankly, `It is not the purpose of this book

Nonequilibrium Phase Transitions and a Nonequilibrium Critical Point from Anti-de Sitter Space and Conformal Field Theory Correspondence

NASA Astrophysics Data System (ADS)

Nakamura, Shin

2012-09-01

We find novel phase transitions and critical phenomena that occur only outside the linear-response regime of current-driven nonequilibrium states. We consider the strongly interacting (3+1)-dimensional N=4 large-Nc SU(Nc) supersymmetric Yang-Mills theory with a single flavor of fundamental N=2 hypermultiplet as a microscopic theory. We compute its nonlinear nonballistic quark-charge conductivity by using the AdS/CFT correspondence. We find that the system exhibits a novel nonequilibrium first-order phase transition where the conductivity jumps and the sign of the differential conductivity flips at finite current density. A nonequilibrium critical point is discovered at the end point of the first-order regime. We propose a nonequilibrium steady-state analogue of thermodynamic potential in terms of the gravity-dual theory in order to define the transition point. Nonequilibrium analogues of critical exponents are proposed as well. The critical behavior of the conductivity is numerically confirmed on the basis of these proposals. The present work provides a new example of nonequilibrium phase transitions and nonequilibrium critical points.

Noncommutative Field Theories and (super)string Field Theories

NASA Astrophysics Data System (ADS)

Aref'eva, I. Ya.; Belov, D. M.; Giryavets, A. A.; Koshelev, A. S.; Medvedev, P. B.

2002-11-01

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations of the covariant string field theory proposed by Witten about 15 years ago. We review main ingredients of cubic (super)string field theories using various formulations: functional, operator, conformal and the half string formalisms. The main technical tools that are used to study conjectured D-brane decay into closed string vacuum through the tachyon condensation are presented. We describe also methods which are used to study the cubic open string field theory around the tachyon vacuum: construction of the sliver state, "comma" and matrix representations of vertices.

Electric field mill network products to improve detection of the lightning hazard

NASA Technical Reports Server (NTRS)

Maier, Launa M.

1987-01-01

An electric field mill network has been used at Kennedy Space Center for over 10 years as part of the thunderstorm detection system. Several algorithms are currently available to improve the informational output of the electric field mill data. The charge distributions of roughly 50 percent of all lightning can be modeled as if they reduced the charged cloud by a point charge or a point dipole. Using these models, the spatial differences in the lightning induced electric field changes, and a least squares algorithm to obtain an optimum solution, the three-dimensional locations of the lightning charge centers can be located. During the lifetime of a thunderstorm, dynamically induced charging, modeled as a current source, can be located spatially with measurements of Maxwell current density. The electric field mills can be used to calculate the Maxwell current density at times when it is equal to the displacement current density. These improvements will produce more accurate assessments of the potential electrical activity, identify active cells, and forecast thunderstorm termination.

On spinodal points and Lee-Yang edge singularities

NASA Astrophysics Data System (ADS)

An, X.; Mesterházy, D.; Stephanov, M. A.

2018-03-01

We address a number of outstanding questions associated with the analytic properties of the universal equation of state of the φ4 theory, which describes the critical behavior of the Ising model and ubiquitous critical points of the liquid–gas type. We focus on the relation between spinodal points that limit the domain of metastability for temperatures below the critical temperature, i.e. T < Tc , and Lee-Yang edge singularities that restrict the domain of analyticity around the point of zero magnetic field H for T > Tc . The extended analyticity conjecture (due to Fonseca and Zamolodchikov) posits that, for T < Tc , the Lee-Yang edge singularities are the closest singularities to the real H axis. This has interesting implications, in particular, that the spinodal singularities must lie off the real H axis for d < 4 , in contrast to the commonly known result of the mean-field approximation. We find that the parametric representation of the Ising equation of state obtained in the \\renewcommandε{\\varepsilon} \

New Results in {mathcal {N}}=2 N = 2 Theories from Non-perturbative String

NASA Astrophysics Data System (ADS)

Bonelli, Giulio; Grassi, Alba; Tanzini, Alessandro

2018-03-01

We describe the magnetic phase of SU(N) $\\mathcal{N}=2$ Super Yang-Mills theories in the self-dual Omega background in terms of a new class of multi-cut matrix models. These arise from a non-perturbative completion of topological strings in the dual four dimensional limit which engineers the gauge theory in the strongly coupled magnetic frame. The corresponding spectral determinants provide natural candidates for the tau functions of isomonodromy problems for flat spectral connections associated to the Seiberg-Witten geometry.

Field-scale investigation of pulverized coal mill power consumption

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ganguli, R.; Bandopadhyay, S.

2008-08-15

Twenty field-scale tests were conducted in a 28 MW pulverized coal power plant in Healy, Alaska, to examine mill power consumption in relation to coal grind size. The intent in this field-scale study was to verify if grind size truly impacted power consumption by a detectable amount. The regression model developed from the data indicates that grind size does impact mill power consumption, with finer grinds consuming significantly more power than coarser grinds. However, other factors such as coal hardness (i.e. the lower the Hardgrove Grindability Index, or the harder the coal, the higher the power consumption) and mill throughputmore » (i.e., the higher the throughput, the higher the power consumption) had to be included before the impact of grind size could be isolated. It was also observed that combining amperage and flow rate into a single parameter, i.e., specific amperage, hurt modeling. Cost analysis based on the regression model indicate a power savings of $19,972 per year if the coal were ground to 50% passing 76 {mu}m rather than the industry standard of 70% passing 76 {mu}m. The study also demonstrated that size reduction constituted a significant portion of the power consumption.« less

Topological resolution of gauge theory singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

2013-08-21

Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit themore » singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.« less

Influence of harvester and weather conditions on field loss and milling quality of rough rice

USDA-ARS?s Scientific Manuscript database

A better understanding of factors affecting field losses and milling quality during harvest is needed to improve the economic value of rice. The main objective of this study was to evaluate the impact of harvester header, harvester type, and weather conditions on field loss and milling quality of ro...

Six-dimensional regularization of chiral gauge theories

NASA Astrophysics Data System (ADS)

Fukaya, Hidenori; Onogi, Tetsuya; Yamamoto, Shota; Yamamura, Ryo

2017-03-01

We propose a regularization of four-dimensional chiral gauge theories using six-dimensional Dirac fermions. In our formulation, we consider two different mass terms having domain-wall profiles in the fifth and the sixth directions, respectively. A Weyl fermion appears as a localized mode at the junction of two different domain walls. One domain wall naturally exhibits the Stora-Zumino chain of the anomaly descent equations, starting from the axial U(1) anomaly in six dimensions to the gauge anomaly in four dimensions. Another domain wall implies a similar inflow of the global anomalies. The anomaly-free condition is equivalent to requiring that the axial U(1) anomaly and the parity anomaly are canceled among the six-dimensional Dirac fermions. Since our formulation is based on a massive vector-like fermion determinant, a nonperturbative regularization will be possible on a lattice. Putting the gauge field at the four-dimensional junction and extending it to the bulk using the Yang-Mills gradient flow, as recently proposed by Grabowska and Kaplan, we define the four-dimensional path integral of the target chiral gauge theory.

Equivalent D = 3 supergravity amplitudes from double copies of three-algebra and two-algebra gauge theories.

PubMed

Huang, Yu-tin; Johansson, Henrik

2013-04-26

We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or two-algebra super-Yang-Mills theory when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions, implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N = 12,10,8 supergravity theories and discuss its validity for all multiplicity.

The Classical Theory of Light Colors: a Paradigm for Description of Particle Interactions

NASA Astrophysics Data System (ADS)

Mazilu, Nicolae; Agop, Maricel; Gatu, Irina; Iacob, Dan Dezideriu; Butuc, Irina; Ghizdovat, Vlad

2016-06-01

The color is an interaction property: of the interaction of light with matter. Classically speaking it is therefore akin to the forces. But while forces engendered the mechanical view of the world, the colors generated the optical view. One of the modern concepts of interaction between the fundamental particles of matter - the quantum chromodynamics - aims to fill the gap between mechanics and optics, in a specific description of strong interactions. We show here that this modern description of the particle interactions has ties with both the classical and quantum theories of light, regardless of the connection between forces and colors. In a word, the light is a universal model in the description of matter. The description involves classical Yang-Mills fields related to color.

Final Report on the Airborne Field Mill Project (ABFM) 2000-2001 Field Campaign

NASA Technical Reports Server (NTRS)

Dye, James E.; Lewis, Sharon; Bateman, Monte, G.; Mach, Douglas M.; Merceret, Francis J.; Ward, Jennifer G.; Grainger, Cedric A.

2004-01-01

The Airborne Field Mill (ABFM) research program conducted under the direction of the John F. Kennedy Space Center during 2000 and 2001 is described. The purpose, methodology and initial results from the program are presented. Extensive appendices detailing the instrumentation used to collect the data are provided.

Pure spinors, function superspaces and supergravity theories in ten and eleven dimensions

NASA Astrophysics Data System (ADS)

Howe, P. S.

1991-12-01

The constraints of d = 10 supergravity coupled to super Yang-Mills and d = 11 supergravity are studied from the viewpoint of the differential geometry of certain function superspaces. For d = 10 the appropriate function space is loop superspace, and the presence of Chern-Simons terms in the coupling of supergravity to Yang-Mills is incorporated into the formalism via a central extension of the loop group of the Yang-Mills group. For d = 11 the function superspace is the space of maps from a compact two-manifold to superspace. In both cases the superspaces include additional commuting coordinates which are pure spinors. Permanent address: Department of Mathematics, King's College, London WC2R 2LS, UK.

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.

Holographic cosmology and phase transitions of SYM theory

NASA Astrophysics Data System (ADS)

Ghoroku, Kazuo; Meyer, René; Toyoda, Fumihiko

2017-10-01

We study the time development of strongly coupled N =4 supersymmetric Yang Mills (SYM) theory on cosmological Friedmann-Robertson-Walker (FRW) backgrounds via the AdS/CFT correspondence. We implement the cosmological background as a boundary metric fulfilling the Friedmann equation with a four-dimensional cosmological constant and a dark radiation term. We analyze the dual bulk solution of the type IIB supergravity and find that the time dependence of the FRW background strongly influences the dynamical properties of the SYM theory. We in particular find a phase transition between a confined and a deconfined phase. We also argue that some cosmological solutions could be related to the inflationary scenario.

Yang-Baxter algebras, integrable theories and Bethe Ansatz

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Vega, H.J.

1990-03-10

This paper presents the Yang-Baxter algebras (YBA) in a general framework stressing their power to exactly solve the lattice models associated to them. The algebraic Behe Ansatz is developed as an eigenvector construction based on the YBA. The six-vertex model solution is given explicitly. The generalization of YB algebras to face language is considered. The algebraic BA for the SOS model of Andrews, Baxter and Forrester is described using these face YB algebras. It is explained how these lattice models yield both solvable massive QFT and conformal models in appropriated scaling (continuous) limits within the lattice light-cone approach. This approachmore » permit to define and solve rigorously massive QFT as an appropriate continuum limit of gapless vertex models. The deep links between the YBA and Lie algebras are analyzed including the quantum groups that underlay the trigonometric/hyperbolic YBA. Braid and quantum groups are derived from trigonometric/hyperbolic YBA in the limit of infinite spectral parameter. To conclude, some recent developments in the domain of integrable theories are summarized.« less

Generalizations of the classical Yang-Baxter equation and O-operators

NASA Astrophysics Data System (ADS)

Bai, Chengming; Guo, Li; Ni, Xiang

2011-06-01

Tensor solutions (r-matrices) of the classical Yang-Baxter equation (CYBE) in a Lie algebra, obtained as the classical limit of the R-matrix solution of the quantum Yang-Baxter equation, is an important structure appearing in different areas such as integrable systems, symplectic geometry, quantum groups, and quantum field theory. Further study of CYBE led to its interpretation as certain operators, giving rise to the concept of {O}-operators. The O-operators were in turn interpreted as tensor solutions of CYBE by enlarging the Lie algebra [Bai, C., "A unified algebraic approach to the classical Yang-Baxter equation," J. Phys. A: Math. Theor. 40, 11073 (2007)], 10.1088/1751-8113/40/36/007. The purpose of this paper is to extend this study to a more general class of operators that were recently introduced [Bai, C., Guo, L., and Ni, X., "Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras," Commun. Math. Phys. 297, 553 (2010)], 10.1007/s00220-010-0998-7 in the study of Lax pairs in integrable systems. Relations between O-operators, relative differential operators, and Rota-Baxter operators are also discussed.

Hadronic density of states from string theory.

PubMed

Pando Zayas, Leopoldo A; Vaman, Diana

2003-09-12

We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Güven limit of the Maldacena-Nùñez embedding of the N=1 super Yang-Mills (SYM) into string theory. It is established that the theory exhibits a Hagedorn density of states. We propose a semiclassical string approximation to the finite temperature partition function for confining gauge theories admitting a supergravity dual, by performing an expansion around classical solutions characterized by temporal windings. This semiclassical approximation reveals a hadronic energy density of states of a Hagedorn type, with the coefficient determined by the gauge theory string tension as expected for confining theories. We argue that our proposal captures primarily information about states of pure N=1 SYM theory, given that this semiclassical approximation does not entail a projection onto states of large U(1) charge.

Analysis of Surface Electric Field Measurements from an Array of Electric Field Mills

NASA Astrophysics Data System (ADS)

Lucas, G.; Thayer, J. P.; Deierling, W.

2016-12-01

Kennedy Space Center (KSC) has operated an distributed array of over 30 electric field mills over the past 18 years, providing a unique data set of surface electric field measurements over a very long timespan. In addition to the electric field instruments there are many meteorological towers around KSC that monitor the local meteorological conditions. Utilizing these datasets we have investigated and found unique spatial and temporal signatures in the electric field data that are attributed to local meteorological effects and the global electric circuit. The local and global scale influences on the atmospheric electric field will be discussed including the generation of space charge from the ocean surf, local cloud cover, and a local enhancement in the electric field that is seen at sunrise.

Integrability of the Ad{{S}_{5}}\\times {{S}^{5}} superstring and its deformations

NASA Astrophysics Data System (ADS)

van Tongeren, Stijn J.

2014-10-01

This article reviews the application of integrability to the spectral problem of strings on Ad{{S}5}× {{S}5} and its deformations. We begin with a pedagogical introduction to integrable field theories culminating in the description of their finite-volume spectra through the thermodynamic Bethe ansatz (TBA). Next, we apply these ideas to the Ad{{S}5}× {{S}5} string and in later sections discuss how to account for particular integrable deformations. Through the AdS/CFT correspondence this gives an exact description of anomalous scaling dimensions of single trace operators in planar N=4 supersymmetry Yang-Mills theory, its ‘orbifolds’, and β and γ-deformed supersymmetric Yang-Mills theory. We also touch upon some subtleties arising in these deformed theories. Furthermore, we consider complex excited states (bound states) in the su(2) sector and give their TBA description. Finally we discuss the TBA for a quantum deformation of the Ad{{S}5}× {{S}5} superstring S-matrix, with close relations to among others Pohlmeyer reduced string theory, and briefly indicate more recent developments in this area.

Equivariance, BRST symmetry, and superspace

NASA Astrophysics Data System (ADS)

Niemi, Antti J.; Tirkkonen, Olav

1994-12-01

The structure of equivariant cohomology in non-Abelian localization formulas and topological field theories is discussed. Equivariance is formulated in terms of a nilpotent Becchi-Rouet-Stora-Tyutin (BRST) symmetry, and another nilpotent operator which restricts the BRST cohomology onto the equivariant, or basic sector. A superfield formulation is presented and connections to reducible [Batalin-Fradkin-Vilkovisky (BFV)] quantization of topological Yang-Mills theory are discussed.

Ultraviolet divergences in non-renormalizable supersymmetric theories

NASA Astrophysics Data System (ADS)

Smilga, A.

2017-03-01

We present a pedagogical review of our current understanding of the ultraviolet structure of N = (1,1) 6D supersymmetric Yang-Mills theory and of N = 8 4 D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higherdimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially, of extended supersymmetric theories) is that these counterterms may not be invariant off shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behaviour.

Correlation between atmospheric electric fields and cloud cover using a field mill and cloud observation data

NASA Astrophysics Data System (ADS)

Nakamori, Kota; Suzuki, Yasuki; Ohya, Hiroyo; Takano, Toshiaki; Kawamura, Yohei; Nakata, Hiroyuki; Yamashita, Kozo

2017-04-01

It is known that lightning and precipitations of rain droplets generated from thunderclouds are a generator of global atmospheric electric circuit. In the fair weather, the atmospheric electric fields (AEF) are downward (positive), while they are upward (negative) during lightning and precipitations. However, the correlations between the AEF, and the cloud parameters such as cloud cover, weather phenomenon, have been not revealed quantitatively yet. In this study, we investigate the correlations between the AEF and the cloud parameters, weather phenomenon using a field mill, the 95 GHz-FALCON (FMCW Radar for Cloud Observations)-I and all-sky camera observations. In this study, we installed a Boltek field mill on the roof of our building in Chiba University, Japan, (Geographic coordinate: 35.63 degree N, 140.10 degree E, the sea level: 55 m) on the first June, 2016. The sampling time of the AEF is 0.5 s. On the other hand, the FALCON-I has observed the cloud parameters far from about 76 m of the field mill throughout 24 hours every day. The vertical cloud profiles and the Doppler velocity of cloud particles can be derived by the FALCON-I with high distance resolutions (48.8 m) (Takano et al., 2010). In addition, the images of the clouds and precipitations are recorded with 30-s sampling by an all-sky camera using a CCD camera on the same roof during 05:00-22:00 LT every day. The distance between the field mill and the all-sky camera is 3.75 m. During 08:30 UT - 10:30 UT, on 4 July, 2016, we found the variation of the AEF due to the approach of thundercloud. The variation consisted of two patterns. One was slow variation due to the movement of thunderclouds, and the other was rapid variation associated with lightning discharges. As for the movement of thunderclouds, the AEF increased when the anvil was located over the field mill, which was opposite direction of the previous studies. This change might be due to the positive charges in the upper anvil more than 14 km

Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories

NASA Astrophysics Data System (ADS)

Alazzawi, Sabina; Lechner, Gandalf

2017-09-01

We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary number of massive particles transforming under an arbitrary compact global gauge group is allowed, thereby generalizing previous constructions of scalar theories. The two-particle S-matrix S is assumed to be an analytic solution of the Yang-Baxter equation with standard properties, including unitarity, TCP invariance, and crossing symmetry. Using methods from operator algebras and complex analysis, we identify sufficient criteria on S that imply the solution of the inverse scattering problem. These conditions are shown to be satisfied in particular by so-called diagonal S-matrices, but presumably also in other cases such as the O( N)-invariant nonlinear {σ}-models.

BF actions for the Husain-Kuchař model

NASA Astrophysics Data System (ADS)

Barbero G., J. Fernando; Villaseñor, Eduardo J.

2001-04-01

We show that the Husain-Kuchař model can be described in the framework of BF theories. This is a first step towards its quantization by standard perturbative quantum field theory techniques or the spin-foam formalism introduced in the space-time description of general relativity and other diff-invariant theories. The actions that we will consider are similar to the ones describing the BF-Yang-Mills model and some mass generating mechanisms for gauge fields. We will also discuss the role of diffeomorphisms in the new formulations that we propose.

Entanglement branes in a two-dimensional string theory

DOE PAGES

Donnelly, William; Wong, Gabriel

2017-09-20

What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large N. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. Here, we derive the modular Hamiltonian for themore » Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an entanglement brane, or E-brane.« less

Landau singularities and symbology: One- and two-loop MHV amplitudes in SYM theory

DOE PAGES

Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia

2016-03-14

We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N = 4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. Finally, we observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.

Léon Rosenfeld's general theory of constrained Hamiltonian dynamics

NASA Astrophysics Data System (ADS)

Salisbury, Donald

Léon Rosenfeld published in Annalen der Physik in 1930 a groundbreaking paper showing how to construct a Hamiltonian formalism for Lagrangian theories which admitted an underlying local gauge symmetry. The theory included both ``internal'' transformations such as the U(1) symmetry group of electromagnetism, and ``external'' symmetries typified by Einstein's general theory of relativity. His comprehensive analysis predated by two decades the formalism known as the Dirac-Bergmann approach, and I will present evidence that each of these giants were to some extent influenced by Rosenfeld's theory. Of particular significance is Rosenfeld's incorporation of arbitrary functions into the phase space generator of temporal evolution, and his construction of the phase space generator of symmetry transformations. The existing Hamiltonian formalisms have of course played a central role both in the demonstration of the renormalizability of Yang-Mills theories and current efforts in constructing a quantum theory of gravity.

Graviweak Unification, Invisible Universe and Dark Energy

NASA Astrophysics Data System (ADS)

Das, C. R.; Laperashvili, L. V.; Tureanu, A.

2013-07-01

We consider a graviweak unification model with the assumption of the existence of a hidden (invisible) sector of our Universe, parallel to the visible world. This Hidden World (HW) is assumed to be a Mirror World (MW) with broken mirror parity. We start with a diffeomorphism invariant theory of a gauge field valued in a Lie algebra g, which is broken spontaneously to the direct sum of the space-time Lorentz algebra and the Yang-Mills algebra: ˜ {g} = {{su}}(2) (grav)L ⊕ {{su}}(2)L — in the ordinary world, and ˜ {g}' = {{su}}(2){' (grav)}R ⊕ {{su}}(2)'R — in the hidden world. Using an extension of the Plebanski action for general relativity, we recover the actions for gravity, SU(2) Yang-Mills and Higgs fields in both (visible and invisible) sectors of the Universe, and also the total action. After symmetry breaking, all physical constants, including the Newton's constants, cosmological constants, Yang-Mills couplings, and other parameters, are determined by a single parameter g present in the initial action, and by the Higgs VEVs. The dark energy problem of this model predicts a too large supersymmetric breaking scale (MSUSY 1010GeV), which is not within the reach of the LHC experiments.

Wilson lines in the MHV action

DOE PAGES

Kotko, P.; Stasto, A. M.

2017-09-12

The MHV action is the Yang-Mills action quantized on the light-front, where the two explicit physical gluonic degrees of freedom have been canonically transformed to a new set of fields. This transformation leads to the action with vertices being off-shell continuations of the MHV amplitudes. We show that the solution to the field transformation expressing one of the new fields in terms of the Yang-Mills field is a certain type of the Wilson line. More precisely, it is a straight infinite gauge link with a slope extending to the light-cone minus and the transverse direction. One of the consequences ofmore » that fact is that certain MHV vertices reduced partially on-shell are gauge invariant — a fact discovered before using conventional light-front perturbation theory. We also analyze the diagrammatic content of the field transformations leading to the MHV action. We found that the diagrams for the solution to the transformation (given by the Wilson line) and its inverse differ only by light-front energy denominators. Further, we investigate the coordinate space version of the inverse solution to the one given by the Wilson line. We find an explicit expression given by a power series in fields. We also give a geometric interpretation to it by means of a specially defined vector field. Finally, we discuss the fact that the Wilson line solution to the transformation is directly related to the all-like helicity gluon wave function, while the inverse functional is a generating functional for solutions of self-dual Yang-Mills equations.« less

Wilson lines in the MHV action

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kotko, P.; Stasto, A. M.

The MHV action is the Yang-Mills action quantized on the light-front, where the two explicit physical gluonic degrees of freedom have been canonically transformed to a new set of fields. This transformation leads to the action with vertices being off-shell continuations of the MHV amplitudes. We show that the solution to the field transformation expressing one of the new fields in terms of the Yang-Mills field is a certain type of the Wilson line. More precisely, it is a straight infinite gauge link with a slope extending to the light-cone minus and the transverse direction. One of the consequences ofmore » that fact is that certain MHV vertices reduced partially on-shell are gauge invariant — a fact discovered before using conventional light-front perturbation theory. We also analyze the diagrammatic content of the field transformations leading to the MHV action. We found that the diagrams for the solution to the transformation (given by the Wilson line) and its inverse differ only by light-front energy denominators. Further, we investigate the coordinate space version of the inverse solution to the one given by the Wilson line. We find an explicit expression given by a power series in fields. We also give a geometric interpretation to it by means of a specially defined vector field. Finally, we discuss the fact that the Wilson line solution to the transformation is directly related to the all-like helicity gluon wave function, while the inverse functional is a generating functional for solutions of self-dual Yang-Mills equations.« less

Topics in string theory

NASA Astrophysics Data System (ADS)

Jejjala, Vishnumohan

2002-01-01

This Thesis explores aspects of superstring theory on orbifold spaces and applies some of the intuition gleaned from the study of the non-commutative geometry of space-time to understanding the fractional quantum Hall effect. The moduli space of vacua of marginal and relevant deformations of N = 4 super-Yang-Mills gauge theory in four dimensions is interpreted in terms of non-commutative geometry. A formalism for thinking about the algebraic geometry of the moduli space is developed. Within this framework, the representation theory of the algebras studied provides a natural exposition of D-brane fractionation. The non-commutative moduli space of deformations preserving N = 1 supersymmetry is examined in detail through various examples. In string theory, by the AdS/CFT correspondence, deformations of the N = 4 field theory are dual to the near-horizon geometries of D-branes on orbifolds of AdS5 x S 5. The physics of D-branes on the dual AdS backgrounds is explored. Quivers encapsulate the matter content of supersymmetric field theories on the worldvolumes of D-branes at orbifold singularities. New techniques for constructing quivers are presented here. When N is a normal subgroup of a finite group G, the quiver corresponding to fixed points of the orbifold M/G is computed from a G/N action on the quiver corresponding to M/G . These techniques prove useful for constructing non-Abelian quivers and for examining discrete torsion orbifolds. Quivers obtained through our constructions contain interesting low-energy phenomenology. The matter content on a brane at an isolated singularity of the Delta27 orbifold embeds the Standard Model. The symmetries of the quiver require exactly three generations of fields in the particle spectrum. Lepton masses are suppressed relative to quark masses because lepton Yukawa couplings do not appear in the superpotential. Lepton masses are generated through the Kahler potential and are related to the supersymmetry breaking scale. The model

Global charges of stationary non-Abelian black holes.

PubMed

Kleihaus, Burkhard; Kunz, Jutta; Navarro-Lérida, Francisco

2003-05-02

We consider stationary axially symmetric black holes in SU(2) Einstein-Yang-Mills-dilaton theory. We present a mass formula for these stationary non-Abelian black holes, which also holds for Abelian black holes. The presence of the dilaton field allows for rotating black holes, which possess nontrivial electric and magnetic gauge fields, but do not carry a non-Abelian charge. We further present a new uniqueness conjecture.

Ambitwistor formulations of R 2 gravity and ( DF)2 gauge theories

NASA Astrophysics Data System (ADS)

Azevedo, Thales; Engelund, Oluf Tang

2017-11-01

We consider D-dimensional amplitudes in R 2 gravities (conformal gravity in D = 4) and in the recently introduced ( DF)2 gauge theory, from the perspective of the CHY formulae and ambitwistor string theory. These theories are related through the BCJ double-copy construction, and the ( DF)2 gauge theory obeys color-kinematics duality. We work out the worldsheet details of these theories and show that they admit a formulation as integrals on the support of the scattering equations, or alternatively, as ambitwistor string theories. For gravity, this generalizes the work done by Berkovits and Witten on conformal gravity to D dimensions. The ambitwistor is also interpreted as a D-dimensional generalization of Witten's twistor string (SYM + conformal supergravity). As part of our ambitwistor investigation, we discover another ( DF)2 gauge theory containing a photon that couples to Einstein gravity. This theory can provide an alternative KLT description of Einstein gravity compared to the usual Yang-Mills squared.

O (a) improvement of 2D N = (2 , 2) lattice SYM theory

NASA Astrophysics Data System (ADS)

Hanada, Masanori; Kadoh, Daisuke; Matsuura, So; Sugino, Fumihiko

2018-04-01

We perform a tree-level O (a) improvement of two-dimensional N = (2 , 2) supersymmetric Yang-Mills theory on the lattice, motivated by the fast convergence in numerical simulations. The improvement respects an exact supersymmetry Q which is needed for obtaining the correct continuum limit without a parameter fine tuning. The improved lattice action is given within a milder locality condition in which the interactions are decaying as the exponential of the distance on the lattice. We also prove that the path-integral measure is invariant under the improved Q-transformation.

Generalized recursion relations for correlators in the gauge-gravity correspondence.

PubMed

Raju, Suvrat

2011-03-04

We show that a generalization of the Britto-Cachazo-Feng-Witten recursion relations gives a new and efficient method of computing correlation functions of the stress tensor or conserved currents in conformal field theories with an (d+1)-dimensional anti-de Sitter space dual, for d≥4, in the limit where the bulk theory is approximated by tree-level Yang-Mills theory or gravity. In supersymmetric theories, additional correlators of operators that live in the same multiplet as a conserved current or stress tensor can be computed by these means.

The moduli space of vacua of $$ \\mathcal{N}=2 $$ class $$ \\mathcal{S} $$ theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xie, Dan; Yonekura, Kazuya

We develop a systematic method to describe the moduli space of vacua of four dimensional N=2 class S theories including Coulomb branch, Higgs branch and mixed branches. In particular, we determine the Higgs and mixed branch roots, and the dimensions of the Coulomb and Higgs components of mixed branches. They are derived by using generalized Hitchin’s equations obtained from twisted compactification of 5d maximal Super-Yang-Mills, with local degrees of freedom at punctures given by (nilpotent) orbits. The crucial thing is the holomorphic factorization of the Seiberg-Witten curve and reduction of singularity at punctures. We illustrate our method by many examplesmore » including N=2 SQCD, T N theory and Argyres-Douglas theories.« less

Gauge-invariant flow equation

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-06-01

We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.

Local subsystems in gauge theory and gravity

DOE PAGES

Donnelly, William; Freidel, Laurent

2016-09-16

We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of space. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedommore » are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Finally, our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon.« less

Einstein’s gravity from a polynomial affine model

NASA Astrophysics Data System (ADS)

Castillo-Felisola, Oscar; Skirzewski, Aureliano

2018-03-01

We show that the effective field equations for a recently formulated polynomial affine model of gravity, in the sector of a torsion-free connection, accept general Einstein manifolds—with or without cosmological constant—as solutions. Moreover, the effective field equations are partially those obtained from a gravitational Yang–Mills theory known as Stephenson–Kilmister–Yang theory. Additionally, we find a generalization of a minimally coupled massless scalar field in General Relativity within a ‘minimally’ coupled scalar field in this affine model. Finally, we present a brief (perturbative) analysis of the propagators of the gravitational theory, and count the degrees of freedom. For completeness, we prove that a Birkhoff-like theorem is valid for the analyzed sector.

Generalizations of holographic renormalization group flows

NASA Astrophysics Data System (ADS)

Suh, Minwoo

The AdS/CFT correspondence conjectures the duality between type IIB supergravity on AdS5 × S5 and N = 4 super Yang-Mills theory. Mass deformations of N = 4 super Yang-Mills theory drive renormalization group (RG) flows. Holographic RG flows are described by domain wall solutions interpolating between AdS5 geometries at critical points of N = 8 gauged supergravity in five dimensions. In this thesis we study two directions of generalizations of holographic RG flows. First, motivated by the Janus solutions, we study holographic RG flows with dilaton and axion fields. To be specific, we consider the SU (3)-invariant flow with dilaton and axion fields, and discover the known supersymmetric Janus solution in five dimensions. Then, by employing the lift ansatz, we uplift the supersymmetric Janus solution of the SU(3)-invariant truncation with dilaton and axion fields to a solution of type IIB supergravity. We identify the uplifted solution to be one of the known supersymmetric Janus solution in type IIB supergravity. Furthermore, we consider the SU(2) × U(1)-invariant N = 2 and N = 1 supersymmetric flows with dilaton and axion fields. Second, motivated by the development in AdS/CMT, we study holographic RG flows with gauge fields. We consider the SU(3)-invariant flow with electric potentials or magnetic fields, and find first-order systems of flow equations for each case.

From Planck Data to Planck Era: Observational Tests of Holographic Cosmology

NASA Astrophysics Data System (ADS)

Afshordi, Niayesh; Corianò, Claudio; Delle Rose, Luigi; Gould, Elizabeth; Skenderis, Kostas

2017-01-01

We test a class of holographic models for the very early Universe against cosmological observations and find that they are competitive to the standard cold dark matter model with a cosmological constant (Λ CDM ) of cosmology. These models are based on three-dimensional perturbative superrenormalizable quantum field theory (QFT), and, while they predict a different power spectrum from the standard power law used in Λ CDM , they still provide an excellent fit to the data (within their regime of validity). By comparing the Bayesian evidence for the models, we find that Λ CDM does a better job globally, while the holographic models provide a (marginally) better fit to the data without very low multipoles (i.e., l ≲30 ), where the QFT becomes nonperturbative. Observations can be used to exclude some QFT models, while we also find models satisfying all phenomenological constraints: The data rule out the dual theory being a Yang-Mills theory coupled to fermions only but allow for a Yang-Mills theory coupled to nonminimal scalars with quartic interactions. Lattice simulations of 3D QFTs can provide nonperturbative predictions for large-angle statistics of the cosmic microwave background and potentially explain its apparent anomalies.

From Planck Data to Planck Era: Observational Tests of Holographic Cosmology.

PubMed

Afshordi, Niayesh; Corianò, Claudio; Delle Rose, Luigi; Gould, Elizabeth; Skenderis, Kostas

2017-01-27

We test a class of holographic models for the very early Universe against cosmological observations and find that they are competitive to the standard cold dark matter model with a cosmological constant (ΛCDM) of cosmology. These models are based on three-dimensional perturbative superrenormalizable quantum field theory (QFT), and, while they predict a different power spectrum from the standard power law used in ΛCDM, they still provide an excellent fit to the data (within their regime of validity). By comparing the Bayesian evidence for the models, we find that ΛCDM does a better job globally, while the holographic models provide a (marginally) better fit to the data without very low multipoles (i.e., l≲30), where the QFT becomes nonperturbative. Observations can be used to exclude some QFT models, while we also find models satisfying all phenomenological constraints: The data rule out the dual theory being a Yang-Mills theory coupled to fermions only but allow for a Yang-Mills theory coupled to nonminimal scalars with quartic interactions. Lattice simulations of 3D QFTs can provide nonperturbative predictions for large-angle statistics of the cosmic microwave background and potentially explain its apparent anomalies.

On the ground state of Yang-Mills theory

NASA Astrophysics Data System (ADS)

Bakry, Ahmed S.; Leinweber, Derek B.; Williams, Anthony G.

2011-08-01

We investigate the overlap of the ground state meson potential with sets of mesonic-trial wave functions corresponding to different gluonic distributions. We probe the transverse structure of the flux tube through the creation of non-uniform smearing profiles for the string of glue connecting two color sources in Wilson loop operator. The non-uniformly UV-regulated flux-tube operators are found to optimize the overlap with the ground state and display interesting features in the ground state overlap.

Fluxes, holography and twistors: String theory paths to four dimensions

NASA Astrophysics Data System (ADS)

Gao, Peng

2007-12-01

There are presently three popular paths to obtain four dimensional physics from string theory: compactification, holography and twistor space. We present results in this thesis on each of them, discussing the geometric structure of flux compactifications, the interplay between holography and S -duality in M-theory and the perturbative amplitudes of the marginally deformed super-Yang-Mills theory obtained from topological string theory on a supertwistor space. First we analyze supersymmetric flux compactifications of ten dimensional string theories to four dimensions. Back reaction of the fluxes on the six dimensional internal geometry is characterized by G-structures. In type IIB compactification on SU(3)-structure manifold with N = 1 supersymmetry, we solve the equations dictating the five components of intrinsic torsion. We find that the six dimensional manifold always retains an integrable almost complex structure compatible with supersymmetry. In terms of the various vacuum fields, the axion/dilaton is found to be generically non-holomorphic, and the four dimensional cosmological constant is nonvanishing only if the SU(3) structure group is reduced to SU(2). The equations are solved by one holomorphic function. Around the poles and zeros of the holomorphic function, the geometry locally looks like the well known type-A and type-B solutions. When this function is a constant, the geometry can be viewed as a holographic RG flow. After classifying the type IIB SU(3)-structure flux vacua, we analyze the effect of non-perturbative corrections on the moduli space of N = 2 flux compactifications. At energy below the Kaluza-Klein scale, the four dimensional effective theory is a gauged supergravity theory with vanishing cosmological constant. The gauging of isometries on the hyper-multiplet moduli space is induced by the fluxes. We show that instanton corrections which could potentially lift the gauged isometries are in fact prohibited both in the type IIA and heterotic

Open string with a background B field as the first order mechanics, noncommutativity, and soldering formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deriglazov, A. A.; Neves, C.; Oliveira, W.

2007-09-15

To study noncommutativity properties of the open string with constant B field, we construct a mechanical action that reproduces classical dynamics of the string sector under consideration. It allows one to apply the Dirac quantization procedure for constrained systems in a direct and unambiguous way. The mechanical action turns out to be the first order system without taking the strong field limit B{yields}{infinity}. In particular, it is true for the zero mode of the string coordinate, which means that the noncommutativity is an intrinsic property of this mechanical system. We describe the arbitrariness in the relation existing between the mechanicalmore » and the string variables and show that noncommutativity of the string variables on the boundary can be removed. This is in correspondence with the result of Seiberg and Witten on the relation among noncommutative and ordinary Yang-Mills theories. The recently developed soldering formalism helps us to establish a connection between the original open string action and the Polyakov action.« less

The Initial Flow of Classical Gluon Fields in Heavy Ion Collisions

NASA Astrophysics Data System (ADS)

Fries, Rainer J.; Chen, Guangyao

2015-03-01

Using analytic solutions of the Yang-Mills equations we calculate the initial flow of energy of the classical gluon field created in collisions of large nuclei at high energies. We find radial and elliptic flow which follows gradients in the initial energy density, similar to a simple hydrodynamic behavior. In addition we find a rapidity-odd transverse flow field which implies the presence of angular momentum and should lead to directed flow in final particle spectra. We trace those energy flow terms to transverse fields from the non-abelian generalization of Gauss' Law and Ampere's and Faraday's Laws.

Particles and strings in six-dimensional (2, 0) theory

NASA Astrophysics Data System (ADS)

Henningson, Måns

2004-11-01

In 1995, we learned of the rather surprising existence of a completely new class of quantum theories in six space-time dimensions with(2,0)superconformal symmetry. Some important reasons to study these theories are: (i) Finding the right conceptual framework to define them is a very challenging problem, that will probably take a long time to solve. It is likely to involve new interesting mathematical structures with connections in particular to algebra and geometry. (ii) They give rise to certain Yang-Mills theories with maximally extended supersymmetry upon compactification on a two-torus. This may be a way to find an S-dual formulation of these lower dimensional theories. (iii) They arise within string/ M-theory as decoupled subsectors localized on certain space-time impurities such as branes or singularities. (This is in fact how these theories were first discovered (see Witten, hep-th/9507121).) This may provide an opportunity to study aspects of these higher dimensional theories without having to deal with the conceptual subtleties of quantum gravity. To cite this article: M. Henningson, C. R. Physique 5 (2004).

Soft-collinear supersymmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cohen, Timothy; Elor, Gilly; Larkoski, Andrew J.

Soft-Collinear E ective Theory (SCET) is a framework for modeling the infrared structure of theories whose long distance behavior is dominated by soft and collinear divergences. This paper demonstrates that SCET can be made compatible with supersymmetry (SUSY). Explicitly, the e ective Lagrangian for N = 1 SUSY Yang-Mills is constructed and shown to be a complete description for the infrared of this model. For contrast, we also construct the e ective Lagrangian for chiral SUSY theories with Yukawa couplings, speci cally the single avor Wess-Zumino model. Only a subset of the infrared divergences are reproduced by the Lagrangian |more » to account for the complete low energy description requires the inclusion of local operators. SCET is formulated by expanding elds along a light-like direction and then subsequently integrating out degrees-of-freedom that are away from the light-cone. De ning the theory with respect to a speci c frame obfuscates Lorentz invariance | given that SUSY is a space-time symmetry, this presents a possible obstruction. The cleanest language with which to expose the congruence between SUSY and SCET requires exploring two novel formalisms: collinear fermions as two-component Weyl spinors, and SCET in light-cone gauge. By expressing SUSY Yang- Mills in \\collinear superspace", a slice of superspace derived by integrating out half the fermionic coordinates, the light-cone gauge SUSY SCET theory can be written in terms of super elds. As a byproduct, bootstrapping up to the full theory yields the rst algorithmic approach for determining the SUSY Yang-Mills on-shell superspace action. As a result, this work paves the way toward discovering the e ective theory for the collinear limit of N = 4 SUSY Yang-Mills.« less

Soft-collinear supersymmetry

DOE PAGES

Cohen, Timothy; Elor, Gilly; Larkoski, Andrew J.

2017-03-03

Soft-Collinear E ective Theory (SCET) is a framework for modeling the infrared structure of theories whose long distance behavior is dominated by soft and collinear divergences. This paper demonstrates that SCET can be made compatible with supersymmetry (SUSY). Explicitly, the e ective Lagrangian for N = 1 SUSY Yang-Mills is constructed and shown to be a complete description for the infrared of this model. For contrast, we also construct the e ective Lagrangian for chiral SUSY theories with Yukawa couplings, speci cally the single avor Wess-Zumino model. Only a subset of the infrared divergences are reproduced by the Lagrangian |more » to account for the complete low energy description requires the inclusion of local operators. SCET is formulated by expanding elds along a light-like direction and then subsequently integrating out degrees-of-freedom that are away from the light-cone. De ning the theory with respect to a speci c frame obfuscates Lorentz invariance | given that SUSY is a space-time symmetry, this presents a possible obstruction. The cleanest language with which to expose the congruence between SUSY and SCET requires exploring two novel formalisms: collinear fermions as two-component Weyl spinors, and SCET in light-cone gauge. By expressing SUSY Yang- Mills in \\collinear superspace", a slice of superspace derived by integrating out half the fermionic coordinates, the light-cone gauge SUSY SCET theory can be written in terms of super elds. As a byproduct, bootstrapping up to the full theory yields the rst algorithmic approach for determining the SUSY Yang-Mills on-shell superspace action. As a result, this work paves the way toward discovering the e ective theory for the collinear limit of N = 4 SUSY Yang-Mills.« less

Hamiltonian Anomalies from Extended Field Theories

NASA Astrophysics Data System (ADS)

Monnier, Samuel

2015-09-01

We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1989-01-01

transform provides a linearization.’ Well known systems include the Kadomtsev - Petviashvili , Davey-Stewartson and Self-Dual Yang-Mills equations . The d...which employs inverse scattering theory in order to linearize the given nonlinear equation . I.S.T. has led to new developments in both fields: inverse...scattering and nonlinear wave equations . Listed below are some of the problems studied and a short description of results. - Multidimensional

Gluon scattering amplitudes from gauge/string duality and integrability

NASA Astrophysics Data System (ADS)

Satoh, Yuji

2014-06-01

We discuss the gluon scattering amplitudes of the four-dimensional maximally supersymmetric Yang-Mills theory. By the gauge/string duality, the amplitudes at strong coupling are given by the area of the minimal surfaces in anti-de Sitter space, which can be analyzed by a set of integral equations of the thermodynamic Bethe ansatz (TBA) type. By using the two-dimensional integrable models and conformal field theories underlying the TBA system, we derive analytic expansions of the amplitudes around certain kinematic configurations.

Interpolating the Coulomb phase of little string theory

DOE PAGES

Lin, Ying -Hsuan; Shao, Shu -Heng; Wang, Yifan; ...

2015-12-03

We study up to 8-derivative terms in the Coulomb branch effective action of (1,1) little string theory, by collecting results of 4-gluon scattering amplitudes from both perturbative 6D super-Yang-Mills theory up to 4-loop order, and tree-level double scaled little string theory (DSLST). In previous work we have matched the 6-derivative term from the 6D gauge theory to DSLST, indicating that this term is protected on the entire Coulomb branch. The 8-derivative term, on the other hand, is unprotected. In this paper we compute the 8-derivative term by interpolating from the two limits, near the origin and near the infinity onmore » the Coulomb branch, numerically from SU(k) SYM and DSLST respectively, for k=2,3,4,5. We discuss the implication of this result on the UV completion of 6D SYM as well as the strong coupling completion of DSLST. As a result, we also comment on analogous interpolating functions in the Coulomb phase of circle-compactified (2,0) little string theory.« less

The first law of black hole mechanics for fields with internal gauge freedom

NASA Astrophysics Data System (ADS)

Prabhu, Kartik

2017-02-01

We derive the first law of black hole mechanics for physical theories based on a local, covariant and gauge-invariant Lagrangian where the dynamical fields transform non-trivially under the action of some internal gauge transformations. The theories of interest include General Relativity formulated in terms of tetrads, Einstein-Yang-Mills theory and Einstein-Dirac theory. Since the dynamical fields of these theories have some internal gauge freedom, we argue that there is no natural group action of diffeomorphisms of spacetime on such dynamical fields. In general, such fields cannot even be represented as smooth, globally well-defined tensor fields on spacetime. Consequently the derivation of the first law by Iyer and Wald cannot be used directly. Nevertheless, we show how such theories can be formulated on a principal bundle and that there is a natural action of automorphisms of the bundle on the fields. These bundle automorphisms encode both spacetime diffeomorphisms and internal gauge transformations. Using this reformulation we define the Noether charge associated to an infinitesimal automorphism and the corresponding notion of stationarity and axisymmetry of the dynamical fields. We first show that we can define certain potentials and charges at the horizon of a black hole so that the potentials are constant on the bifurcate Killing horizon, giving a generalised zeroth law for bifurcate Killing horizons. We further identify the gravitational potential and perturbed charge as the temperature and perturbed entropy of the black hole which gives an explicit formula for the perturbed entropy analogous to the Wald entropy formula. We then obtain a general first law of black hole mechanics for such theories. The first law relates the perturbed Hamiltonians at spatial infinity and the horizon, and the horizon contributions take the form of a ‘potential times perturbed charge’ term. We also comment on the ambiguities in defining a prescription for the total entropy

Interpersonal Harmony and Conflict for Chinese People: A Yin-Yang Perspective.

PubMed

Huang, Li-Li

2016-01-01

This article provides an overview on a series of original studies conducted by the author. The aim here is to present the ideas that the author reconstructed, based on the dialectics of harmonization, regarding harmony and conflict embodied in traditional Chinese thought, and to describe how a formal psychological theory/model on interpersonal harmony and conflict was developed based on the Yin-Yang perspective. The paper also details how essential theories on interpersonal harmony and conflict were constructed under this formal model by conducting a qualitative study involving in-depth interviews with 30 adults. Psychological research in Western society has, intriguingly, long been focused more on interpersonal conflict than on interpersonal harmony. By contrast, the author's work started from the viewpoint of a materialist conception of history and dialectics of harmonization in order to reinterpret traditional Chinese thought. Next, a "dynamic model of interpersonal harmony and conflict" was developed, as a formal psychological theory, based on the real-virtual notions in the Yin-Yang perspective. Under this model, interpersonal harmony and conflict can be classified into genuine versus superficial harmony and authentic versus virtual focus conflict, and implicit/hidden conflict is regarded as superficial harmony. Subsequently, the author conducted a series of quantitative studies on interpersonal harmony and conflict within parent-child, supervisor-subordinate, and friend-friend relationships in order to verify the construct validity and the predictive validity of the dynamic model of interpersonal harmony and conflict. The claim presented herein is that Chinese traditional thought and the psychological theory/model based on the Yin-Yang perspective can be combined. Accordingly, by combining qualitative and quantitative empirical research, the relative substantial theory can be developed and the concepts can be validated. Thus, this work represents the

Interpersonal Harmony and Conflict for Chinese People: A Yin–Yang Perspective

PubMed Central

Huang, Li-Li

2016-01-01

This article provides an overview on a series of original studies conducted by the author. The aim here is to present the ideas that the author reconstructed, based on the dialectics of harmonization, regarding harmony and conflict embodied in traditional Chinese thought, and to describe how a formal psychological theory/model on interpersonal harmony and conflict was developed based on the Yin–Yang perspective. The paper also details how essential theories on interpersonal harmony and conflict were constructed under this formal model by conducting a qualitative study involving in-depth interviews with 30 adults. Psychological research in Western society has, intriguingly, long been focused more on interpersonal conflict than on interpersonal harmony. By contrast, the author’s work started from the viewpoint of a materialist conception of history and dialectics of harmonization in order to reinterpret traditional Chinese thought. Next, a “dynamic model of interpersonal harmony and conflict” was developed, as a formal psychological theory, based on the real-virtual notions in the Yin–Yang perspective. Under this model, interpersonal harmony and conflict can be classified into genuine versus superficial harmony and authentic versus virtual focus conflict, and implicit/hidden conflict is regarded as superficial harmony. Subsequently, the author conducted a series of quantitative studies on interpersonal harmony and conflict within parent–child, supervisor–subordinate, and friend–friend relationships in order to verify the construct validity and the predictive validity of the dynamic model of interpersonal harmony and conflict. The claim presented herein is that Chinese traditional thought and the psychological theory/model based on the Yin–Yang perspective can be combined. Accordingly, by combining qualitative and quantitative empirical research, the relative substantial theory can be developed and the concepts can be validated. Thus, this work

Further Development of HS Field Theory

NASA Astrophysics Data System (ADS)

Abdurrahman, Abdulmajeed; Faridani, Jacqueline; Gassem, Mahmoud

2006-04-01

We present a systematic treatment of the HS Field theory of the open bosonic string and discuss its relationship to other full string field theories of the open bosonic string such as Witten's theory and the CVS theory. In the development of the HS field theory we encounter infinite dimensional matrices arising from the change of representation between the two theories, i.e., the HS field theory and the full string field theory. We give a general procedure of how to invert these gigantic matrices. The inversion of these matrices involves the computation of many infinite sums. We give the values of these sums and state their generalizations arising from considering higher order vertices (i.e., more than three strings) in string field theory. Moreover, we give a general procedure, on how to evaluate the generalized sums, that can be extended to many generic sums of similar properties. We also discuss the conformal operator connecting the HS field theory to that of the CVS string field theory.

Pions as gluons in higher dimensions

NASA Astrophysics Data System (ADS)

Cheung, Clifford; Remmen, Grant N.; Shen, Chia-Hsien; Wen, Congkao

2018-04-01

We derive the nonlinear sigma model as a peculiar dimensional reduction of Yang-Mills theory. In this framework, pions are reformulated as higher-dimensional gluons arranged in a kinematic configuration that only probes cubic interactions. This procedure yields a purely cubic action for the nonlinear sigma model that exhibits a symmetry enforcing color-kinematics duality. Remarkably, the associated kinematic algebra originates directly from the Poincaré algebra in higher dimensions. Applying the same construction to gravity yields a new quartic action for Born-Infeld theory and, applied once more, a cubic action for the special Galileon theory. Since the nonlinear sigma model and special Galileon are subtly encoded in the cubic sectors of Yang-Mills theory and gravity, respectively, their double copy relationship is automatic.

Can a Linear Sigma Model Describe Walking Gauge Theories at Low Energies?

NASA Astrophysics Data System (ADS)

Gasbarro, Andrew

2018-03-01

In recent years, many investigations of confining Yang Mills gauge theories near the edge of the conformal window have been carried out using lattice techniques. These studies have revealed that the spectrum of hadrons in nearly conformal ("walking") gauge theories differs significantly from the QCD spectrum. In particular, a light singlet scalar appears in the spectrum which is nearly degenerate with the PNGBs at the lightest currently accessible quark masses. This state is a viable candidate for a composite Higgs boson. Presently, an acceptable effective field theory (EFT) description of the light states in walking theories has not been established. Such an EFT would be useful for performing chiral extrapolations of lattice data and for serving as a bridge between lattice calculations and phenomenology. It has been shown that the chiral Lagrangian fails to describe the IR dynamics of a theory near the edge of the conformal window. Here we assess a linear sigma model as an alternate EFT description by performing explicit chiral fits to lattice data. In a combined fit to the Goldstone (pion) mass and decay constant, a tree level linear sigma model has a Χ2/d.o.f. = 0.5 compared to Χ2/d.o.f. = 29.6 from fitting nextto-leading order chiral perturbation theory. When the 0++ (σ) mass is included in the fit, Χ2/d.o.f. = 4.9. We remark on future directions for providing better fits to the σ mass.

Four-dimensional \\mathcal{N} = 2 supersymmetric theory with boundary as a two-dimensional complex Toda theory

NASA Astrophysics Data System (ADS)

Luo, Yuan; Tan, Meng-Chwan; Vasko, Petr; Zhao, Qin

2017-05-01

We perform a series of dimensional reductions of the 6d, \\mathcal{N} = (2, 0) SCFT on S 2 × Σ × I × S 1 down to 2d on Σ. The reductions are performed in three steps: (i) a reduction on S 1 (accompanied by a topological twist along Σ) leading to a supersymmetric Yang-Mills theory on S 2 × Σ × I, (ii) a further reduction on S 2 resulting in a complex Chern-Simons theory defined on Σ × I, with the real part of the complex Chern-Simons level being zero, and the imaginary part being proportional to the ratio of the radii of S 2 and S 1, and (iii) a final reduction to the boundary modes of complex Chern-Simons theory with the Nahm pole boundary condition at both ends of the interval I, which gives rise to a complex Toda CFT on the Riemann surface Σ. As the reduction of the 6d theory on Σ would give rise to an \\mathcal{N} = 2 supersymmetric theory on S 2 × I × S 1, our results imply a 4d-2d duality between four-dimensional \\mathcal{N} = 2 supersymmetric theory with boundary and two-dimensional complex Toda theory.

Strings from massive higher spins: the asymptotic uniqueness of the Veneziano amplitude

NASA Astrophysics Data System (ADS)

Caron-Huot, Simon; Komargodski, Zohar; Sever, Amit; Zhiboedov, Alexander

2017-10-01

We consider weakly coupled theories of massive higher-spin particles. This class of models includes, for instance, tree-level String Theory and Large-N Yang-Mills theory. The S-matrix in such theories is a meromorphic function obeying unitarity and crossing symmetry. We discuss the (unphysical) regime s, t ≫ 1, in which we expect the amplitude to be universal and exponentially large. We develop methods to study this regime and show that the amplitude necessarily coincides with the Veneziano amplitude there. In particular, this implies that the leading Regge trajectory, j( t), is asymptotically linear in Yang-Mills theory. Further, our analysis shows that any such theory of higherspin particles has stringy excitations and infinitely many asymptotically parallel subleading trajectories. More generally, we argue that, under some assumptions, any theory with at least one higher-spin particle must have strings.

Donaldson-Witten theory and indefinite theta functions

NASA Astrophysics Data System (ADS)

Korpas, Georgios; Manschot, Jan

2017-11-01

We consider partition functions with insertions of surface operators of topologically twisted N=2 , SU(2) supersymmetric Yang-Mills theory, or Donaldson-Witten theory for short, on a four-manifold. If the metric of the compact four-manifold has positive scalar curvature, Moore and Witten have shown that the partition function is completely determined by the integral over the Coulomb branch parameter a, while more generally the Coulomb branch integral captures the wall-crossing behavior of both Donaldson polynomials and Seiberg-Witten invariants. We show that after addition of a \\overlineQ -exact surface operator to the Moore-Witten integrand, the integrand can be written as a total derivative to the anti-holomorphic coordinate ā using Zwegers' indefinite theta functions. In this way, we reproduce Göttsche's expressions for Donaldson invariants of rational surfaces in terms of indefinite theta functions for any choice of metric.

Super Yang Mills, matrix models and geometric transitions

NASA Astrophysics Data System (ADS)

Ferrari, Frank

2005-03-01

I explain two applications of the relationship between four-dimensional N=1 supersymmetric gauge theories, zero-dimensional gauged matrix models, and geometric transitions in string theory. The first is related to the spectrum of BPS domain walls or BPS branes. It is shown that one can smoothly interpolate between a D-brane state, whose weak coupling tension scales as N˜1/g, and a closed string solitonic state, whose weak coupling tension scales as N˜1/gs2. This is part of a larger theory of N=1 quantum parameter spaces. The second is a new purely geometric approach to sum exactly over planar diagrams in zero dimension. It is an example of open/closed string duality. To cite this article: F. Ferrari, C. R. Physique 6 (2005).

Phases of QCD3 from non-SUSY Seiberg duality and brane dynamics

NASA Astrophysics Data System (ADS)

Armoni, Adi; Niarchos, Vasilis

2018-05-01

We consider a nonsupersymmetric USp Yang-Mills Chern-Simons gauge theory coupled to fundamental flavors. The theory is realised in type-IIB string theory via an embedding in a Hanany-Witten brane configuration which includes an orientifold and antibranes. We argue that the theory admits a magnetic Seiberg dual. Using the magnetic dual we identify dynamics in field theory and brane physics that correspond to various phases, obtaining a better understanding of three-dimensional bosonization and dynamical breaking of flavor symmetry in USp QCD3 theory. In field theory both phases correspond to magnetic "squark" condensation. In string theory, they correspond to open string tachyon condensation and brane reconnection. We also discuss other phases where the magnetic `squark' is massive. Finally, we briefly comment on the case of unitary gauge groups.

Coulomb branches with complex singularities

NASA Astrophysics Data System (ADS)

Argyres, Philip C.; Martone, Mario

2018-06-01

We construct 4d superconformal field theories (SCFTs) whose Coulomb branches have singular complex structures. This implies, in particular, that their Coulomb branch coordinate rings are not freely generated. Our construction also gives examples of distinct SCFTs which have identical moduli space (Coulomb, Higgs, and mixed branch) geometries. These SCFTs thus provide an interesting arena in which to test the relationship between moduli space geometries and conformal field theory data. We construct these SCFTs by gauging certain discrete global symmetries of N = 4 superYang-Mills (sYM) theories. In the simplest cases, these discrete symmetries are outer automorphisms of the sYM gauge group, and so these theories have lagrangian descriptions as N = 4 sYM theories with disconnected gauge groups.

Supersymmetric gauge theory with space-time-dependent couplings

NASA Astrophysics Data System (ADS)

Choi, Jaewang; Fernández-Melgarejo, José J.; Sugimoto, Shigeki

2018-01-01

We study deformations of N=4 supersymmetric Yang-Mills theory with couplings and masses depending on space-time. The conditions to preserve part of the supersymmetry are derived and a lot of solutions of these conditions are found. The main example is the case with ISO(1,1)× SO(3)× SO(3) symmetry, in which couplings, as well as masses and the theta parameter, can depend on two spatial coordinates. In the case in which ISO(1,1) is enhanced to ISO(1,2), it reproduces the supersymmetric Janus configuration found by Gaiotto and Witten [J. High Energy Phys. 06, 097 (2010)]. When SO(3)× SO(3) is enhanced to SO(6), it agrees with the world-volume theory of D3-branes embedded in F-theory (a background with 7-branes in type IIB string theory). We have also found the general solution of the supersymmetry conditions for the cases with ISO(1,1)× SO(2)× SO(4) symmetry. Cases with time-dependent couplings and/or masses are also considered.

Inflation, the Higgs field and the resolution of the Cosmological Constant Paradox

NASA Astrophysics Data System (ADS)

De Martini, Francesco

2017-08-01

The nature of the scalar field responsible for the cosmological inflation, the ”inflaton”, is found to be rooted in the most fundamental concept of the Weyl’s differential geometry: the parallel displacement of vectors in curved space-time. Within this novel dynamical scenario, the standard electroweak theory of leptons based on the SU(2) L ⊗ U(1) Y as well as on the conformal groups of spacetime Weyl’s transformations is analyzed within the framework of a general-relativistic, co-covariant scalar-tensor theory that includes the electromagnetic and the Yang-Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An ”Effective Cosmological Potential”: Veff is expressed in terms of the dark energy potential: {V}{{Λ }}\\equiv {M}{{Λ }}2 via the ”mass reduction parameter”: \\zeta \\equiv \\sqrt{\\frac{|{V}eff|}{|{V}{{Λ }}|}}, a general property of the Universe. The mass of the Higgs boson, which is considered a ”free parameter” by the standard electroweak theory, by our theory is found to be proportional to the geometrical mean: {M}H\\propto \\sqrt{{M}eff× {M}P} of the Planck mass, MP and of the mass {M}eff\\equiv \\sqrt{|{V}eff|} which accounts for the measured Cosmological Constant, i.e. the measured content of vacuum-energy in the Universe. The experimental result obtained by the ATLAS and CMS Collaborations at CERN in the year 2012: MH = 125.09(GeV/c 2) leads by our theory to a value: Meff ~ 3.19 · 10-6(eV/c 2). The peculiar mathematical structure of Veff offers a clue towards the resolution of a most intriguing puzzle of modern quantum field theory, the ”Cosmological Constant Paradox”.

Study on Finite Element Method of Stress Field in Aluminum Alloy High-Speed Milling Process

NASA Astrophysics Data System (ADS)

Zhang, Wei; Li, Shunming; Wu, Qijun; An, Zenghui

2017-11-01

Three-dimensional numerical simulation model has been built by means of Advantage FEM. Perform simulation the stress fields of 7050-T7451 aluminum alloy in high speed milling process at the speed range of 628 m/min∼5946 m/min. The dynamic change and speed’s influence of stress fields and residual stress in machined layer is systematically analyzed. Some conclusions were drawn. With the cutting process development, the stress field converts to the stress state that crushing stress occupies a leading position. The magnitudes of crushing stress in all directions reduce with milling processes as the effect of Thermal-Mechanical-Coupled weakens; With the cutting speed increasing the magnitudes of crushing stress in all directions fluctuate near -950Mpa first, and then increase at the speed of 3000m/min; The residual pulling stress beneath the surface 0.03mm has been found and the magnitude increases with the cutting speed. A good agreement was obtained between predictions and experiments.

The Nonlinear Field Space Theory

NASA Astrophysics Data System (ADS)

Mielczarek, Jakub; Trześniewski, Tomasz

2016-08-01

In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the ;Principle of finiteness; of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.

A superstring field theory for supergravity

NASA Astrophysics Data System (ADS)

Reid-Edwards, R. A.; Riccombeni, D. A.

2017-09-01

A covariant closed superstring field theory, equivalent to classical tendimensional Type II supergravity, is presented. The defining conformal field theory is the ambitwistor string worldsheet theory of Mason and Skinner. This theory is known to reproduce the scattering amplitudes of Cachazo, He and Yuan in which the scattering equations play an important role and the string field theory naturally incorporates these results. We investigate the operator formalism description of the ambitwsitor string and propose an action for the string field theory of the bosonic and supersymmetric theories. The correct linearised gauge symmetries and spacetime actions are explicitly reproduced and evidence is given that the action is correct to all orders. The focus is on the NeveuSchwarz sector and the explicit description of tree level perturbation theory about flat spacetime. Application of the string field theory to general supergravity backgrounds and the inclusion of the Ramond sector are briefly discussed.

T -folds from Yang-Baxter deformations

NASA Astrophysics Data System (ADS)

Fernández-Melgarejo, José J.; Sakamoto, Jun-ichi; Sakatani, Yuho; Yoshida, Kentaroh

2017-12-01

Yang-Baxter (YB) deformations of type IIB string theory have been well studied from the viewpoint of classical integrability. Most of the works, however, are focused upon the local structure of the deformed geometries and the global structure still remains unclear. In this work, we reveal a non-geometric aspect of YB-deformed backgrounds as T -fold by explicitly showing the associated O( D, D; ℤ) T -duality monodromy. In particular, the appearance of an extra vector field in the generalized supergravity equations (GSE) leads to the non-geometric Q-flux. In addition, we study a particular solution of GSE that is obtained by a non-Abelian T-duality but cannot be expressed as a homogeneous YB deformation, and show that it can also be regarded as a T -fold. This result indicates that solutions of GSE should be non-geometric quite in general beyond the YB deformation.

Asymptotically free theory with scale invariant thermodynamics

NASA Astrophysics Data System (ADS)

Ferrari, Gabriel N.; Kneur, Jean-Loïc; Pinto, Marcus Benghi; Ramos, Rudnei O.

2017-12-01

A recently developed variational resummation technique, incorporating renormalization group properties consistently, has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework of approximations such as in the hard-thermal-loop resummed perturbation theory. This method is used in the present work to evaluate thermodynamical quantities within the two-dimensional nonlinear sigma model, which, apart from providing a technically simpler testing ground, shares some common features with Yang-Mills theories, like asymptotic freedom, trace anomaly and the nonperturbative generation of a mass gap. The present application confirms that nonperturbative results can be readily generated solely by considering the lowest-order (quasiparticle) contribution to the thermodynamic effective potential, when this quantity is required to be renormalization group invariant. We also show that when the next-to-leading correction from the method is accounted for, the results indicate convergence, apart from optimally preserving, within the approximations here considered, the sought-after scale invariance.

Experimental realization of the Yang-Baxter Equation via NMR interferometry.

PubMed

Vind, F Anvari; Foerster, A; Oliveira, I S; Sarthour, R S; Soares-Pinto, D O; Souza, A M; Roditi, I

2016-02-10

The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation.

Asymptotic Charges at Null Infinity in Any Dimension

NASA Astrophysics Data System (ADS)

Campoleoni, Andrea; Francia, Dario; Heissenberg, Carlo

2018-03-01

We analyse the conservation laws associated with large gauge transformations of massless fields in Minkowski space. Our aim is to highlight the interplay between boundary conditions and finiteness of the asymptotically conserved charges in any space-time dimension, both even and odd, greater than or equal to three. After discussing non-linear Yang-Mills theory and revisiting linearised gravity, our investigation extends to cover the infrared behaviour of bosonic massless quanta of any spin.

Towards weakly constrained double field theory

NASA Astrophysics Data System (ADS)

Lee, Kanghoon

2016-08-01

We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon) transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X-ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.

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.

New contributions to physics by Prof. C. N. Yang: 2009-2011

NASA Astrophysics Data System (ADS)

Ma, Zhong-Qi

2016-01-01

In a seminal paper of 1967, Professor Chen Ning Yang found the full solution of the one-dimensional Fermi gas with a repulsive delta function interaction by using the Bethe ansatz and group theory. This work with a brilliant discovery of the Yang-Baxter equation has been inspiring new developments in mathematical physics, statistical physics, and many-body physics. Based on experimental developments in simulating many-body physics of one-dimensional systems of ultracold atoms, during a period from 2009 to 2011, Prof. Yang published seven papers on the exact properties of the ground state of bosonic and fermionic atoms with the repulsive delta function interaction and a confined potential to one dimension. Here I would like to share my experience in doing research work fortunately under the direct supervision of Prof. Yang in that period.

New Contributions to Physics by Prof. C. N. Yang: 2009-2011

NASA Astrophysics Data System (ADS)

Ma, Zhong-Qi

In a seminal paper of 1967, Professor Chen Ning Yang found the full solution of the one-dimensional Fermi gas with a repulsive delta function interaction by using the Bethe ansatz and group theory. This work with a brilliant discovery of the Yang-Baxter equation has been inspiring new developments in mathematical physics, statistical physics, and many-body physics. Based on experimental developments in simulating many-body physics of one-dimensional systems of ultracold atoms, during a period from 2009 to 2011, Prof. Yang published seven papers on the exact properties of the ground state of bosonic and fermionic atoms with the repulsive delta function interaction and a confined potential to one dimension. Here I would like to share my experience in doing research work fortunately under the direct supervision of Prof. Yang in that period.

Scattering of massless particles: scalars, gluons and gravitons

NASA Astrophysics Data System (ADS)

Cachazo, Freddy; He, Song; Yuan, Ellis Ye

2014-07-01

In a recent note we presented a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimension. In this paper we show that a natural formulation also exists for a massless colored cubic scalar theory. In Yang-Mills, the formula is an integral over the space of n marked points on a sphere and has as integrand two factors. The first factor is a combination of Parke-Taylor-like terms dressed with U( N ) color structures while the second is a Pfaffian. The S-matrix of a U( N ) × U( Ñ ) cubic scalar theory is obtained by simply replacing the Pfaffian with a U( Ñ ) version of the previous U( N ) factor. Given that gravity amplitudes are obtained by replacing the U( N ) factor in Yang-Mills by a second Pfaffian, we are led to a natural color-kinematics correspondence. An expansion of the integrand of the scalar theory leads to sums over trivalent graphs and are directly related to the KLT matrix. Combining this and the Yang-Mills formula we find a connection to the BCJ color-kinematics duality as well as a new proof of the BCJ doubling property that gives rise to gravity amplitudes. We end by considering a special kinematic point where the partial amplitude simply counts the number of color-ordered planar trivalent trees, which equals a Catalan number. The scattering equations simplify dramatically and are equivalent to a special Y-system with solutions related to roots of Chebyshev polynomials. The sum of the integrand over the solutions gives rise to a representation of Catalan numbers in terms of eigenvectors and eigenvalues of the adjacency matrix of an A-type Dynkin diagram.

Automated Identification of Initial Storm Electrification and End-of-Storm Electrification Using Electric Field Mill Sensors

NASA Technical Reports Server (NTRS)

Maier, Launa M.; Huddleston, Lisa L.

2017-01-01

Kennedy Space Center (KSC) operations are located in a region which experiences one of the highest lightning densities across the United States. As a result, on average, KSC loses almost 30 minutes of operational availability each day for lightning sensitive activities. KSC is investigating using existing instrumentation and automated algorithms to improve the timeliness and accuracy of lightning warnings. Additionally, the automation routines will be warning on a grid to minimize under-warnings associated with not being located in the center of the warning area and over-warnings associated with encompassing too large an area. This study discusses utilization of electric field mill data to provide improved warning times. Specifically, this paper will demonstrate improved performance of an enveloping algorithm of the electric field mill data as compared with the electric field zero crossing to identify initial storm electrification. End-of-Storm-Oscillation (EOSO) identification algorithms will also be analyzed to identify performance improvement, if any, when compared with 30 minutes after the last lightning flash.

Nonlinear modes of the tensor Dirac equation and CPT violation

NASA Technical Reports Server (NTRS)

Reifler, Frank J.; Morris, Randall D.

1993-01-01

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.

Functional renormalization group approach to the Yang-Lee edge singularity

DOE PAGES

An, X.; Mesterházy, D.; Stephanov, M. A.

2016-07-08

Here, we determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean dimensions. We find very good agreement with high-temperature series data in d = 3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ϵ = 6 - d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O(∂more » 4) truncations of the scale-dependent effective action.« less

Functional renormalization group approach to the Yang-Lee edge singularity

DOE Office of Scientific and Technical Information (OSTI.GOV)

An, X.; Mesterházy, D.; Stephanov, M. A.

Here, we determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean dimensions. We find very good agreement with high-temperature series data in d = 3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ϵ = 6 - d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O(∂more » 4) truncations of the scale-dependent effective action.« less

Measurement of surface charges on the dielectric film based on field mills under the HVDC corona wire

NASA Astrophysics Data System (ADS)

Donglai, WANG; Tiebing, LU; Yuan, WANG; Bo, CHEN; Xuebao, LI

2018-05-01

The ion flow field on the ground is one of the significant parameters used to evaluate the electromagnetic environment of high voltage direct current (HVDC) power lines. HVDC lines may cross the greenhouses due to the restricted transmission corridors. Under the condition of ion flow field, the dielectric films on the greenhouses will be charged, and the electric fields in the greenhouses may exceed the limit value. Field mills are widely used to measure the ground-level direct current electric fields under the HVDC power lines. In this paper, the charge inversion method is applied to calculate the surface charges on the dielectric film according to the measured ground-level electric fields. The advantages of hiding the field mill probes in the ground are studied. The charge inversion algorithm is optimized in order to decrease the impact of measurement errors. Based on the experimental results, the surface charge distribution on a piece of quadrate dielectric film under a HVDC corona wire is studied. The enhanced effect of dielectric film on ground-level electric field is obviously weakened with the increase of film height. Compared with the total electric field strengths, the normal components of film-free electric fields at the corresponding film-placed positions have a higher effect on surface charge accumulation.

Supersymmetric extensions of K field theories

NASA Astrophysics Data System (ADS)

Adam, C.; Queiruga, J. M.; Sanchez-Guillen, J.; Wereszczynski, A.

2012-02-01

We review the recently developed supersymmetric extensions of field theories with non-standard kinetic terms (so-called K field theories) in two an three dimensions. Further, we study the issue of topological defect formation in these supersymmetric theories. Specifically, we find supersymmetric K field theories which support topological kinks in 1+1 dimensions as well as supersymmetric extensions of the baby Skyrme model for arbitrary nonnegative potentials in 2+1 dimensions.

Two-spectral Yang-Baxter operators in topological quantum computation

NASA Astrophysics Data System (ADS)

Sanchez, William F.

2011-05-01

One of the current trends in quantum computing is the application of algebraic topological methods in the design of new algorithms and quantum computers, giving rise to topological quantum computing. One of the tools used in it is the Yang-Baxter equation whose solutions are interpreted as universal quantum gates. Lately, more general Yang-Baxter equations have been investigated, making progress as two-spectral equations and Yang-Baxter systems. This paper intends to apply these new findings to the field of topological quantum computation, more specifically, the proposition of the two-spectral Yang-Baxter operators as universal quantum gates for 2 qubits and 2 qutrits systems, obtaining 4x4 and 9x9 matrices respectively, and further elaboration of the corresponding Hamiltonian by the use of computer algebra software Mathematica® and its Qucalc package. In addition, possible physical systems to which the Yang-Baxter operators obtained can be applied are considered. In the present work it is demonstrated the utility of the Yang-Baxter equation to generate universal quantum gates and the power of computer algebra to design them; it is expected that these mathematical studies contribute to the further development of quantum computers

Gauge engineering and propagators

NASA Astrophysics Data System (ADS)

Maas, Axel

2017-03-01

Beyond perturbation theory gauge-fixing becomes more involved due to the Gribov-Singer ambiguity: The appearance of additional gauge copies requires to define a procedure how to handle them. For the case of Landau gauge the structure and properties of these additional gauge copies will be investigated. Based on these properties gauge conditions are constructed to account for these gauge copies. The dependence of the propagators on the choice of these complete gauge-fixings will then be investigated using lattice gauge theory for Yang-Mills theory. It is found that the implications for the infrared, and to some extent mid-momentum behavior, can be substantial. In going beyond the Yang-Mills case it turns out that the influence of matter can generally not be neglected. This will be briefly discussed for various types of matter.

Torus Knot Polynomials and Susy Wilson Loops

NASA Astrophysics Data System (ADS)

Giasemidis, Georgios; Tierz, Miguel

2014-12-01

We give, using an explicit expression obtained in (Jones V, Ann Math 126:335, 1987), a basic hypergeometric representation of the HOMFLY polynomial of ( n, m) torus knots, and present a number of equivalent expressions, all related by Heine's transformations. Using this result, the symmetry and the leading polynomial at large N are explicit. We show the latter to be the Wilson loop of 2d Yang-Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang-Mills theory, which is known to give averages of Wilson loops in = 4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones-Rosso representation in terms of q-harmonic oscillators.

Spin connection as Lorentz gauge field in Fairchild’s action

NASA Astrophysics Data System (ADS)

Cianfrani, Francesco; Montani, Giovanni; Scopelliti, Vincenzo

2016-06-01

We propose a modified gravitational action containing besides the Einstein-Cartan term some quadratic contributions resembling the Yang-Mills Lagrangian for the Lorentz spin connections. We outline how a propagating torsion arises and we solve explicitly the linearized equations of motion on a Minkowski background. We identify among torsion components six degrees of freedom: one is carried by a pseudo-scalar particle, five by a tachyon field. By adding spinor fields and neglecting backreaction on the geometry, we point out how only the pseudo-scalar particle couples directly with fermions, but the resulting coupling constant is suppressed by the ratio between fermion and Planck masses. Including backreaction, we demonstrate how the tachyon field provides causality violation in the matter sector, via an interaction mediated by gravitational waves.

Field testing of fugitive dust control techniques at a uranium mill tailings pile - 1982 Field Test, Gas Hills, Wyoming.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Elmore, M.R.; Hartley, J.N.

A field test was conducted on a uranium tailings pile to evaluate the effectiveness of 15 chemical stabilizers for control of fugitive dust from uranium mill tailings. A tailings pile at the Federal American Partners (FAP) Uranium Mill, Gas Hills, Wyoming, was used for the field test. Preliminary laboratory tests using a wing tunnel were conducted to select the more promising stabilizers for field testing. Fourteen of the chemical stabilizers were applied with a field spray system pulled behind a tractor; one--Hydro Mulch--was applied with a hydroseeder. A portable weather station and data logger were installed to record the weathermore » conditions at the test site. After 1 year of monitoring (including three site visits), all of the stabilizers have degraded to some degree; but those applied at the manufacturers' recommended rate are still somewhat effective in reducing fugitive emissions. The following synthetic polymer emulsions appear to be the more effective stabilizers: Wallpol 40-133 from Reichold Chemicals, SP-400 from Johnson and March Corporation, and CPB-12 from Wen Don Corporation. Installed costs for the test plots ranged from $8400 to $11,300/ha; this range results from differences in stabilizer costs. Large-scale stabilization costs of the test materials are expected to range from $680 to $3600/ha based on FAP experience. Evaluation of the chemical stabilizers will continue for approximately 1 year. 2 references, 33 figures, 22 tables.« less

Prescriptive unitarity

DOE PAGES

Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav

2017-06-12

We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in the case of planar, maximally supersymmetric Yang-Mills theory (SYM), where we construct closed-form representations of all (n-point N k MHV) scattering amplitudes through three loops. The prescriptive approach contrasts with the ordinary description of unitarity-based methods by avoiding any need for linear algebra to determine integrand coefficients. We describe this approach in general terms as it should have applications to many quantum field theories, including those withoutmore » planarity, supersymmetry, or massless spectra defined in any number of dimensions.« less

(In)dependence of 𝜃 in the Higgs regime without axions

NASA Astrophysics Data System (ADS)

Shifman, Mikhail; Vainshtein, Arkady

2017-05-01

We revisit the issue of the vacuum angle 𝜃 dependence in weakly coupled (Higgsed) Yang-Mills theories. Two most popular mechanisms for eliminating physical 𝜃 dependence are massless quarks and axions. Anselm and Johansen noted that the vacuum angle 𝜃EW, associated with the electroweak SU(2) in the Glashow-Weinberg-Salam model (Standard Model, SM), is unobservable although all fermion fields obtain masses through Higgsing and there is no axion. We generalize this idea to a broad class of Higgsed Yang-Mills theories. In the second part, we consider the consequences of Grand Unification. We start from a unifying group, e.g. SU(5), at a high ultraviolet scale and evolve the theory down within the Wilson procedure. If on the way to infrared the unifying group is broken down into a few factors, all factor groups inherit one and the same 𝜃 angle — that of the unifying group. We show that embedding the SM in SU(5) drastically changes the Anselm-Johansen conclusion: the electroweak vacuum angle 𝜃EW, equal to 𝜃QCD becomes in principle observable in ΔB = ΔL = ±1 processes. We also note in passing that if the axion mechanism is set up above the unification scale, we have one and the same axion in the electroweak theory and QCD, and their impacts are interdependent.

Nonminimal couplings, gravitational waves, and torsion in Horndeski's theory

NASA Astrophysics Data System (ADS)

Barrientos, José; Cordonier-Tello, Fabrizio; Izaurieta, Fernando; Medina, Perla; Narbona, Daniela; Rodríguez, Eduardo; Valdivia, Omar

2017-10-01

The Horndeski Lagrangian brings together all possible interactions between gravity and a scalar field that yield second-order field equations in four-dimensional spacetime. As originally proposed, it only addresses phenomenology without torsion, which is a non-Riemannian feature of geometry. Since torsion can potentially affect interesting phenomena such as gravitational waves and early universe inflation, in this paper we allow torsion to exist and propagate within the Horndeski framework. To achieve this goal, we cast the Horndeski Lagrangian in Cartan's first-order formalism and introduce wave operators designed to act covariantly on p -form fields that carry Lorentz indices. We find that nonminimal couplings and second-order derivatives of the scalar field in the Lagrangian are indeed generic sources of torsion. Metric perturbations couple to the background torsion, and new torsional modes appear. These may be detected via gravitational waves but not through Yang-Mills gauge bosons.

Expression Profiling of Transcriptome and Its Associated Disease Risk in Yang Deficiency Constitution of Healthy Subjects

PubMed Central

Yu, Ruoxi; Yang, Yin; Han, Yuanyuan; Hou, Pengwei; Li, Yingshuai; Li, Siqi

2016-01-01

Objectives. Differences among healthy subjects and associated disease risks are of substantial interest in clinical medicine. According to the theory of “constitution-disease correlation” in traditional Chinese medicine, we try to find out if there is any connection between intolerance of cold in Yang deficiency constitution and molecular evidence and if there is any gene expression basis in specific disorders. Methods. Peripheral blood mononuclear cells were collected from Chinese Han individuals with Yang deficiency constitution (n = 20) and balanced constitution (n = 8) (aged 18–28) and global gene expression profiles were determined between them using the Affymetrix HG-U133 Plus 2.0 array. Results. The results showed that when the fold change was ≥1.2 and q ≤ 0.05, 909 genes were upregulated in the Yang deficiency constitution, while 1189 genes were downregulated. According to our research differential genes found in Yang deficiency constitution were usually related to lower immunity, metabolic disorders, and cancer tendency. Conclusion. Gene expression disturbance exists in Yang deficiency constitution, which corresponds to the concept of constitution and gene classification. It also suggests people with Yang deficiency constitution are susceptible to autoimmune diseases, enteritis, arthritis, metabolism disorders, and cancer, which provides molecular evidence for the theory of “constitution-disease correlation.” PMID:28484499

Conformal field theories from deformations of theories with Wn symmetry

NASA Astrophysics Data System (ADS)

Babaro, Juan Pablo; Giribet, Gaston; Ranjbar, Arash

2016-10-01

We construct a set of nonrational conformal field theories that consist of deformations of Toda field theory for s l (n ). In addition to preserving conformal invariance, the theories may still exhibit a remnant infinite-dimensional affine symmetry. The case n =3 is used to illustrate this phenomenon, together with further deformations that yield enhanced Kac-Moody symmetry algebras. For generic n we compute N -point correlation functions on the Riemann sphere and show that these can be expressed in terms of s l (n ) Toda field theory ((N -2 )n +2 ) -point correlation functions.

Development of an electromechanical principle for wet and dry milling

NASA Astrophysics Data System (ADS)

Halbedel, Bernd; Kazak, Oleg

2018-05-01

The paper presents a novel electromechanical principle for wet and dry milling of different materials, in which the milling beads are moved under a time- and local-variable magnetic field. A possibility to optimize the milling process in such a milling machine by simulation of the vector gradient distribution of the electromagnetic field in the process room is presented. The mathematical model and simulation methods based on standard software packages are worked out. The results of numerical simulations and experimental measurements of the electromagnetic field in the working chamber of a developed and manufactured laboratory plant correlate well with each other. Using the obtained operating parameters, dry milling experiments with crushed cement clinker and wet milling experiments of organic agents in the laboratory plant are performed and the results are discussed here.

The delayed theory of fields

NASA Astrophysics Data System (ADS)

Poormohammadi, Jaber; Rezagholizadeh, Hessam

The idea of action immediate propagation has been in physicists' mind from the beginning, until Faraday raised the idea of delayed propagation. Using this idea and the delayed theory of fields, we face consequences which can be interesting for anyone who has learned physics. We can mention non-equivalency between stationary frames and moving frames, dependency of field to medium, different velocity barriers for different mediums and non-equivalency of inertial reference frames are among these consequences. By designing an experiment we can challenge this theory and its consequences. All of these sections processed in the article titled ''The delayed theory of fields''.

Ostrogradsky in theories with multiple fields

DOE PAGES

de Rham, Claudia; Matas, Andrew

2016-06-23

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamicalmore » or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.« less

Ostrogradsky in theories with multiple fields

NASA Astrophysics Data System (ADS)

de Rham, Claudia; Matas, Andrew

2016-06-01

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.

Ostrogradsky in theories with multiple fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

de Rham, Claudia; Matas, Andrew

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamicalmore » or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.« less

Non-Abelian clouds around Reissner-Nordström black holes: The existence line

NASA Astrophysics Data System (ADS)

Radu, Eugen; Tchrakian, D. H.; Yang, Yisong

2016-06-01

A known feature of electrically charged Reissner-Nordström-anti-de Sitter planar black holes is that they can become unstable when considered as solutions of Einstein-Yang-Mills theory. The mechanism for this is that the linearized Yang-Mills equations in the background of the Reissner-Nordström (RN) black holes possess a normalizable zero mode, resulting in non-Abelian (nA) magnetic clouds near the horizon. In this work we show that the same pattern may occur also for asymptotically flat RN black holes. Different from the anti-de Sitter case, in the Minkowskian background the prerequisites for the existence of the nA clouds are (i) a large enough gauge group, and (ii) the presence of some extra interaction terms in the matter Lagrangian. To illustrate this mechanism we present two specific examples, one in four- and the other in five-dimensional asymptotically flat spacetime. In the first case, we augment the usual S U (3 ) Yang-Mills Lagrangian with a higher-order (quartic) curvature term, while for the second one we add the Chern-Simons density to the S O (6 ) Yang-Mills system. In both cases, an Abelian gauge symmetry is spontaneously broken near a RN black hole horizon with the appearance of a condensate of nA gauge fields. In addition to these two examples, we review the corresponding picture for anti-de Sitter black holes. All these solutions are studied both analytically and numerically, existence proofs being provided for nA clouds in the background of RN black holes. The proofs use shooting techniques which are suggested by and in turn offer insights for our numerical methods. They indicate that, for a black hole of given mass, appropriate electric charge values are required to ensure the existence of solutions interpolating desired boundary behavior at the horizons and spatial infinity.

The Theory of High Energy Collision Processes - Final Report DOE/ER/40158-1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Tai, T.

In 1984, DOE awarded Harvard University a new Grant DE-FG02-84ER40158 to continue their support of Tai Tsun Wu as Principal Investigator of research on the theory of high energy collision processes. This Grant was renewed and remained active continuously from June 1, 1984 through November 30, 2007. Topics of interest during the 23-year duration of this Grant include: the theory and phenomenology of collision and production processes at ever higher energies; helicity methods of QED and QCD; neutrino oscillations and masses; Yang-Mills gauge theory; Beamstrahlung; Fermi pseudopotentials; magnetic monopoles and dyons; cosmology; classical confinement; mass relations; Bose-Einstein condensation; and large-momentum-transfermore » scattering processes. This Final Report describes the research carried out on Grant DE-FG02-84ER40158 for the period June 1, 1984 through November 30, 2007. Two books resulted from this project and a total of 125 publications.« less

Gauge assisted quadratic gravity: A framework for UV complete quantum gravity

NASA Astrophysics Data System (ADS)

Donoghue, John F.; Menezes, Gabriel

2018-06-01

We discuss a variation of quadratic gravity in which the gravitational interaction remains weakly coupled at all energies, but is assisted by a Yang-Mills gauge theory which becomes strong at the Planck scale. The Yang-Mills interaction is used to induce the usual Einstein-Hilbert term, which was taken to be small or absent in the original action. We study the spin-two propagator in detail, with a focus on the high mass resonance which is shifted off the real axis by the coupling to real decay channels. We calculate scattering in the J =2 partial wave and show explicitly that unitarity is satisfied. The theory will in general have a large cosmological constant and we study possible solutions to this, including a unimodular version of the theory. Overall, the theory satisfies our present tests for being a ultraviolet completion of quantum gravity.

Large N phase transitions and the fate of small Schwarzschild-AdS black holes

NASA Astrophysics Data System (ADS)

Yaffe, Laurence G.

2018-01-01

Sufficiently small Schwarzschild-AdS black holes in asymptotically global AdS5×S5 spacetime are known to become dynamically unstable toward deformation of the internal S5 geometry. The resulting evolution of such an unstable black hole is related, via holography, to the dynamics of supercooled plasma which has reached the limit of metastability in maximally supersymmetric large-N Yang-Mills theory on R ×S3. Puzzles related to the resulting dynamical evolution are discussed, with a key issue involving differences between the large-N limit in the dual field theory and typical large volume thermodynamic limits.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pawellek, Michael

Using anti-de Sitter-space/conformal-field-theory correspondence we derive from the folded spinning string ordinary differential equations for the anomalous dimension of the dual N=4 super Yang-Mills theory twist-two operators at strong coupling. We show that for large spin the asymptotic solutions have the Gribov-Lipatov reciprocity property. To obtain this result we use a hidden modular invariance of the energy-spin relation of the folded spinning string. Furthermore, we identify the Moch-Vermaseren-Vogt relations, which were first recognized in plain QCD calculations, as the recurrence relations of the asymptotic series ansatz.

Holography and off-center collisions of localized shock waves

DOE PAGES

Chesler, Paul M.; Yaffe, Laurence G.

2015-10-12

Using numerical holography, we study the collision, at non-zero impact parameter, of bounded, localized distributions of energy density chosen to mimic relativistic heavy ion collisions, in strongly coupled N=4 supersymmetric Yang-Mills theory. Both longitudinal and transverse dynamics in the dual field theory are properly described. Using the gravitational description, we solve 5D Einstein equations with no dimensionality reducing symmetry restrictions to find the asymptotically anti-de Sitter spacetime geometry. Here, the implications of our results on the understanding of early stages of heavy ion collisions, including the development of transverse radial flow, are discussed.

Instantons and Large N

NASA Astrophysics Data System (ADS)

Mariño, Marcos

2015-09-01

Preface; Part I. Instantons: 1. Instantons in quantum mechanics; 2. Unstable vacua in quantum field theory; 3. Large order behavior and Borel summability; 4. Non-perturbative aspects of Yang-Mills theories; 5. Instantons and fermions; Part II. Large N: 6. Sigma models at large N; 7. The 1=N expansion in QCD; 8. Matrix models and matrix quantum mechanics at large N; 9. Large N QCD in two dimensions; 10. Instantons at large N; Appendix A. Harmonic analysis on S3; Appendix B. Heat kernel and zeta functions; Appendix C. Effective action for large N sigma models; References; Author index; Subject index.

Quantum supergroups and solutions of the Yang-Baxter equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bracken, A.J.; Gould, M.D.; Zhang, R.B.

1990-05-10

A method is developed for systematically constructing trigonometric and rational solutions of the Yang-Baxter equation using the representation theory of quantum supergroups. New quantum R-matrices are obtained by applying the method to the vector representations of quantum osp(1/2) and gl(m/n).

Nonperturbative light-front Hamiltonian methods

NASA Astrophysics Data System (ADS)

Hiller, J. R.

2016-09-01

We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, ϕ4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

Combinatorial quantization of the Hamiltonian Chern-Simons theory II

NASA Astrophysics Data System (ADS)

Alekseev, Anton Yu.; Grosse, Harald; Schomerus, Volker

1996-01-01

This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in [1]. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observables A CS of the Chern Simons model. It is a *-algebra of “functions on the quantum moduli space of flat connections” and comes equipped with a positive functional ω (“integration”). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly [2], the algebra A CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group.

Lee-Yang zero analysis for the study of QCD phase structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ejiri, Shinji

2006-03-01

We comment on the Lee-Yang zero analysis for the study of the phase structure of QCD at high temperature and baryon number density by Monte-Carlo simulations. We find that the sign problem for nonzero density QCD induces a serious problem in the finite volume scaling analysis of the Lee-Yang zeros for the investigation of the order of the phase transition. If the sign problem occurs at large volume, the Lee-Yang zeros will always approach the real axis of the complex parameter plane in the thermodynamic limit. This implies that a scaling behavior which would suggest a crossover transition will notmore » be obtained. To clarify this problem, we discuss the Lee-Yang zero analysis for SU(3) pure gauge theory as a simple example without the sign problem, and then consider the case of nonzero density QCD. It is suggested that the distribution of the Lee-Yang zeros in the complex parameter space obtained by each simulation could be more important information for the investigation of the critical endpoint in the (T,{mu}{sub q}) plane than the finite volume scaling behavior.« less

Radiation and the classical double copy for color charges

NASA Astrophysics Data System (ADS)

Goldberger, Walter D.; Ridgway, Alexander K.

2017-06-01

We construct perturbative classical solutions of the Yang-Mills equations coupled to dynamical point particles carrying color charge. By applying a set of color to kinematics replacement rules first introduced by Bern, Carrasco and Johansson, these are shown to generate solutions of d -dimensional dilaton gravity, which we also explicitly construct. Agreement between the gravity result and the gauge theory double copy implies a correspondence between non-Abelian particles and gravitating sources with dilaton charge. When the color sources are highly relativistic, dilaton exchange decouples, and the solutions we obtain match those of pure gravity. We comment on possible implications of our findings to the calculation of gravitational waveforms in astrophysical black hole collisions, directly from computationally simpler gluon radiation in Yang-Mills theory.

Effective Field Theory on Manifolds with Boundary

NASA Astrophysics Data System (ADS)

Albert, Benjamin I.

In the monograph Renormalization and Effective Field Theory, Costello made two major advances in rigorous quantum field theory. Firstly, he gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. Secondly, he gave a rigorous formulation of quantum gauge theory within effective field theory that makes use of the BV formalism. In this work, we extend Costello's renormalization procedure to a class of manifolds with boundary and make preliminary steps towards extending his formulation of gauge theory to manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.

Particle yields from numerical simulations

NASA Astrophysics Data System (ADS)

Homor, Marietta M.; Jakovác, Antal

2018-04-01

In this paper we use numerical field theoretical simulations to calculate particle yields. We demonstrate that in the model of local particle creation the deviation from the pure exponential distribution is natural even in equilibrium, and an approximate Tsallis-Pareto-like distribution function can be well fitted to the calculated yields, in accordance with the experimental observations. We present numerical simulations in the classical Φ4 model as well as in the SU(3) quantum Yang-Mills theory to clarify this issue.

Supermultiplet of β-deformations from twistors

NASA Astrophysics Data System (ADS)

Milián, Segundo P.

2017-09-01

We consider the supermultiplet of linearized beta-deformation of 𝒩 = 4 super-Yang-Mills (SYM). It was previously studied on the gravitational side. We study the supermultiplet of beta-deformations on the field theory side and we compare two finite-dimensional representations of psl(4|4,R) algebra. We show that they are related by an intertwining operator. We develop a twistor-based approach which could be useful for studying other finite-dimensional and nonunitary representations in AdS/CFT correspondence.

Group field theory with noncommutative metric variables.

PubMed

Baratin, Aristide; Oriti, Daniele

2010-11-26

We introduce a dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. We give a new definition of the Barrett-Crane model for gravity by imposing the simplicity constraints directly at the level of the group field theory action.

Hamilton-Jacobi theory in multisymplectic classical field theories

NASA Astrophysics Data System (ADS)

de León, Manuel; Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso; Vilariño, Silvia

2017-09-01

The geometric framework for the Hamilton-Jacobi theory developed in the studies of Cariñena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Cariñena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 (2015)], and de León et al. [Variations, Geometry and Physics (Nova Science Publishers, New York, 2009)] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.

Pure field theories and MACSYMA algorithms

NASA Technical Reports Server (NTRS)

Ament, W. S.

1977-01-01

A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.

Continuum modes of nonlocal field theories

NASA Astrophysics Data System (ADS)

Saravani, Mehdi

2018-04-01

We study a class of nonlocal Lorentzian quantum field theories, where the d’Alembertian operator \\Box is replaced by a non-analytic function of the d’Alembertian, f(\\Box) . This is inspired by the causal set program where such an evolution arises as the continuum limit of a wave equation on causal sets. The spectrum of these theories contains a continuum of massive excitations. This is perhaps the most important feature which leads to distinct/interesting phenomenology. In this paper, we study properties of the continuum massive modes in depth. We derive the path integral formulation of these theories. Meanwhile, this derivation introduces a dual picture in terms of local fields which clearly shows how continuum massive modes of the nonlocal field interact. As an example, we calculate the leading order modification to the Casimir force of a pair of parallel planes. The dual picture formulation opens the way for future developments in the study of nonlocal field theories using tools already available in local quantum field theories.

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

Double field theory at order α'

NASA Astrophysics Data System (ADS)

Hohm, Olaf; Zwiebach, Barton

2014-11-01

We investigate α' corrections of bosonic strings in the framework of double field theory. The previously introduced "doubled α'-geometry" gives α'-deformed gauge transformations arising in the Green-Schwarz anomaly cancellation mechanism but does not apply to bosonic strings. These require a different deformation of the duality-covariantized Courant bracket which governs the gauge structure. This is revealed by examining the α' corrections in the gauge algebra of closed string field theory. We construct a four-derivative cubic double field theory action invariant under the deformed gauge transformations, giving a first glimpse of the gauge principle underlying bosonic string α' corrections. The usual metric and b-field are related to the duality covariant fields by non-covariant field redefinitions.

Vafa-Witten theorem and Lee-Yang singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguado, M.; Asorey, M.

2009-12-15

We prove the analyticity of the finite volume QCD partition function for complex values of the {theta}-vacuum parameter. The absence of singularities different from Lee-Yang zeros only permits and cusp singularities in the vacuum energy density and never or cusps. This fact together with the Vafa-Witten diamagnetic inequality implies the vanishing of the density of Lee-Yang zeros at {theta}=0 and has an important consequence: the absence of a first order phase transition at {theta}=0. The result provides a key missing link in the Vafa-Witten proof of parity symmetry conservation in vectorlike gauge theories and follows from renormalizability, unitarity, positivity, andmore » existence of Bogomol'nyi-Prasad-Sommerfield bounds. Generalizations of this theorem to other physical systems are also discussed, with particular interest focused on the nonlinear CP{sup N} sigma model.« less

Dynamics of polymers: A mean-field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fredrickson, Glenn H.; Materials Research Laboratory, University of California, Santa Barbara, California 93106; Department of Materials, University of California, Santa Barbara, California 93106

2014-02-28

We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose (MSR) type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field ρ and a conjugate MSR response field ϕ, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamicsmore » involving hybrid particle-field simulation techniques such as the single-chain in mean-field method.« less

Quantum field theory with infinite component local fields as an alternative to the string theories

NASA Astrophysics Data System (ADS)

Krasnikov, N. V.

1987-09-01

We show that the introduction of the infinite component local fields with higher-order derivatives in the interaction makes the theory completely ultraviolet finite. For the γ5-anomalous theories the introduction of the infinite component field makes the theory renormalizable or even superrenormalizable. I am indebted to J. Ambjōrn, P. Di Vecchia, H.B. Nielsen and L. Rozhansky for useful discussions. It is a pleasure to thank the Niels Bohr Institute (Copenhagen) where this work was completed for kind hospitality.

Classical Field Theory and the Stress-Energy Tensor

NASA Astrophysics Data System (ADS)

Swanson, Mark S.

2015-09-01

This book is a concise introduction to the key concepts of classical field theory for beginning graduate students and advanced undergraduate students who wish to study the unifying structures and physical insights provided by classical field theory without dealing with the additional complication of quantization. In that regard, there are many important aspects of field theory that can be understood without quantizing the fields. These include the action formulation, Galilean and relativistic invariance, traveling and standing waves, spin angular momentum, gauge invariance, subsidiary conditions, fluctuations, spinor and vector fields, conservation laws and symmetries, and the Higgs mechanism, all of which are often treated briefly in a course on quantum field theory. The variational form of classical mechanics and continuum field theory are both developed in the time-honored graduate level text by Goldstein et al (2001). An introduction to classical field theory from a somewhat different perspective is available in Soper (2008). Basic classical field theory is often treated in books on quantum field theory. Two excellent texts where this is done are Greiner and Reinhardt (1996) and Peskin and Schroeder (1995). Green's function techniques are presented in Arfken et al (2013).

Modeling the milling tool wear by using an evolutionary SVM-based model from milling runs experimental data

NASA Astrophysics Data System (ADS)

Nieto, Paulino José García; García-Gonzalo, Esperanza; Vilán, José Antonio Vilán; Robleda, Abraham Segade

2015-12-01

The main aim of this research work is to build a new practical hybrid regression model to predict the milling tool wear in a regular cut as well as entry cut and exit cut of a milling tool. The model was based on Particle Swarm Optimization (PSO) in combination with support vector machines (SVMs). This optimization mechanism involved kernel parameter setting in the SVM training procedure, which significantly influences the regression accuracy. Bearing this in mind, a PSO-SVM-based model, which is based on the statistical learning theory, was successfully used here to predict the milling tool flank wear (output variable) as a function of the following input variables: the time duration of experiment, depth of cut, feed, type of material, etc. To accomplish the objective of this study, the experimental dataset represents experiments from runs on a milling machine under various operating conditions. In this way, data sampled by three different types of sensors (acoustic emission sensor, vibration sensor and current sensor) were acquired at several positions. A second aim is to determine the factors with the greatest bearing on the milling tool flank wear with a view to proposing milling machine's improvements. Firstly, this hybrid PSO-SVM-based regression model captures the main perception of statistical learning theory in order to obtain a good prediction of the dependence among the flank wear (output variable) and input variables (time, depth of cut, feed, etc.). Indeed, regression with optimal hyperparameters was performed and a determination coefficient of 0.95 was obtained. The agreement of this model with experimental data confirmed its good performance. Secondly, the main advantages of this PSO-SVM-based model are its capacity to produce a simple, easy-to-interpret model, its ability to estimate the contributions of the input variables, and its computational efficiency. Finally, the main conclusions of this study are exposed.

Uranium Mill Tailings Remedial Action Project Safety Advancement Field Effort (SAFE) Program

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1994-02-01

In 1992, the Uranium Mill Tailings Remedial Action (UMTRA) Project experienced several health and safety related incidents at active remediation project sites. As a result, the U.S. Department of Energy (DOE) directed the Technical Assistance Contractor (TAC) to establish a program increasing the DOE`s overall presence at operational remediation sites to identify and minimize risks in operations to the fullest extent possible (Attachments A and B). In response, the TAC, in cooperation with the DOE and the Remedial Action Contractor (RAC), developed the Safety Advancement Field Effort (SAFE) Program.

Quantum Field Theory in (0 + 1) Dimensions

ERIC Educational Resources Information Center

Boozer, A. D.

2007-01-01

We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…

Toward a proof of Montonen-Olive duality via multiple M2-branes

NASA Astrophysics Data System (ADS)

Hashimoto, Koji; Tai, Ta-Sheng; Terashima, Seiji

2009-04-01

We derive 4-dimensional Script N = 4 U(N) supersymmetric Yang-Mills theory from a 3-dimensional Chern-Simons-matter theory with product gauge group (U(N))2n. The latter describes M2-branes probing an orbifold where a torus emerges in a scaling limit. It is expected that the SL(2,Z) duality of the 4-dimensional Yang-Mills theory will be shown in M-theory point of view since it is trivially realized as modular transformations of the torus. Indeed, starting from one single Chern-Simons-matter theory, we find infinitely many equivalent 4-dimensional theories differing up to T-transformation of the SL(2,Z) redefinition of the gauge coupling τ = θ/2π + 4πi/g2 and a parity transformation in 4 dimensions. Although S-transformation can not be shown in our work, it is important that a part of the SL(2,Z) transformation is realized via the M2-brane action. Thus we think our work can be a step toward a proof of Montonen-Olive duality via M2-branes.

Democratic Superstring Field Theory and Its Gauge Fixing

NASA Astrophysics Data System (ADS)

Kroyter, M.

This work is my contribution to the proceedings of the conference``SFT2010 -- the third international conference on string field theory and related topics'' and it reflects my talk there, which described the democratic string field theory and its gauge fixing. The democratic string field theory is the only fully RNS string field theory to date. It lives in the large Hilbert space and includes all picture numbers. Picture changing amounts in this formalism to a gauge transformation. We describe the theory and its properties and show that when partially gauge fixed it can be reduced to the modified theory and to the non-polynomial theory. In the latter case we can even include the Ramond sector in the picture-fixed action. We also show that another partial gauge-fixing leads to a new consistent string field theory at picture number -1.

Dark SU (N ) glueball stars on fluid branes

NASA Astrophysics Data System (ADS)

da Rocha, Roldão

2017-06-01

The glueball dark matter, in the pure SU (N ) Yang-Mills theory, engenders dark SU (N ) stars that comprise self-gravitating compact configurations of scalar glueball fields. Corrections to the highest frequency of gravitational wave radiation emitted by dark SU (N ) star mergers on a fluid brane with variable tension, implemented by the minimal geometric deformation, are derived, and their consequences are analyzed. Hence, dark SU (N ) star mergers on a fluid braneworld are shown to be better detectable by the LIGO and the eLISA experiments.

Semi-abelian Z-theory: NLSM+ ϕ 3 from the open string

NASA Astrophysics Data System (ADS)

Carrasco, John Joseph M.; Mafra, Carlos R.; Schlotterer, Oliver

2017-08-01

We continue our investigation of Z-theory, the second double-copy component of open-string tree-level interactions besides super-Yang-Mills (sYM). We show that the amplitudes of the extended non-linear sigma model (NLSM) recently considered by Cachazo, Cha, and Mizera are reproduced by the leading α '-order of Z-theory amplitudes in the semi-abelian case. The extension refers to a coupling of NLSM pions to bi-adjoint scalars, and the semi-abelian case involves to a partial symmetrization over one of the color orderings that characterize the Z-theory amplitudes. Alternatively, the partial symmetrization corresponds to a mixed interaction among abelian and non-abelian states in the underlying open-superstring amplitude. We simplify these permutation sums via monodromy relations which greatly increase the efficiency in extracting the α '-expansion of these amplitudes. Their α '-corrections encode higher-derivative interactions between NLSM pions and bi-colored scalars all of which obey the duality between color and kinematics. Through double-copy, these results can be used to generate the predictions of supersymmetric Dirac-Born-Infeld-Volkov-Akulov theory coupled with sYM as well as a complete tower of higher-order α '-corrections.

GL/sub 3/-invariant solutions of the Yang-Baxter equation and associated quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kulish, P.P.; Reshetikhin, N.Yu.

1987-05-20

The authors investigate the GL/sub 3/-invariant finite-dimensional solutions of the Yang-Baxter equation acting in the tensor product of two irreducible representations of the GL/sub 3/ group. Relationships obtained for the transfer matrices demonstrate the link between representation theory and the Bethe ansatz in GL/sub 3/-invariant models. Some examples of quantum and classical integrable systems associated with GL/sub 3/-invariant solutions of the Yang-Baxter equation are given.

Yang Monopoles and Emergent Three-Dimensional Topological Defects in Interacting Bosons

NASA Astrophysics Data System (ADS)

Yan, Yangqian; Zhou, Qi

2018-06-01

The Yang monopole as a zero-dimensional topological defect has been well established in multiple fields in physics. However, it remains an intriguing question to understand the interaction effects on Yang monopoles. Here, we show that the collective motion of many interacting bosons gives rise to exotic topological defects that are distinct from Yang monopoles seen by a single particle. Whereas interactions may distribute Yang monopoles in the parameter space or glue them to a single giant one of multiple charges, three-dimensional topological defects also arise from continuous manifolds of degenerate many-body eigenstates. Their projections in lower dimensions lead to knotted nodal lines and nodal rings. Our results suggest that ultracold bosonic atoms can be used to create emergent topological defects and directly measure topological invariants that are not easy to access in solids.

Variations on the seventh route to relativity

NASA Astrophysics Data System (ADS)

Anderson, Edward

2003-11-01

Wheeler asked how one might derive the Einstein-Hamilton-Jacobi equation from plausible first principles without any use of the Einstein field equations themselves. In addition to Hojman, Kuchař and Teitelboim’s “seventh route to relativity” partial answer to this, there is now a “3-space” partial answer due to Barbour, Foster and Ó Murchadha (BFÓ) which principally differs in that general covariance is no longer presupposed. BFÓ’s formulation of the 3-space approach is based on best-matched actions such as the lapse-eliminated Baierlein-Sharp-Wheeler (BSW) action of general relativity (GR). These give rise to several branches of gravitational theories including GR on superspace and a theory of gravity on conformal superspace. This paper investigates the 3-space approach further, motivated both by the hierarchies of increasingly well-defined and weakened simplicity postulates present in all routes to relativity, and by the requirement that all the known fundamental matter fields be included. We further the study of configuration spaces of gravity-matter systems upon which BFÓ’s formulation leans. We note that in further developments the lapse-eliminated BSW actions used by BFÓ become impractical and require generalization. We circumvent many of these problems by the equivalent use of lapse-uneliminated actions, which furthermore permit us to interpret BFÓ’s formulation within Kuchař’s generally covariant hypersurface framework. This viewpoint provides alternative reasons to BFÓ’s as to why the inclusion of bosonic fields in the 3-space approach gives rise to minimally coupled scalar fields, electromagnetism and Yang-Mills theory. This viewpoint also permits us to quickly exhibit further GR-matter theories admitted by the 3-space formulation. In particular, we show that the spin-1/2 fermions of the theories of Dirac, Maxwell-Dirac and Yang-Mills-Dirac, all coupled to GR, are admitted by the generalized 3-space formulation we present

Mass inflation and chaotic behaviour inside hairy black holes

NASA Astrophysics Data System (ADS)

Breitenlohner, Peter; Lavrelashvili, George; Maison, Dieter

1998-07-01

We analyze the interior geometry of static, spherically symmetric black holes of the Einstein-Yang-Mills-Higgs theory. Generically the solutions exhibit a behaviour that may be described as ``mass inflation'', although with a remarkable difference between the cases with and without a Higgs field. Without Higgs field the YM field induces a kind of cyclic behaviour leading to repeated cycles of mass inflation - taking the form of violent explosions - interrupted by quiescent periods and subsequent approaches to an almost Cauchy horizon. With the Higgs field no such cycles occur in the asymptotic behaviour. In addition there are non-generic families with a Schwarzschild and a Reissner-Nordstrøm type singularity at r=0, respectively.

Quantum Field Theory Approach to Condensed Matter Physics

NASA Astrophysics Data System (ADS)

Marino, Eduardo C.

2017-09-01

Preface; Part I. Condensed Matter Physics: 1. Independent electrons and static crystals; 2. Vibrating crystals; 3. Interacting electrons; 4. Interactions in action; Part II. Quantum Field Theory: 5. Functional formulation of quantum field theory; 6. Quantum fields in action; 7. Symmetries: explicit or secret; 8. Classical topological excitations; 9. Quantum topological excitations; 10. Duality, bosonization and generalized statistics; 11. Statistical transmutation; 12. Pseudo quantum electrodynamics; Part III. Quantum Field Theory Approach to Condensed Matter Systems: 13. Quantum field theory methods in condensed matter; 14. Metals, Fermi liquids, Mott and Anderson insulators; 15. The dynamics of polarons; 16. Polyacetylene; 17. The Kondo effect; 18. Quantum magnets in 1D: Fermionization, bosonization, Coulomb gases and 'all that'; 19. Quantum magnets in 2D: nonlinear sigma model, CP1 and 'all that'; 20. The spin-fermion system: a quantum field theory approach; 21. The spin glass; 22. Quantum field theory approach to superfluidity; 23. Quantum field theory approach to superconductivity; 24. The cuprate high-temperature superconductors; 25. The pnictides: iron based superconductors; 26. The quantum Hall effect; 27. Graphene; 28. Silicene and transition metal dichalcogenides; 29. Topological insulators; 30. Non-abelian statistics and quantum computation; References; Index.

Collective coordinates and constrained hamiltonian systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dayi, O.F.

1992-07-01

A general method of incorporating collective coordinates (transformation of fields into an overcomplete basis) with constrained hamiltonian systems is given where the original phase space variables and collective coordinates can be bosonic or/and fermionic. This method is illustrated by applying it to the SU(2) Yang-Mills-Higgs theory and its BFV-BRST quantization is discussed. Moreover, this formalism is used to give a systematic way of converting second class constraints into effectively first class ones, by considering second class constraints as first class constraints and gauge fixing conditions. This approach is applied to the massive superparticle. Proca lagrangian, and some topological quantum fieldmore » theories.« less

Diagrammar in classical scalar field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cattaruzza, E., E-mail: Enrico.Cattaruzza@gmail.com; Gozzi, E., E-mail: gozzi@ts.infn.it; INFN, Sezione di Trieste

2011-09-15

In this paper we analyze perturbatively a g{phi}{sup 4}classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplifymore » the calculations and make the classical perturbative calculations almost 'identical' formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem. - Highlights: > We provide the Feynman diagrams of perturbation theory for a classical field theory. > We give a super-formalism which links the quantum diagrams to the classical ones. > We check perturbatively the fluctuation-dissipation theorem.« less

Classical gluon and graviton radiation from the bi-adjoint scalar double copy

NASA Astrophysics Data System (ADS)

Goldberger, Walter D.; Prabhu, Siddharth G.; Thompson, Jedidiah O.

2017-09-01

We find double-copy relations between classical radiating solutions in Yang-Mills theory coupled to dynamical color charges and their counterparts in a cubic bi-adjoint scalar field theory which interacts linearly with particles carrying bi-adjoint charge. The particular color-to-kinematics replacements we employ are motivated by the Bern-Carrasco-Johansson double-copy correspondence for on-shell amplitudes in gauge and gravity theories. They are identical to those recently used to establish relations between classical radiating solutions in gauge theory and in dilaton gravity. Our explicit bi-adjoint solutions are constructed to second order in a perturbative expansion, and map under the double copy onto gauge theory solutions which involve at most cubic gluon self-interactions. If the correspondence is found to persist to higher orders in perturbation theory, our results suggest the possibility of calculating gravitational radiation from colliding compact objects, directly from a scalar field with vastly simpler (purely cubic) Feynman vertices.

Symmetry Analysis of Gauge-Invariant Field Equations via a Generalized Harrison-Estabrook Formalism.

NASA Astrophysics Data System (ADS)

Papachristou, Costas J.

The Harrison-Estabrook formalism for the study of invariance groups of partial differential equations is generalized and extended to equations that define, through their solutions, sections on vector bundles of various kinds. Applications include the Dirac, Yang-Mills, and self-dual Yang-Mills (SDYM) equations. The latter case exhibits interesting connections between the internal symmetries of SDYM and the existence of integrability characteristics such as a linear ("inverse scattering") system and Backlund transformations (BT's). By "verticalizing" the generators of coordinate point transformations of SDYM, nine nonlocal, generalized (as opposed to local, point) symmetries are constructed. The observation is made that the prolongations of these symmetries are parametric BT's for SDYM. It is thus concluded that the entire point group of SDYM contributes, upon verticalization, BT's to the system.

The quantum theory of free automorphic fields

NASA Astrophysics Data System (ADS)

Banach, R.

1980-06-01

Heuristic spectral theory is developed for a symmetric operator on the universal covering space of a multiply connected static spacetime and is used to construct the quantum field theory of a multiplet of scalar fields in the customary sum-over-modes fashion. The non-local symmetries necessary to the theory are explicitly constructed, as are the projection on the field operators. The non-existence of a standard charge conjugation for certain types of representation is noted. Gauge transformations are used to give a simple and complete classification of automorphic field theories. The relationship between the unprojected and projected field algebras is clarified, and the implications for Fock space (vacuum degeneracy, etc.) are discussed - earlier work being criticized. The analogy to black hole physics is pointed out, and the possible role of the Reeh-Schlieder theorems is speculated upon.

A simple proof of orientability in colored group field theory.

PubMed

Caravelli, Francesco

2012-01-01

Group field theory is an emerging field at the boundary between Quantum Gravity, Statistical Mechanics and Quantum Field Theory and provides a path integral for the gluing of n-simplices. Colored group field theory has been introduced in order to improve the renormalizability of the theory and associates colors to the faces of the simplices. The theory of crystallizations is instead a field at the boundary between graph theory and combinatorial topology and deals with n-simplices as colored graphs. Several techniques have been introduced in order to study the topology of the pseudo-manifold associated to the colored graph. Although of the similarity between colored group field theory and the theory of crystallizations, the connection between the two fields has never been made explicit. In this short note we use results from the theory of crystallizations to prove that color in group field theories guarantees orientability of the piecewise linear pseudo-manifolds associated to each graph generated perturbatively. Colored group field theories generate orientable pseudo-manifolds. The origin of orientability is the presence of two interaction vertices in the action of colored group field theories. In order to obtain the result, we made the connection between the theory of crystallizations and colored group field theory.

Free field theory as a string theory?

NASA Astrophysics Data System (ADS)

Gopakumar, Rajesh

2004-11-01

An approach to systematically implement open-closed string duality for free large N gauge theories is summarised. We show how the relevant closed string moduli space emerges from a reorganisation of the Feynman diagrams contributing to free field correlators. We also indicate why the resulting integrand on moduli space has the right features to be that of a string theory on AdS. To cite this article: R. Gopakumar, C. R. Physique 5 (2004).

Field analyses of (238)U and (226)Ra in two uranium mill tailings piles from Niger using portable HPGe detector.

PubMed

Déjeant, Adrien; Bourva, Ludovic; Sia, Radia; Galoisy, Laurence; Calas, Georges; Phrommavanh, Vannapha; Descostes, Michael

2014-11-01

The radioactivities of (238)U and (226)Ra in mill tailings from the U mines of COMINAK and SOMAÏR in Niger were measured and quantified using a portable High-Purity Germanium (HPGe) detector. The (238)U and (226)Ra activities were measured under field conditions on drilling cores with 600s measurements and without any sample preparation. Field results were compared with those obtained by Inductive Coupled Plasma Atomic Emission Spectroscopy (ICP-AES) and emanometry techniques. This comparison indicates that gamma-ray absorption by such geological samples does not cause significant deviations. This work shows the feasibility of using portable HPGe detector in the field as a preliminary method to observe variations of radionuclides concentration with the aim of identifying samples of interest. The HPGe is particularly useful for samples with strong secular disequilibrium such as mill tailings. Copyright © 2014 Elsevier Ltd. All rights reserved.

GL/sub 3/-invariant solutions of the Yang-Baxter equation and associated quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kulish, P.P.; Reshetikin N.Y.

1986-09-01

GL/sub 3/-invariant, finite-dimensional solutions of the Yang-Baxter equations acting in the tensor product of two irreducible representations of the group GL/sub 3/ are investigated. A number of relations are obtained for the transfer matrices which demonstrate the connection of representation theory and the Bethe Ansatz in GL/sub 3/invariant models. Some of the most interesting quantum and classical integrable systems connected with GL/sub 3/-invariant solutions of the Yang-Baxter equation are presented.

GL/sub 3/-invariant solutions of the Yang-Baxter equation and associated quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kulish, P.P.; Reshetikhin, N.Yu.

1986-09-10

GL/sub 3/-invariant, finite-dimensional solutions of the Yang-Baxter equations acting in the tensor product of two irreducible representations of the group GL/sub 3/ are investigated. A number of relations are obtained for the transfer matrices which demonstrate the connection of representation theory and the Bethe Ansatz in GL/sub 3/-invariant models. Some of the most interesting quantum and classical integrable systems connected with GL/sub 3/-invariant solutions of the Yang-Baxter equation are presented.

Low-energy dynamics of gravitation

NASA Astrophysics Data System (ADS)

Torma, Tibor

The present status of theories of quantum gravity are reviewed from the low energy point of view. String theory relates classical black-hole type solutions of Einstein- like equations (e.g. axidilaton gravity) to the string vacuum. Several such solutions are proposed and their properties are investigated, including their behavior under supersymmetry transformations. A general feature of all possible quantum theories of gravitation is that they lead to a field theory description at low (as compared to the Planck mass) energies. The theoretical consistency, uniqueness and consequences of such an effective theory are investigated. I show that a power counting theorem allows for the momentum expansion that defines the effective theory even in the presence of large masses. I also show that graviton-graviton scattering is free of potential infrared and collinear divergencies that plague perturbative discussions of Yang-Mills theories.

Magnetic monopole versus vortex as gauge-invariant topological objects for quark confinement

NASA Astrophysics Data System (ADS)

Kondo, Kei-Ichi; Sasago, Takaaki; Shinohara, Toru; Shibata, Akihiro; Kato, Seikou

2017-12-01

First, we give a gauge-independent definition of chromomagnetic monopoles in SU(N) Yang-Mills theory which is derived through a non-Abelian Stokes theorem for the Wilson loop operator. Then we discuss how such magnetic monopoles can give a nontrivial contribution to the Wilson loop operator for understanding the area law of the Wilson loop average. Next, we discuss how the magnetic monopole condensation picture are compatible with the vortex condensation picture as another promising scenario for quark confinement. We analyze the profile function of the magnetic flux tube as the non-Abelian vortex solution of U(N) gauge-Higgs model, which is to be compared with numerical simulations of the SU(N) Yang-Mills theory on a lattice. This analysis gives an estimate of the string tension based on the vortex condensation picture, and possible interactions between two non-Abelian vortices.

Loop Integrands for Scattering Amplitudes from the Riemann Sphere

NASA Astrophysics Data System (ADS)

Geyer, Yvonne; Mason, Lionel; Monteiro, Ricardo; Tourkine, Piotr

2015-09-01

The scattering equations on the Riemann sphere give rise to remarkable formulas for tree-level gauge theory and gravity amplitudes. Adamo, Casali, and Skinner conjectured a one-loop formula for supergravity amplitudes based on scattering equations on a torus. We use a residue theorem to transform this into a formula on the Riemann sphere. What emerges is a framework for loop integrands on the Riemann sphere that promises to have a wide application, based on off-shell scattering equations that depend on the loop momentum. We present new formulas, checked explicitly at low points, for supergravity and super-Yang-Mills amplitudes and for n -gon integrands at one loop. Finally, we show that the off-shell scattering equations naturally extend to arbitrary loop order, and we give a proposal for the all-loop integrands for supergravity and planar super-Yang-Mills theory.

Magnetically charged calorons with non-trivial holonomy

NASA Astrophysics Data System (ADS)

Kato, Takumi; Nakamula, Atsushi; Takesue, Koki

2018-06-01

Instantons in pure Yang-Mills theories on partially periodic space R^3× {S}^1 are usually called calorons. The background periodicity brings on characteristic features of calorons such as non-trivial holonomy, which plays an essential role for confinement/deconfinement transition in pure Yang-Mills gauge theory. For the case of gauge group SU(2), calorons can be interpreted as composite objects of two constituent "monopoles" with opposite magnetic charges. There are often the cases that the two monopole charges are unbalanced so that the calorons possess net magnetic charge in R3. In this paper, we consider several mechanism how such net magnetic charges appear for certain types of calorons through the ADHM/Nahm construction with explicit examples. In particular, we construct analytically the gauge configuration of the (2 , 1)-caloron with U(1)-symmetry, which has intrinsically magnetic charge.

Negative energy, superluminosity, and holography

NASA Astrophysics Data System (ADS)

Polchinski, Joseph; Susskind, Leonard; Toumbas, Nicolaos

1999-10-01

The holographic connection between large N super Yang-Mills (SYM) theory and gravity in anti-de Sitter (AdS) space requires unfamiliar behavior of the SYM theory in the limit that the curvature of the AdS geometry becomes small. The paradoxical behavior includes superluminal oscillations and negative energy density. These effects typically occur in the SYM description of events which take place far from the boundary of AdS when the signal from the event arrives at the boundary. The paradoxes can be resolved by assuming a very rich collection of hidden degrees of freedom of the SYM theory which store information but give rise to no local energy density. These degrees of freedom, called precursors, are needed to make possible sudden apparently acausal energy momentum flows. Such behavior would be impossible in classical field theory as a consequence of the positivity of the energy density. However we show that these effects are not only allowed in quantum field theory but that we can model them in free quantum field theory.

Gravitation. [consideration of black holes in gravity theories

NASA Technical Reports Server (NTRS)

Fennelly, A. J.

1978-01-01

Investigations of several problems of gravitation are discussed. The question of the existence of black holes is considered. While black holes like those in Einstein's theory may not exist in other gravity theories, trapped surfaces implying such black holes certainly do. The theories include those of Brans-Dicke, Lightman-Lee, Rosen, and Yang. A similar two-tensor theory of Yilmaz is investigated and found inconsistent and nonviable. The Newman-Penrose formalism for Riemannian geometries is adapted to general gravity theories and used to implement a search for twisting solutions of the gravity theories for empty and nonempty spaces. The method can be used to find the gravitational fields for all viable gravity theories. The rotating solutions are of particular importance for strong field interpretation of the Stanford/Marshall gyroscope experiment. Inhomogeneous cosmologies are examined in Einstein's theory as generalizations of homogeneous ones by raising the dimension of the invariance groups by one more parameter. The nine Bianchi classifications are extended to Rosen's theory of gravity for homogeneous cosmological models.

Higher-derivative operators and effective field theory for general scalar-tensor theories

NASA Astrophysics Data System (ADS)

Solomon, Adam R.; Trodden, Mark

2018-02-01

We discuss the extent to which it is necessary to include higher-derivative operators in the effective field theory of general scalar-tensor theories. We explore the circumstances under which it is correct to restrict to second-order operators only, and demonstrate this using several different techniques, such as reduction of order and explicit field redefinitions. These methods are applied, in particular, to the much-studied Horndeski theories. The goal is to clarify the application of effective field theory techniques in the context of popular cosmological models, and to explicitly demonstrate how and when higher-derivative operators can be cast into lower-derivative forms suitable for numerical solution techniques.

Infrared conductivity of cuprates using Yang-Rice-Zhang ansatz: Review of our recent investigations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Navinder; Sharma, Raman

2015-05-15

A review of our recent investigations related to the ac transport properties in the psedogapped state of cuprate high temperature superconductors is presented. For our theoretical calculations we use a phenomenological Green’s function proposed by Yang, Rice and Zhang (YRZ). This is based upon the renormalized mean-field theory of the Hubbard model and takes into account the strong electron-electron interaction present in Cuprates. The pseudogap is also taken into account through a proposed self energy. We have tested the form of the Green’s function by computing ac conductivity of cuprates and then compared with experimental results. We found agreement betweenmore » theory and experiment in reproducing the doping evolution of ac conductivity but there is a problem with absolute magnitudes and their frequency dependence. This shows a partial success of the YRZ ansatz. The ways to rectify it are suggested and worked out.« less

N=2 gauge theories and degenerate fields of Toda theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kanno, Shoichi; Matsuo, Yutaka; Shiba, Shotaro

We discuss the correspondence between degenerate fields of the W{sub N} algebra and punctures of Gaiotto's description of the Seiberg-Witten curve of N=2 superconformal gauge theories. Namely, we find that the type of degenerate fields of the W{sub N} algebra, with null states at level one, is classified by Young diagrams with N boxes, and that the singular behavior of the Seiberg-Witten curve near the puncture agrees with that of W{sub N} generators. We also find how to translate mass parameters of the gauge theory to the momenta of the Toda theory.

Geometry in transition in four dimensions: A model of emergent geometry in the early universe

NASA Astrophysics Data System (ADS)

Ydri, Badis; Khaled, Ramda; Ahlam, Rouag

2016-10-01

We study a six matrix model with global S O (3 )×S O (3 ) symmetry containing at most quartic powers of the matrices. This theory exhibits a phase transition from a geometrical phase at low temperature to a Yang-Mills matrix phase with no background geometrical structure at high temperature. This is an exotic phase transition in the same universality class as the three matrix model but with important differences. The geometrical phase is determined dynamically, as the system cools, and is given by a fuzzy sphere background SN2×SN2, with an Abelian gauge field which is very weakly coupled to two normal scalar fields.

Radially separated classical lumps in non-Abelian gauge models

NASA Astrophysics Data System (ADS)

Burzlaff, Jürgen

1985-04-01

We search for smooth and time-independent finite-energy solutions to Yang-Mills-Higgs theory with an arbitrary compact gauge group. Excluding the monopole solutions which have been studied before, we concentrate on configurations with no long-range fields, which include the saddle points corresponding to noncontractible (hyper-) loops. It is shown that if the radial dependence of the fields is factorized, only one solution satisfies all these conditions. This solution is the one which has been studied before by Dashen, Hasslacher, and Neveu and by Boguta, and whose existence has recently been proved rigorously. Formulas for the asymptotic behavior of this solution are given.

String Theory on five dimensional Anti de Sitter space-times: Fundamental aspects and applications

NASA Astrophysics Data System (ADS)

Hofman, Diego M.

2009-12-01

In this thesis we study basic properties and applications of String Theory on AdS5 backgrounds. We do this in the framework of the AdS/CFT Correspondence and use our results to learn about four dimensional Conformal Field Theories. The first part of this work deals fundamentally with the problem of solving the exact spectrum of anomalous dimensions of planar N = 4 Super Yang Mills theory for all values of the 't Hooft coupling lambda. We study the problem for operators of large SO(6) charge J and identify the string configurations dual to magnons in the spin chain picture of the gauge theory. We name these states Giant Magnons. Furthermore we study their interactions and discuss the implications of the spectrum of states on the analytic structure of the exact scattering matrix of the theory. It is found that BPS states account for all the poles present in the full S-matrix. We also study the spectrum of Giant Magnons attached to D3-branes (Giant Gravitons). The dual operators in N = 4 SYM are long strings of SO(6) scalars connected to baryonic operators constructed of order N fields. The problem turns out to be mapped to solving the mulitparticle spectrum of a spin chain with non trivial boundary conditions. We study the properties of the boundary reflection matrix in detail and write equations that determine the associated phase factor. The second part of this work deals with applications of this type of string theories to the collider physics of conformal theories. We study infrared safe observables in the CFT given by energy correlation functions. We discuss the short distance behavior of these objects and explain that this physics is controlled by non local light ray operators. We find the dual String Theory description of these observables and use these results to study the strong coupling physics of conformal theories. We also describe the precise string states dual to the light ray operators. We argue that the energy operators that account for the energy

Quantum algorithms for quantum field theories.

PubMed

Jordan, Stephen P; Lee, Keith S M; Preskill, John

2012-06-01

Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.

Unification Principle and a Geometric Field Theory

NASA Astrophysics Data System (ADS)

Wanas, Mamdouh I.; Osman, Samah N.; El-Kholy, Reham I.

2015-08-01

In the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.

Pure natural inflation

NASA Astrophysics Data System (ADS)

Nomura, Yasunori; Watari, Taizan; Yamazaki, Masahito

2018-01-01

We point out that a simple inflationary model in which the axionic inflaton couples to a pure Yang-Mills theory may give the scalar spectral index (ns) and tensor-to-scalar ratio (r) in complete agreement with the current observational data.

A Philosophical Approach to Quantum Field Theory

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-01-01

Preface; Acknowledgements; 1. Approach to quantum field theory; 2. Scalar field theory; 3. Quantum electrodynamics; 4. Perspectives; Appendix A. An efficient perturbation scheme; Appendix B. Properties of Dirac matrices; Appendix C. Baker-Campbell-Hausdorff formulas; References; Author index; Subject index.

Zero Dimensional Field Theory of Tachyon Matter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dimitrijevic, D. D.; Djordjevic, G. S.

2007-04-23

The first issue about the object (now) called tachyons was published almost one century ago. Even though there is no experimental evidence of tachyons there are several reasons why tachyons are still of interest today, in fact interest in tachyons is increasing. Many string theories have tachyons occurring as some of the particles in the theory. In this paper we consider the zero dimensional version of the field theory of tachyon matter proposed by A. Sen. Using perturbation theory and ideas of S. Kar, we demonstrate how this tachyon field theory can be connected with a classical mechanical system, suchmore » as a massive particle moving in a constant field with quadratic friction. The corresponding Feynman path integral form is proposed using a perturbative method. A few promising lines for further applications and investigations are noted.« less