Classical Solutions of SU(3) Pure Yang-Mills Theory
2002-01-01
Regular classical solutions of pure SU(3) gauge theories, in Minkowsky spacetime, are computed in the Landau gauge. The classical fields have an intrinsic energy scale and produce quark confinement if interpreted in the sense of a nonrelativistic potential. Moreover, the quark propagator in the background of these fields vanishes at large positive and negative time and space separations.
Topological susceptibility for the SU(3) Yang--Mills theory
DEFF Research Database (Denmark)
Del Debbio, Luigi; Giusti, Leonardo; Pica, Claudio
2004-01-01
We present the results of a computation of the topological susceptibility in the SU(3) Yang--Mills theory performed by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3), which corresponds to c...
Topological susceptibility for the SU(3) Yang--Mills theory
Del Debbio, L; Pica, C; Debbio, Luigi Del; Giusti, Leonardo; Pica, Claudio
2005-01-01
We present the results of a computation of the topological susceptibility in the SU(3) Yang--Mills theory performed by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3), which corresponds to chi=(191 \\pm 5 MeV)^4 if F_K is used to set the scale. Our result supports the Witten--Veneziano explanation for the large mass of the eta'.
Unconstrained Hamiltonian formulation of low energy SU(3) Yang-Mills quantum theory
Pavel, Hans-Peter
2012-01-01
An unconstrained Hamiltonian formulation of the SU(3) Yang-Mills quantum mechanics of spatially constant fields is given using the method of minimal embedding of SU(2) into SU(3) by Kihlberg and Marnelius. Using a canonical transformation of the gluon fields to a new set of adapted coordinates (a non-standard type polar decomposition), which Abelianizes the Non-Abelian Gauss law constraints to be implemented, the corresponding unconstrained Hamiltonian and total angular momentum are derived. This reduces the colored spin-1 gluons to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields. The obtained unconstrained Hamiltonian is then rewritten into a form, which separates the rotational from the scalar degrees of freedom. It is shown that the chromomagnetic potential has classical zero-energy valleys for two arbitrarily large classical glueball fields, which are the unconstrained analogs of the well-known "constant Abelian fields". On the quantum level, practically all glueball excitation e...
Exact solutions for classical Yang-Mills fields
2014-01-01
We provide a set of exact solutions of the classical Yang-Mills equations. They have the property to satisfy a massive dispersion relation and hold in all gauges. These solutions can be used to describe the vacuum of the quantum Yang-Mills theory and so, they provide a general framework to build a quantum field theory. The components of the field become separated on a generic gauge but are all equal just in the Lorenz (Landau) gauge.
Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories
Caselle, Michele; Panero, Marco
2015-01-01
We present a high-precision lattice calculation of the equation of state in the confining phase of SU(2) Yang-Mills theory. We show that the results are described very well by a gas of massive, non-interacting glueballs, provided one assumes an exponentially growing Hagedorn spectrum. The latter can be derived within an effective bosonic closed-string model, leading to a parameter-free theoretical prediction, which is in perfect agreement with our lattice results. Furthermore, when applied to SU(3) Yang-Mills theory, this effective model accurately describes the lattice results reported by Bors\\'anyi et al. in JHEP 07 (2012) 056.
A new sphaleron in SU(3) Yang-Mills-Higgs theory
Energy Technology Data Exchange (ETDEWEB)
Nagel, Pascal; Klinkhamer, Frans [Karlsruher Institut fuer Technologie (KIT), Karlsruhe (Germany)
2016-07-01
The sphaleron solution S is known to contribute to baryon-number violation within the electroweak Standard Model. To gain further insight into the nonperturbative dynamics of QCD (and GUTs), we study a new sphaleron solution of SU(3) Yang-Mills-Higgs theory, the solution S. Two independent numerical approaches yield solutions of the reduced field equations and a surprising structure of the energy barrier in configuration space.
A Classical Solution of Massive Yang-Mills Fields
Mogami, Tsuguo
2016-01-01
Recent researches on the solution of Schwinger-Dyson equations, as well as lattice simulations of pure QCD, suggest that the gluon propagator is massive. In this letter, we assume that the classical counterpart of this massive gluon field may be represented with the equation of motion for Yang-Mills theory with a mass term added. A new classical solution is given for this equation. It is discussed that this solution may have some role in confinement.
Exact solutions for classical Yang-Mills fields
Frasca, Marco
2014-01-01
Some years ago we displayed a set of classical solutions for the classical Yang-Mills field theory having the property to satisfy a dispersion relation typical of a massive theory. But such solutions seemed to be exact only in the Landau gauge making all the argument an asymptotic one for the most general case of a generic gauge. These solutions can be used to describe the vacuum of the quantum Yang-Mills theory and so, to prove that they are always exact can grant a general framework to build a quantum field theory. Here we show that these solutions are always exact changing just the normalization factor. The components of the field become separated on a generic gauge being all equal just in the Landau gauge.
A novel computation of the thermodynamics of the SU(3) Yang-Mills theory
Giusti, Leonardo
2015-01-01
We present an accurate computation of the Equation of State of the SU(3) Yang-Mills theory using shifted boundary conditions in the temporal direction. In this framework, the entropy density s can be obtained in a simple way from the expectation value of the space-time components T0k of the energy-momentum tensor. At each given value of the temperature, s is measured in an independent way at several values of the lattice spacing. The extrapolation to the continuum limit shows small discretization effects with respect to the statistical errors of approximatively 0.5%.
Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
Cé, Marco; Engel, Georg P; Giusti, Leonardo
2015-01-01
We study the topological charge distribution of the SU(3) Yang--Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo simulations by implementing a naive discretization of the topological charge evolved with the Yang--Mills gradient flow. This definition is far less demanding than the one suggested from Neuberger's fermions and, as shown in this paper, in the continuum limit its cumulants coincide with those of the universal definition appearing in the chiral Ward identities. Thanks to the range of lattice volumes and spacings considered, we can extrapolate the results for the second and fourth cumulant of the topological charge distribution to the continuum limit with confidence by keeping finite volume effects negligible with respect to the statistical errors. Our best results for the topological susceptibility is t_0^2*chi=6.67(7)*10^-4, where t_0 is a standard reference scale, while for the...
Non-perturbative renormalization of the energy-momentum tensor in SU(3) Yang-Mills theory
Giusti, Leonardo
2014-01-01
We present a strategy for a non-perturbative determination of the finite renormalization constants of the energy-momentum tensor in the SU(3) Yang-Mills theory. The computation is performed by imposing on the lattice suitable Ward Identites at finite temperature in presence of shifted boundary conditions. We show accurate preliminary numerical data for values of the bare coupling g_0^2 ranging for 0 to 1.
Classical and semi-classical solutions of the Yang--Mills theory. [Review
Energy Technology Data Exchange (ETDEWEB)
Jackiw, R.; Nohl, C.; Rebbi, C.
1977-12-01
This review summarizes what is known at present about classical solutions to Yang-Mills theory both in Euclidean and Minkowski space. The quantal meaning of these solutions is also discussed. Solutions in Euclidean space expose multiple vacua and tunnelling of the quantum theory. Those in Minkowski space-time provide a semi-classical spectrum for a conformal generator.
SU(3) Yang-Mills Hamiltonian in the flux-tube gauge: Strong coupling expansion and glueball dynamics
Pavel, Hans-Peter
2016-01-01
It is shown that the formulation of the SU(3) Yang-Mills quantum Hamiltonian in the "flux-tube gauge" A_{a1}=0 for all a=1,2,4,5,6,7 and A_{a2}=0 for all a=5,7 allows for a systematic and practical strong coupling expansion of the Hamiltonian in \\lambda\\equiv g^{-2/3}, equivalent to an expansion in the number of spatial derivatives. Introducing an infinite spatial lattice with box length a, the "free part" is the sum of Hamiltonians of Yang-Mills quantum mechanics of constant fields for each box, and the "interaction terms" contain higher and higher number of spatial derivatives connecting different boxes. The Faddeev-Popov operator, its determinant and inverse, are rather simple, but show a highly non-trivial periodic structure of six Gribov-horizons separating six Weyl-chambers. The energy eigensystem of the gauge reduced Hamiltonian of SU(3) Yang-Mills mechanics of spatially constant fields can be calculated in principle with arbitrary high precision using the orthonormal basis of all solutions of the corr...
Surface-Invariants in 2D Classical Yang-Mills Theory
Díaz, R; Leal, L; D\\'{\\i}az, Rafael; Leal, Lorenzo
2006-01-01
We study a method to obtain invariants under area-preserving diffeomorphisms associated to closed curves in the plane from classical Yang-Mills theory in two dimensions. Taking as starting point the Yang-Mills field coupled to non dynamical particles carrying chromo-electric charge, and by means of a perturbative scheme, we obtain the first two contributions to the on shell action, which are area-invariants. A geometrical interpretation of these invariants is given.
Non-Gaussianity of the topological charge distribution in $\\mathrm{SU}(3)$ Yang-Mills theory
Cè, Marco
2015-01-01
In Yang-Mills theory, the cumulants of the na\\"ive lattice discretization of the topological charge evolved with the Yang-Mills gradient flow coincide, in the continuum limit, with those of the universal definition. We sketch in these proceedings the main points of the proof. By implementing the gradient-flow definition in numerical simulations, we report the results of a precise computation of the second and the fourth cumulant of the $\\mathrm{SU}(3)$ Yang-Mills theory topological charge distribution, in order to measure the deviation from Gaussianity. A range of high-statistics Monte Carlo simulations with different lattice volumes and spacings is used to extrapolate the results to the continuum limit with confidence by keeping finite-volume effects negligible with respect to the statistical errors. Our best result for the topological susceptibility is $t_0^2\\chi=6.67(7)\\times 10^{-4}$, while for the ratio between the fourth and the second cumulant we obtain $R=0.233(45)$.
Equation of state of the SU($3$) Yang-Mills theory: a precise determination from a moving frame
Giusti, Leonardo
2016-01-01
The equation of state of the SU($3$) Yang-Mills theory is determined in the deconfined phase with a precision of about 0.5%. The calculation is carried out by numerical simulations of lattice gauge theory with shifted boundary conditions in the time direction. At each given temperature, up to $230\\, T_c$ with $T_c$ being the critical temperature, the entropy density is computed at several lattice spacings so to be able to extrapolate the results to the continuum limit with confidence. Taken at face value, above a few $T_c$ the results exhibit a striking linear behaviour in $\\ln(T/T_c)^{-1}$ over almost 2 orders of magnitude. Within errors, data point straight to the Stefan-Boltzmann value but with a slope grossly different from the leading-order perturbative prediction. The pressure is determined by integrating the entropy in the temperature, while the energy density is extracted from $T s=(\\epsilon + p )$. The continuum values of the potentials are well represented by Pad\\'e interpolating formulas, which als...
A two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond
Reinosa, U; Tissier, M; Wschebor, N
2015-01-01
We study the confinement-deconfinement phase transition of pure Yang-Mills theories at finite temperature within a simple massive extension of standard background field methods. We generalize our recent next-to-leading-order perturbative calculation of the Polyakov loop and the related background field effective potential for the SU(2) theory to any compact and connex Lie group with a simple Lie algebra. We discuss in detail the SU(3) theory, where the two-loop corrections yield improved values for the first order transition temperature as compared to the one-loop result. We show that certain one-loop artifacts of thermodynamical observables disappear at two-loop order, as was already the case for the SU(2) theory. In particular, the entropy and the pressure are positive for all temperatures. We also discuss the groups SU(4) and Sp(2) which shed interesting light, respectively, on the relation between the (de)confinement of static matter sources in the various representations of the gauge group and on the use...
Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang-Mills theory
Nakagawa, Y.; Voigt, A.; Ilgenfritz, E.-M.; Müller-Preussker, M.; Nakamura, A.; Saito, T.; Sternbeck, A.; Toki, H.
2009-06-01
We study the momentum dependence of the ghost propagator and of the space and time components of the gluon propagator at equal time in pure SU(3) lattice Coulomb-gauge theory carrying out a joint analysis of data collected independently at the Research Center for Nuclear Physics, Osaka and Humboldt University, Berlin. We focus on the scaling behavior of these propagators at β=5.8,…,6.2 and apply a matching technique to relate the data for the different lattice cutoffs. Thereby, lattice artifacts are found to be rather strong for both instantaneous gluon propagators at a large momentum. As a byproduct we obtain the respective lattice scale dependences a(β) for the transversal gluon and the ghost propagator which indeed run faster with β than two-loop running, but slightly slower than what is known from the Necco-Sommer analysis of the heavy quark potential. The abnormal a(β) dependence as determined from the instantaneous time-time gluon propagator, D44, remains a problem, though. The role of residual gauge-fixing influencing D44 is discussed.
Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang-Mills theory
Nakagawa, Y; Ilgenfritz, E -M; Müller-Preussker, M; Nakamura, A; Saitô, T; Sternbeck, A; Toki, H
2009-01-01
We study the momentum dependence of the ghost propagator and of the space and time components of the gluon propagator at equal time in pure SU(3) lattice Coulomb gauge theory carrying out a joint analysis of data collected independently at RCNP Osaka and Humboldt University Berlin. We focus on the scaling behavior of these propagators at beta=5.8,...,6.2 and apply a matching technique to relate the data for the different lattice cutoffs. Thereby, lattice artifacts are found to be rather strong for both instantaneous gluon propagators at large momentum. As a byproduct we obtain the respective lattice scale dependences a(beta) for the transversal gluon and the ghost propagator which indeed run faster with beta than two-loop running, but slightly slower than what is known from the Necco-Sommer analysis of the heavy quark potential. The abnormal a(beta) dependence as determined from the instantaneous time-time gluon propagator, D_{44}, remains a problem, though. The role of residual gauge-fixing influencing D_{44...
Navarro-Lérida, Francisco; Tchrakian, D. H.
2015-05-01
We study spherically symmetric finite energy solutions of two Higgs-Chern-Simons-Yang-Mills-Higgs (HCS-YMH) models in 3+1 dimensions, one with gauge group SO(5) and the other with SU(3). The Chern-Simons (CS) densities are defined in terms of both the Yang-Mills (YM) and Higgs fields and the choice of the two gauge groups is made so that they do not vanish. The solutions of the SO(5) model carry only electric charge and zero magnetic charge, while the solutions of the SU(3) model are dyons carrying both electric and magnetic charges like the Julia-Zee (JZ) dyon. Unlike the latter, however, the electric charge in both models receives an important contribution from the CS dynamics. We pay special attention to the relation between the energies and charges of these solutions. In contrast with the electrically charged JZ dyon of the Yang-Mills-Higgs (YMH) system, whose mass is larger than that of the electrically neutral (magnetic monopole) solutions, the masses of the electrically charged solutions of our HCS-YMH models can be smaller than their electrically neutral counterparts in some parts of the parameter space. To establish this is the main task of this work, which is performed by constructing the HCS-YMH solutions numerically. In the case of the SU(3) HCS-YMH, we have considered the question of angular momentum and it turns out that it vanishes.
Navarro-Lerida, Francisco
2014-01-01
We study spherically symmetric finite energy solutions of two Higgs-Chern-Simons--Yang-Mills-Higgs (HCS-YMH) models in $3+1$ dimensions, one with gauge group $SO(5)$ and the other with $SU(3)$. The Chern-Simons (CS) densities are defined in terms of both the Yang-Mills (YM) and Higgs fields and the choice of the two gauge groups is made so they do not vanish. The solutions of the $SO(5)$ model carry only electric charge and zero magnetic charge, while the solutions of the $SU(3)$ model are dyons carrying both electric and magnetic charges like the Julia-Zee (JZ) dyon. Unlike the latter however, the electric charge in both models receives an important contribution from the CS dynamics. We pay special attention to the relation between the energies and charges of these solutions. In contrast with the electrically charged JZ dyon of the Yang-Mills-Higgs (YMH) system, whose mass is larger than that of the electrically neutral (magnetic monopole) solutions, the masses of the electrically charged solutions of our HC...
Perturbative quantization of Yang-Mills theory with classical double as gauge algebra
Ruiz, F Ruiz
2015-01-01
Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary.
Perturbative quantization of Yang-Mills theory with classical double as gauge algebra
Energy Technology Data Exchange (ETDEWEB)
Ruiz Ruiz, F. [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2016-02-15
Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary. (orig.)
Parametric Instability of Classical Yang-Mills Fields in an Expanding Geometry
Tsutsui, Shoichiro; Ohnishi, Akira
2015-01-01
We investigate the instability of classical Yang-Mills field in an expanding geometry under a color magnetic background field within the linear regime. We consider homogeneous, boost-invariant and time-dependent color magnetic fields simulating the glasma configuration. We introduce the conformal coordinates which enable us to map an expanding problem approximately into a nonexpanding problem. We find that the fluctuations with finite longitudinal momenta can grow exponentially due to parametric instability. Fluctuations with finite transverse momenta can also show parametric instability, but their momenta are restricted to be small. The most unstable modes start to grow exponentially in the early stage of the dynamics and they may affect the thermalization in heavy-ion collisions.
Parametric instability of classical Yang-Mills fields in an expanding geometry
Tsutsui, Shoichiro; Kunihiro, Teiji; Ohnishi, Akira
2016-07-01
We investigate the instability of a classical Yang-Mills field in an expanding geometry under a color magnetic background field within the linear regime. We consider homogeneous, boost-invariant, and time-dependent color magnetic fields simulating the glasma configuration. We introduce the conformal coordinates which enable us to map an expanding problem approximately into a nonexpanding problem. We find that the fluctuations with finite longitudinal momenta can grow exponentially due to parametric instability. Fluctuations with finite transverse momenta can also show parametric instability, but their momenta are restricted to be small. The most unstable modes start to grow exponentially in the early stage of the dynamics, and they may affect the thermalization in heavy-ion collisions.
Drechsler, Wolfgang; Havas, Peter; Rosenblum, Arnold
1984-02-01
In two recent papers, the general form of the laws of motion for point particles which are multipole sources of the classical coupled Yang-Mills-Higgs fields was determined by Havas, and for the special case of monopole singularities of a Yang-Mills field an iteration procedure was developed by Drechsler and Rosenblum to obtain the equations of motion of mass points, i.e., the laws of motion including the explicit form of the fields of all interacting particles. In this paper we give a detailed derivation of the laws of motion of monopole-dipole singularities of the coupled Yang-Mills-Higgs fields for point particles with mass and spin, following a procedure first applied by Mathisson and developed by Havas. To obtain the equations of motion, a systematic approximation method is developed in the following paper for the solution of the nonlinear field equations and determination of the fields entering the laws of motion found here to any given order in the coupling constant g.
Duarte, Anthony G.; Oliveira, Orlando; Silva, Paulo J.
2016-07-01
The dependence of the Landau gauge two-point gluon and ghost correlation functions on the lattice spacing and on the physical volume are investigated for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations. We present data from very large lattices up to 1284 and for two lattice spacings 0.10 fm and 0.06 fm corresponding to volumes of ˜(13 fm )4 and ˜(8 fm )4 , respectively. Our results show that, for sufficiently large physical volumes, both propagators have a mild dependence on the lattice volume. On the other hand, the gluon and ghost propagators change with the lattice spacing a in the infrared region, with the gluon propagator having a stronger dependence on a compared to the ghost propagator. In what concerns the strong coupling constant αs(p2), as defined from gluon and ghost two-point functions, the simulations show a sizeable dependence on the lattice spacing for the infrared region and for momenta up to ˜1 GeV .
Duarte, Anthony G; Silva, Paulo J
2016-01-01
The dependence of the Landau gauge two point gluon and ghost correlation functions on the lattice spacing and on the physical volume are investigated for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations. We present data from very large lattices up to $128^4$ and for two lattice spacings $0.10$ fm and $0.06$ fm corresponding to volumes of $\\sim$ (13 fm)$^4$ and $\\sim$ (8 fm)$^4$, respectively. Our results show that, for sufficiently large physical volumes, both propagators have a mild dependence on the lattice volume. On the other hand, the gluon and ghost propagators change with the lattice spacing $a$ in the infrared region, with the gluon propagator having a stronger dependence on $a$ compared to the ghost propagator. In what concerns the strong coupling constant $\\alpha_s (p^2)$, as defined from gluon and ghost two point functions, the simulations show a sizeable dependence on the lattice spacing for the infrared region and for momenta up to $\\sim 1$ GeV.
Directory of Open Access Journals (Sweden)
Trunev A. P.
2015-10-01
Full Text Available The article presents a project of the capacitor in the Yang-Mills theory. Model capacitor represents the equipotential surfaces separated by a space. To describe the mechanism of condensation chromodynamics field used numerical models developed based on an average of the Yang-Mills theory. In the present study, we used eight-scalar component model that in the linear case is divided into two groups containing three or five fields respectively. In contrast to classical electrodynamics, a static model of the Yang-Mills is not divided into independent equations because of the nonlinearity of the model itself. However, in the case of a linear theory separation is possible. It is shown that in this particular case, the Yang-Mills theory is reduced to Poisson theory, which describes the electrostatic and magnetostatic phenomena. In the present work it is shown that in a certain region of the parameters of the capacitor of the Yang-Mills theory on the functional properties of the charge accumulation and retention of the field is similar to the capacitor of the electrostatic field or a magnet in magnetostatics. This means that in nature there are two types of charges, which are sources of macroscopic Yang-Mills field, which are similar to the properties of electric and magnetic charges in the Poisson theory. It is shown that in Yang-Mills only one type of charge may be associated with the distribution density of the substance, while another type of charge depends on the charge distribution of the first type. This allows us to provide an explanation for the lack of symmetry between electric and magnetic charges
N = 4 super-Yang-Mills in LHC superspace part I: classical and quantum theory
Chicherin, Dmitry; Sokatchev, Emery
2017-02-01
We present a formulation of the maximally supersymmetric N = 4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N =4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the N = 4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the N = 2 gauge and hypermultiplet matter theories. In the twin paper arXiv:1601.06804 we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the N = 4 stress-tensor supermultiplet.
N=4 super-Yang-Mills in LHC superspace. Part I: Classical and quantum theory
Chicherin, Dmitry
2016-01-01
We present a formulation of the maximally supersymmetric N=4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N=4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the N=4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the N=2 gauge and hypermultiplet matter theories. In the twin paper \\cite{twin} we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the N=4 stress-tensor supermultiplet.
On Landau gauge Yang-Mills correlation functions
Cyrol, Anton K; Mitter, Mario; Pawlowski, Jan M; Strodthoff, Nils
2016-01-01
We investigate Landau gauge $SU(3)$ Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalisation group. Particular focus is put on the dynamical creation of the gluon mass gap at non-perturbative momenta and the consistent treatment of quadratic divergences. The non-perturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated self-consistently with the classical action as only input. The apparent convergence of the expansion scheme is discussed and within the errors, our numerical results are in quantitative agreement with available lattice results.
Lin, C -J David; Ramos, Alberto
2015-01-01
We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g_GF, is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g_GF. For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g^2_GF ~ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, altho...
A model of unified quantum chromodynamics and Yang-Mills gravity
Institute of Scientific and Technical Information of China (English)
HSU Jong-Ping
2012-01-01
Based on a generalized Yang-Mills framework,gravitational and strong interactions can be unified in analogy with the unification in the clectroweak theory.By gauging T(4) × [SU(3)]color in fiat space-time,we have a unified model of chromo-gravity with a new tensor gauge field,which couples universally to all gluons,quarks and anti-quarks.The space-time translational gauge symmetry assures that all wave equations of quarks and gluons reduce to a Hamilton-Jacobi equation with the same ‘effective Riemann metric tensors' in the geometric-optics (or classical) limit.The emergence of effective metric tensors in the classical limit is essential for the unified model to agree with experiments.The unified model suggests that all gravitational,strong and electroweak interactions appear to be dictated by gauge symmetries in the generalized Yang-Mills framework.
Drechsler, Wolfgang; Havas, Peter; Rosenblum, Arnold
1984-02-01
In the preceding paper, the laws of motion were established for classical particles with spin which are monopole-dipole singularities of Yang-Mills-Higgs fields. In this paper, a systematic approximation scheme is developed for solving the coupled nonlinear field equations in any order and for determining the corresponding equations of motion. In zeroth order the potentials are taken as the usual Liénard-Wiechert and Bhabha-Harish-Chandra potentials (generalized to isospace); in this order the solutions are necessarily Abelian, since the isovector describing the charge is constant. The regularization necessary to obtain expressions finite on the world lines of the particles is achieved by the method of Riesz potentials. All fields are taken as retarded and are expressed in integral form. Omitting dipole interactions, the integrals for the various terms are carried out as far as possible for general motions, including radiation-reaction terms. In first order, the charge isovectors are no longer necessarily constant; thus the solutions are not necessarily Abelian, and it is possible for charge to be radiated away. The cases of time-symmetric field theory and of an action-at-a-distance formulation of the theory are discussed in an appendix.
Directory of Open Access Journals (Sweden)
Trunev A. P.
2015-09-01
Full Text Available The article presents a project of the Yang-Mills amplifier. Amplifier model is a multilayer spherical shell with increasing density towards the center. In the center of the amplifier is the core of high-density material. It is shown that in such a system, the amplitude of the Yang-Mills waves rises from the periphery to the center of several orders of magnitude. The role of the Yang-Mills field in the processes occurring in the nuclei of galaxies, stars and planets is discussed. The data modeling to strengthen the Yang-Mills field in the bowels of the planet, with an atomic explosion, and in some special devices such as the voltaic pile. To describe the mechanism of amplification chromodynamics field used as accurate results in Yang-Mills theory and numerical models developed based on an average and the exact equations as well. Among the exact solutions of the special role played by the centralsymmetric metric describing the contribution of the Yang-Mills field in the speed of recession of galaxies. Among the approximate numerical models can be noted the eight-scalar model we have developed for the simulation of non-linear color oscillations and chaos in the Yang-Mills theory. Earlier models were investigated spatio-temporal oscillations of the YangMills theory in the case of three and eight colors. The results of numerical simulation show that the nonlinear interaction does not lead to a spatial mixing of colors as it might be in the case of turbulent diffusion. Depending on the system parameters there is a suppression of the amplitude of the oscillations the first three by five colors or vice versa. The kinetic energy fluctuations or shared equally between the color components, or dominated by the kinetic energy of repressed groups of colors. In the present study, we found that amplification chromodynamic field leads to a sharp increase in the amplitude of the suppressed color, which can lead to an increase in entropy, excitation of nuclear
Landau gauge Yang-Mills correlation functions
Cyrol, Anton K.; Fister, Leonard; Mitter, Mario; Pawlowski, Jan M.; Strodthoff, Nils
2016-09-01
We investigate Landau gauge S U (3 ) Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalization group. Particular focus is put on the dynamical creation of the gluon mass gap at nonperturbative momenta and the consistent treatment of quadratic divergences. The nonperturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated self-consistently with the classical action as the only input. The apparent convergence of the expansion scheme is discussed and within the errors, our numerical results are in quantitative agreement with available lattice results.
Yang-Mills Connections On Orientable and Nonorientable Surfaces
Ho, Nan-Kuo
2007-01-01
In math.SG/0605587, we studied Yang-Mills functional on the space of connections on a principal G_R-bundle over a closed, connected, nonorientable surface, where G_R is any compact connected Lie group. In this sequel, we generalize the discussion in "The Yang-Mills equations over Riemann surfaces" by Atiyah and Bott, and math.SG/0605587. We obtain explicit descriptions (as representation varieties) of Morse strata of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups SO(n) and Sp(n). It turns out to be quite different from the unitary case. In the orientable case, we give a slightly modified version of Laumon and Rapoport's solution to the Atiyah-Bott recursion relation, and use it to write down explicit formulas of rational equivariant Poincar\\'{e} series of the top stratum for SO(n) and Sp(n).
Integrability in Yang-Mills theory on the light cone beyond leading order
Belitsky, A V; Müller, D
2004-01-01
The one-loop dilatation operator in Yang-Mills theory possesses a hidden integrability symmetry in the sector of maximal helicity Wilson operators. We calculate two-loop corrections to the dilatation operator and demonstrate that while integrability is broken for matter in the fundamental representation of the SU(3) gauge group, for the adjoint SU(N_c) matter it survives the conformal symmetry breaking and persists in supersymmetric N=1, N=2 and N=4 Yang-Mills theories.
SU(2) Yang-Mills Theory: Waves, Particles, and Quantum Thermodynamics
Hofmann, Ralf
2016-01-01
We elucidate how Quantum Thermodynamics at temperature $T$ emerges from pure and classical SU(2) Yang-Mills theory on a four-dimensional Euclidean spacetime slice $S_1\\times {\\bf R}^3$. The concept of a (deconfining) thermal ground state, composed of certain solutions to the fundamental, classical Yang-Mills equation, allows for a unified addressation of both (classical) wave- and (quantum) particle-like excitations thereof.
Quantum Yang-Mills field theory
Frasca, Marco
2017-01-01
We show that the Dyson-Schwinger set of equations for the Yang-Mills theory can be exactly solved till the two-point function. This is obtained given a set of nonlinear waves solving the classical equations of motion. Translation invariance is maintained by the proper choice of the solution of the equation for the two-point function as devised by Coleman. The computation of the Dyson-Schwinger equations is performed in the same way as devised by Bender, Milton and Savage providing a set of partial differential equations whose proof of existence of the solutions is standard. So, the correlation functions of the theory could be proved to exist and the two-point function manifests a mass gap.
Stabilization of the Yang-Mills chaos in non-Abelian Born-Infeld theory
Galtsov, D V
2003-01-01
We investigate dynamics of the homogeneous time-dependent SU(2) Yang-Mills fields governed by the non-Abelian Born-Infeld lagrangian which arises in superstring theory as a result of summation of all orders in the string slope parameter $\\alpha'$. It is shown that generically the Born-Infeld dynamics is less chaotic than that in the ordinary Yang-Mills theory, and at high enough field strength the Yang-Mills chaos is stabilized. More generally, a smothering effect of the string non-locality on behavior of classical fields is conjectured.
Galtsov, D V; Volkov, M S; Davydov, Evgeny A.; Gal'tsov, Dmitri V.; Volkov, Mikhail S.
2006-01-01
We present globally regular vortex-type solutions for a pure SU(2) Yang-Mills field coupled to gravity in 3+1 dimensions. These gravitating vortices are static, cylindrically symmetric and purely magnetic, and they support a non-zero chromo-magnetic flux through their cross section. In addition, they carry a constant non-Abelian current, and so in some sense they are analogs of the superconducting cosmic strings. They have a compact central core dominated by a longitudinal magnetic field and endowed with an approximately Melvin geometry. This magnetic field component gets color screened in the exterior part of the core, outside of which the fields approach exponentially fast those of the electrovacuum Bonnor solutions with a circular magnetic field. In the far field zone the solutions are not asymptotically flat but tend to vacuum Kasner metrics.
Form Invariance, Topological Fluctuations and Mass Gap of Yang-Mills Theory
Qian, Yachao
2016-01-01
In order to have a new perspective on the long-standing problem of the mass gap in Yang-Mills theory, we study the quantum Yang-Mills theory in the presence of topologically nontrivial backgrounds in this paper. The topologically stable gauge fields are constrained by the form invariance condition and the topological properties. Obeying these constraints, the known classical solutions to the Yang-Mills equation in the 3- and 4-dimensional Euclidean spaces are recovered, and the other allowed configurations form the nontrivial topological fluctuations at quantum level. Together, they constitute the background configurations, upon which the quantum Yang-Mills theory can be constructed. We demonstrate that the theory mimics the Higgs mechanism in a certain limit and develops a mass gap at semi-classical level on a flat space with finite size or on a sphere.
Yang-Mills origin of gravitational symmetries
Anastasiou, A; Duff, M J; Hughes, L J; Nagy, S
2014-01-01
By regarding gravity as the convolution of left and right Yang-Mills theories, we derive in linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincar\\'e. As a concrete example we focus on the new-minimal (12+12) off-shell version of simple four-dimensional supergravity obtained by tensoring the off-shell Yang-Mills multiplets (4 + 4, N_L = 1) and (3 + 0, N_R = 0).
Wilson Loops in Noncommutative Yang Mills
Ishibashi, N; Kawai, H; Kitazawa, Y; Ishibashi, Nobuyuki; Iso, Satoshi; Kawai, Hikaru; Kitazawa, Yoshihisa
2000-01-01
We study the correlation functions of the Wilson loops in noncommutative Yang-Mills theory based upon its equivalence to twisted reduced models. We point out that there is a crossover at the noncommutativity scale. At large momentum scale, the Wilson loops in noncommmutative Yang-Mills represent extended objects. They coincide with those in ordinary Yang-Mills theory in low energy limit. The correlation functions on D-branes in IIB matrix model exhibit the identical crossover behavior. It is observed to be consistent with the supergravity description with running string coupling. We also explain that the results of Seiberg and Witten can be simply understood in our formalism.
Observables in Topological Yang-Mills Theories With Extended Shift Supersymmetry
Constantinidis, C P; Spalenza, W; Constantinidis, Clisthenis P.; Piguet, Olivier; Spalenza, Wesley
2006-01-01
We present a complete classification, at the classical level, of the observables of topological Yang-Mills theories with an extended shift supersymmetry of N generators, in any space-time dimension. The observables are defined as the Yang-Mills BRST cohomology classes of shift supersymmetry invariants. These cohomology classes turn out to be solutions of an N-extension of Witten's equivariant cohomology. This work generalizes results known in the case of shift supersymmetry with a single generator.
Special Geometries Emerging from Yang-Mills Type Matrix Models
Blaschke, Daniel N
2011-01-01
I review some recent results which demonstrate how various geometries, such as Schwarzschild and Reissner-Nordstroem, can emerge from Yang-Mills type matrix models with branes. Furthermore, explicit embeddings of these branes as well as appropriate Poisson structures and star-products which determine the non-commutativity of space-time are provided. These structures are motivated by higher order terms in the effective matrix model action which semi-classically lead to an Einstein-Hilbert type action.
HYM-flation: Yang-Mills cosmology with Horndeski coupling
Davydov, E
2016-01-01
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.
HYM-flation: Yang-Mills cosmology with Horndeski coupling
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.
Hagedorn spectrum and equation of state of Yang-Mills theories
Caselle, Michele; Panero, Marco
2015-01-01
We present a novel lattice calculation of the equation of state of SU(2) Yang-Mills theory in the confining phase. We show that a gas of massive, non-interacting glueballs describes remarkably well the results, provided that a bosonic closed-string model is used to derive an exponentially growing Hagedorn spectrum for the heavy glueball states with no free parameters. This effective model can be applied to SU(3) Yang-Mills theory and the theoretical prediction agrees nicely with the lattice results reported by Bors\\'anyi et al. in JHEP 07 (2012) 056.
Deconfinement in Yang-Mills Theory through Toroidal Compactification
Energy Technology Data Exchange (ETDEWEB)
Simic, Dusan; Unsal, Mithat; /Stanford U., Phys. Dept. /SLAC
2011-08-12
We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double-trace deformation of toroidally compactified Yang-Mills theory on R{sup 2} x S{sub L}{sup 1} x S{sub {beta}}{sup 1}. At large N, fixed-L, and arbitrary {beta}, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N, small L and a range of {beta}, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak regarding the magnetic component of the quark-gluon plasma at RHIC.
Supermembrane limit of Yang-Mills theory
Lechtenfeld, Olaf
2015-01-01
We consider Yang-Mills theory with $N{=}1$ super translation group in eleven auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold $\\Sigma_3\\times S^1$, where $\\Sigma_3$ is a three-dimensional Lorentzian manifold and $S^1$ is a circle. We show that in the infrared limit, when the metric on $S^1$ is scaled down, the Yang-Mills action supplemented by a Wess-Zumino-type term reduces to the action of an M2-brane.
Einstein-Yang-Mills-Lorentz Black Holes
Cembranos, Jose A R
2015-01-01
Different black hole solutions of the coupled Einstein-Yang-Mills equations are well known from long time. They have attracted much attention from mathematicians and physicists from their discovery. In this work, we analyze black holes associated with the gauge Lorentz group. In particular, we study solutions which identify the gauge connection with the spin connection. This ansatz allows to find exact solutions to the complete system of equations. By using this procedure, we show the equivalence between the Yang-Mills-Lorentz model in curved space-time and a particular set of extended gravitational theories.
Lectures on Supersymmetric Yang-Mills Theory and Integrable Systems
D'Hoker, Eric; Phong, D. H.
Introduction Supersymmetry and the Standard Model Supersymmetry and Unification of Forces Supersymmetric Yang-Mills Dynamics Supersymmetric Yang-Mills in 4 Dimensions Supersymmetry Algebra Massless Particle Representations Massive Particle Representations Field Contents of Supersymmetric Field Theories N = 1 Supersymmetric Lagrangians N = 1 Superfield Methods Irreducible Superfields of N = 1 General N = 1 Susy Lagrangians via Superfields Renormalizable N = 2,4 Susy Lagrangians N = 2 Superfield Methods: Unconstrained Superspace N = 2 Superfield Methods: Harmonic/Analytic Superspaces Seiberg-Witten Theory Wilson Effective Couplings and Actions Holomorphicity and Nonrenormalization Low Energy Dynamics of N = 2 Super-Yang-Mills Particle and Field Contents Form of the N = 2 Low Energy Effective Lagrangian Physical Properties of the Prepotential Electric-Magnetic Duality Monodromy via Elliptic Curves for SU(2) Gauge Group Physical Interpretation of Singularities Hypergeometric Function Representation More General Gauge Groups, Hypermultiplets Model of Riemann Surfaces Identifying Seiberg-Witten and Riemann Surface Data SU(N) Gauge Algebras, Fundamental Hypermultiplets Classical Gauge Algebras, Fundamental Hypermultiplets Mechanical Integrable Systems Lax Pairs with Spectral Parameter-Spectral Curves The Toda Systems The Calogero-Moser Systems for SU(N) Relation between Calogero-Moser and Toda for SU(N) Relations with KdV and KP Systems Calogero-Moser Systems for General Lie Algebras Scaling of Calogero-Moser to Toda for General Lie Algebras Calogero-Moser Lax Pairs for General Lie Algebras Lax Pairs with Spectral Parameter for Classical Lie Algebras The General Ansatz Lax Pairs for Untwisted Calogero-Moser Systems Lax Pairs for Twisted Calogero-Moser Systems Scaling Limits of Lax Pairs Super-Yang-Mills and Calogero-Moser Systems Correspondence of Seiberg-Witten and Integrable Systems Calogero-Moser and Seiberg-Witten Theory for SU(N) Four Fundamental Theorems Partial
Nonlinear Schrodinger solitons in massive Yang-Mills theory and partial localization of Dirac matter
Maintas, X N; Diakonos, F K; Frantzeskakis, D J
2013-01-01
We investigate the classical dynamics of the massive SU(2) Yang-Mills field in the framework of multiple scale perturbation theory. We show analytically that there exists a subset of solutions having the form of a kink soliton, modulated by a plane wave, in a linear subspace transverse to the direction of free propagation. Subsequently, we explore how these solutions affect the dynamics of a Dirac field possessing an SU(2) charge. We find that this class of Yang-Mills configurations, when regarded as an external field, leads to the localization of the fermion along a line in the transverse space. Our analysis reveals a mechanism for trapping SU(2) charged fermions in the presence of an external Yang-Mills field indicating the non-abelian analogue of Landau localization in electrodynamics.
Topological susceptibility in lattice Yang-Mills theory with open boundary condition
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, Abhishek; Harindranath, A. [Theory Division, Saha Institute of Nuclear Physics,1/AF Bidhan Nagar, Kolkata 700064 (India); Maiti, Jyotirmoy [Department of Physics, Barasat Government College,10 KNC Road, Barasat, Kolkata 700124 (India); Majumdar, Pushan [Department of Theoretical Physics, Indian Association for the Cultivation of Science,Kolkata 700032 (India)
2014-02-11
We find that using open boundary condition in the temporal direction can yield the expected value of the topological susceptibility in lattice SU(3) Yang-Mills theory. As a further check, we show that the result agrees with numerical simulations employing the periodic boundary condition. Our results support the preferability of the open boundary condition over the periodic boundary condition as the former allows for computation at smaller lattice spacings needed for continuum extrapolation at a lower computational cost.
Analytic representations of Yang-Mills amplitudes
Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L.; Damgaard, Poul H.; Feng, Bo
2016-12-01
Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space-fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Möbius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is the foundations of a systematic procedure to obtain analytic, covariant forms of Yang-Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.
Analytic Representations of Yang-Mills Amplitudes
Bjerrum-Bohr, N E J; Damgaard, Poul H; Feng, Bo
2016-01-01
Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space---fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Mobius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is a systematic procedure to obtain analytic, covariant forms of Yang-Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.
Higher derivative super Yang-Mills theories
Bergshoeff, E.; Rakowski, M.; Sezgin, E.
1987-01-01
The most general higher derivative Yang-Mills actions of the type (F^2 + Î±^2F^4) which are globally supersymmetric up to order Î±^2 in six- and ten-dimensional spacetimes are given. The F^4-terms turn out to occur in the combination Î±^2[tr F^4 - Â¼(tr F^2)^2], where the trace is over the Lorentz i
Twin Supergravities from Yang-Mills Squared
Anastasiou, A; Duff, M J; Hughes, M J; Marrani, A; Nagy, S; Zoccali, M
2016-01-01
We consider `twin supergravities' - pairs of supergravities with $\\mathcal{N}_+$ and $\\mathcal{N}_-$ supersymmetries, $\\mathcal{N}_+>\\mathcal{N}_-$, with identical bosonic sectors - in the context of tensoring super Yang-Mills multiplets. It is demonstrated that the pairs of twin supergravity theories are related through their left and right super Yang-Mills factors. This procedure generates new theories from old. In particular, the matter coupled $\\mathcal{N}_-$ twins in $D=3,5,6$ and the $\\mathcal{N}_-=1$ twins in $D=4$ have not, as far as we are aware, been obtained previously using the double-copy construction, adding to the growing list of double-copy constructible theories. The use of fundamental matter multiplets in the double-copy construction leads us to introduce a bi-fundamental scalar that couples to the well-known bi-adjoint scalar field. It is also shown that certain matter coupled supergravities admit more than one factorisation into left and right super Yang-Mills-matter theories.
Superstring limit of Yang-Mills theories
Lechtenfeld, Olaf; Popov, Alexander D.
2016-11-01
It was pointed out by Shifman and Yung that the critical superstring on X10 =R4 ×Y6, where Y6 is the resolved conifold, appears as an effective theory for a U(2) Yang-Mills-Higgs system with four fundamental Higgs scalars defined on Σ2 ×R2, where Σ2 is a two-dimensional Lorentzian manifold. Their Yang-Mills model supports semilocal vortices on R2 ⊂Σ2 ×R2 with a moduli space X10. When the moduli of slowly moving thin vortices depend on the coordinates of Σ2, the vortex strings can be identified with critical fundamental strings. We show that similar results can be obtained for the low-energy limit of pure Yang-Mills theory on Σ2 × Tp2, where Tp2 is a two-dimensional torus with a puncture p. The solitonic vortices of Shifman and Yung then get replaced by flat connections. Various ten-dimensional superstring target spaces can be obtained as moduli spaces of flat connections on Tp2, depending on the choice of the gauge group. The full Green-Schwarz sigma model requires extending the gauge group to a supergroup and augmenting the action with a topological term.
Dynamical Breaking of Generalized Yang-Mills Theory
Institute of Scientific and Technical Information of China (English)
WANGDian-Fu; SONGHe-Shan
2004-01-01
The dynamical breaking of a generalized Yang-Mills theory is discussed. It is shown, in terms of the Nambu Jona-Lasinio mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills theory. The combination of the generalized Yang-Mills theory and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.
Dynamical Breaking of Generalized Yang-Mills Theory
Institute of Scientific and Technical Information of China (English)
WANG Dian-Fu; SONG He-Shah
2004-01-01
The dynamical breaking of a generalized Yang-Mills theory is discussed. It is shown, in terms of the Nambu-Jona-Lasinio mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills theory. The combination of the generalized Yang-Mills theory and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.
HEAT FLOW FOR YANG-MILLS-HIGGS FIELDS, PART I
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The Yang-Mills-Higgs field generalizes the Yang-Mills field. The authors establish the local existence and uniqueness of the weak solution to the heat flow for the Yang-Mills-Higgs field in a vector bundle over a compact Riemannian 4-manifold, and show that the weak solution is gauge-equivalent to a smooth solution and there are at most finite singularities at the maximum existing time.
Confinement in a three-dimensional Yang-Mills theory
Frasca, Marco
2016-01-01
We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a confining theory. The potential we obtain agrees fairly well with preceding findings in literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depends on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory.
The exact decomposition of gauge variables in lattice Yang-Mills theory
Shibata, Akihiro; Kondo, Kei-Ichi; Shinohara, Toru
2010-07-01
In this Letter, we consider lattice versions of the decomposition of the Yang-Mills field a la Cho-Faddeev-Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU (N) gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU (2) and SU (3). As a result, we obtain the general form of the decomposition for SU (N) gauge link variables and confirm the previous results obtained for SU (2) and SU (3).
Yang-Mills theory in Coulomb gauge; Yang-Mills-theorie in Coulombeichung
Energy Technology Data Exchange (ETDEWEB)
Feuchter, C.
2006-07-01
In this thesis we study the Yang-Mills vacuum structure by using the functional Schroedinger picture in Coulomb gauge. In particular we discuss the scenario of colour confinement, which was originally formulated by Gribov. After a short introduction, we recall some basic aspects of Yang-Mills theories, its canonical quantization in the Weyl gauge and the functional Schroedinger picture. We then consider the minimal Coulomb gauge and the Gribov problem of the gauge theory. The gauge fixing of the Coulomb gauge is done by using the Faddeev-Popov method, which enables the resolution of the Gauss law - the constraint on physical states. In the third chapter, we variationally solve the stationary Yang-Mills Schroedinger equation in Coulomb gauge for the vacuum state. Therefor we use a vacuum wave functional, which is strongly peaked at the Gribov horizon. The vacuum energy functional is calculated and minimized resulting in a set of coupled Schwinger-Dyson equations for the gluon energy, the ghost and Coulomb form factors and the curvature in gauge orbit space. Using the angular approximation these integral equations have been solved analytically in both the infrared and the ultraviolet regime. The asymptotic analytic solutions in the infrared and ultraviolet regime are reasonably well reproduced by the full numerical solutions of the coupled Schwinger-Dyson equations. In the fourth chapter, we investigate the dependence of the Yang-Mills wave functional in Coulomb gauge on the Faddeev-Popov determinant. (orig.)
Perturbative spacetimes from Yang-Mills theory
Luna, Andres; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2016-01-01
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
String Scale in Noncommutative Yang-Mills
Ishibashi, N; Kawai, H; Kitazawa, Y
2000-01-01
We identify the effective string scale of noncommutative Yang-Mills theory (NCYM) with the noncommutativity scale through its dual supergravity description. We argue that Newton's force law may be obtained with 4 dimensional NCYM with maximal SUSY. It provides a nonperturbative compactification mechanism of IIB matrix model. We can associate NCYM with the von Neumann lattice by the bi-local representation. We argue that it is superstring theory on the von Neumann lattice. We show that our identification of its effective string scale is consistent with exact T-duality (Morita equivalence) of NCYM.
Duality in supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Peskin, M.E.
1997-02-01
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N{sub f} < N{sub c}, in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N{sub f} large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs.
Excluded-volume effects for a hadron gas in Yang-Mills theory
Alba, Paolo; Nada, Alessandro; Panero, Marco; Stöcker, Horst
2016-01-01
When the multiplicities of particles produced in heavy-ion collisions are fitted to the hadron-resonance-gas model, excluded-volume effects play a significant role. In this work, we study the impact of such effects onto the equation of state of pure Yang-Mills theory at low temperatures, comparing the predictions of the statistical model with lattice results. In particular, we present a detailed analysis of the SU(2) and SU(3) Yang-Mills theories: we find that, for both of them, the best fits to the equilibrium thermodynamic quantities are obtained when one assumes that the volume of different glueball states is inversely proportional to their mass. The implications of these findings for QCD are discussed.
Accurate Determination of Reference Scales for Wilson Gauge Action from Yang--Mills Gradient Flow
Asakawa, Masayuki; Iritani, Takumi; Itou, Etsuko; Kitazawa, Masakiyo; Suzuki, Hiroshi
2015-01-01
A high precision parametrization of the lattice spacing ($a$) in terms of the bare coupling ($\\beta$) for the SU(3) Yang--Mills theory with the Wilson gauge action is given in a wide range of $\\beta$ with high accuracy. The Yang--Mills gradient flow with respect to the flow time $t$ for the dimensionless observable, $t\\frac{d}{dt}t^2\\langle E(t)\\rangle$, is utilized to determine the parametrization. With fine lattice spacings ($6.3\\le\\beta\\le7.5$) and large lattice volumes ($N_{\\rm s}=64$--$128$), the discretization and finite-volume errors are significantly reduced to the same level as the statistical error. With this lattice setup, the lattice and perturbative estimates of $t^2\\langle E\\rangle$ are also compared as a function of $t$.
Universal aspects in the equation of state for Yang-Mills theories
Nada, Alessandro
2015-01-01
We present high-precision lattice calculations of the thermodynamics of Yang-Mills theories with different gauge groups. In the confining phase, we show that the equation of state is described remarkably well by a gas of massive, non-interacting glueballs, provided that an effective bosonic closed-string model is used to derive an exponentially growing Hagedorn spectrum for the heavy states. In particular, this model describes very accurately the results for the SU(3) theory reported by Bors\\'anyi et al. in JHEP 07 (2012) 056, as well as a novel set of lattice data for the SU(2) theory. In addition, we also also show that the equation of state in the deconfined phase exhibits a near perfect proportionality to the number of gluon degrees of freedom, including for the Yang-Mills theory based on the exceptional, center-less gauge group $G_2$.
Function group approach to unconstrained Hamiltonian Yang-Mills theory
Salmela, A
2004-01-01
Starting from the temporal gauge Hamiltonian for classical pure Yang-Mills theory with the gauge group SU(2) a canonical transformation is initiated by parametrising the Gauss law generators with three new canonical variables. The construction of the remaining variables of the new set proceeds through a number of intermediate variables in several steps, which are suggested by the Poisson bracket relations and the gauge transformation properties of these variables. The unconstrained Hamiltonian is obtained from the original one by expressing it in the new variables and then setting the Gauss law generators to zero. This Hamiltonian turns out to be local and it decomposes into a finite Laurent series in powers of the coupling constant.
Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory
DEFF Research Database (Denmark)
Caron-Huot, Simon; Henn, Johannes M.
2014-01-01
he classical Kepler problem, as well as its quantum mechanical version, the hydrogen atom, enjoys a well-known hidden symmetry, the conservation of the Laplace-Runge-Lenz vector, which makes these problems superintegrable. Is there a relativistic quantum field theory extension that preserves...... this symmetry? In this Letter we show that the answer is positive: in the nonrelativistic limit, we identify the dual conformal symmetry of planar N=4 super Yang-Mills theory with the well-known symmetries of the hydrogen atom. We point out that the dual conformal symmetry offers a novel way to compute...... the spectrum of bound states of massive W bosons in the theory. We perform nontrivial tests of this setup at weak and strong coupling and comment on the possible extension to arbitrary values of the coupling....
Chaotic behavior of the lattice Yang-Mills on CUDA
Directory of Open Access Journals (Sweden)
Forster Richárd
2015-12-01
Full Text Available The Yang-Mills fields plays important role in the strong interaction, which describes the quark gluon plasma. The non-Abelian gauge theory provides the theoretical background understanding of this topic. The real time evolution of the classical fields is derived by the Hamiltonian for SU(2 gauge field tensor. The microcanonical equations of motion is solved on 3 dimensional lattice and chaotic dynamics was searched by the monodromy matrix. The entropy-energy relation was presented by Kolmogorov-Sinai entropy. We used block Hessenberg reduction to compute the eigenvalues of the current matrix. While the purely CPU based algorithm can handle effectively only a small amount of values, the GPUs provide enough performance to give more computing power to solve the problem.
Deformations of Yang-Mills theory
Cofano, Marco; Krasnov, Kirill
2015-01-01
We introduce and study a new class of power-counting non-renormalisable gauge theories in four space-time dimensions. The Lagrangian is an arbitrary function of the self-dual part of the field strength. The resulting perturbation theory has the property that whenever two derivatives act on an internal line propagator, the result is a delta-function and the line collapses to a point. This means that there remains at most one derivative on each internal line, which gives improved ulta-violet behaviour. For many purposes, this class of theories behaves just like ordinary Yang-Mills theory. In particular, they all share the Yang-Mills theory MHV amplitudes. Moreover, these theories remain constructible in the sense that higher-point tree level scattering amplitudes can be obtained from the lower-point amplitudes using the BCFW recursion relations. Also, the square of these gauge-theory amplitudes gives the scattering amplitudes of "deformations" of General Relativity, at least for the low particle numbers that we...
Quantum Yang--Mills Dark Energy
Pasechnik, Roman
2016-01-01
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 co...
Nonperturbative aspects of Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Schleifenbaum, Wolfgang
2008-07-01
The subject of this thesis is the theory of strong interactions of quarks and gluons, with particular emphasis on nonperturbative aspects of the gluon sector. Continuum methods are used to investigate in particular the confinement phenomenon. Confinement which states that the elementary quarks and gluons cannot be detected as free particles requires an understanding of large-scale correlations. In perturbation theory, only short-range correlations can be reliably described. A nonperturbative approach is given by the set of integral Dyson Schwinger equations involving all Green functions of the theory. A solution for the gluon propagator is obtained in the infrared and ultraviolet asymptotic limits. In chapter 1, redundant degrees of freedom of the Yang Mills gauge theory are removed by fixing the Weyl and Coulomb gauge prior to quantization. The constrained quantization in the Dirac bracket formalism is then performed explicitly to produce the quantized Yang Mills Hamiltonian. The asymptotic infrared limits of Coulomb gauge correlation functions are studied analytically in chapter 2 in the framework of the Gribov Zwanziger confinement scenario. The Coulomb potential between heavy quarks as part of the Yang Mills Hamiltonian is calculated in this limit. A connection between the infrared limits of Coulomb and Landau gauge is established. The Hamiltonian derived paves the way in chapter 3 for finding the Coulomb gauge vacuum wave functional by means of the variational principle. Numerical solutions for the propagators in this vacuum state are discussed and seen to reproduce the anticipated infrared limit. The discussion is extended to the vertex functions. The effect of the approximations on the results is examined. Chapter 4 is mainly devoted to the ultraviolet behavior of the propagators. The discussion is issued in both Coulomb and Landau gauge. A nonperturbative running coupling is defined and calculated. The ultraviolet tails of the variational solutions from
Band Structure in Yang-Mills Theories
Bachas, Constantin
2016-01-01
We show how Yang-Mills theory on $S^3\\times R$ can exhibit a spectrum with continuous bands if coupled either to a topological 3-form gauge field, or to a dynamical axion with heavy Peccei-Quinn scale. The basic mechanism consists in associating winding histories to a bosonic zero mode whose role is to convert a circle in configuration space into a helix. The zero mode is, respectively, the holonomy of the 3-form field or the axion momentum. In these models different theta sectors coexist but are not mixed by local operators. Our analysis sheds light on, and extends Seiberg's proposal for modifying the topological sums in quantum field theories. It refutes a recent claim that $B+L$ violation at LHC is unsuppressed.
Quark confinement, new cosmic expansion and general Yang-Mills symmetry
Hsu, Jong-Ping
2017-01-01
We discuss a unified model of quark confinement and new cosmic expansion with linear potentials based on a general (SU 3)color×(U 1)baryon symmetry. The phase functions in the usual gauge transformations are generalized to new ‘action integrals’. The general Yang-Mills transformations have group properties and reduce to usual gauge transformations in special cases. Both quarks and ‘gauge bosons’ are permanently confined by linear potentials. In this unified model of particle-cosmology, physics in the largest cosmos and that in the smallest quark system appear to both be dictated by the general Yang-Mills symmetry and characterized by a universal length. The basic force between two baryons is independent of distance. However, the cosmic repulsive force exerted on a baryonic supernova by a uniform sphere of galaxies is proportional to the distance from the center of the sphere. The new general Yang-Mills field may give a field-theoretic explanation of the accelerated cosmic expansion. The prediction could be tested experimentally by measuring the frequency shifts of supernovae at different distances. Supported in part by the Jingshin Resealch Fund of the UMassD Foundation
Quark Confinement, New Cosmic Expansion and General Yang-Mills Symmetry
Hsu, Jong-Ping
2016-01-01
We discuss a unified model of quark confinement and new cosmic expansion with linear potentials based on a general $(SU_3)_{color} \\times (U_1)_{baryon}$ symmetry. The phase functions in the usual gauge transformations are generalized to new `action integrals'. The general Yang-Mills transformations have group properties and reduce to usual gauge transformations in special cases. Both quarks and `gauge bosons' are permanently confined by linear potentials. In this unified model of particle-cosmology, physics in the largest cosmos and that in the smallest quark system appear to both be dictated by the general Yang-Mills symmetry and characterized by a universal length. The basic force between two baryons is independent of distance. However, the cosmic repulsive force exerted on a baryonic supernova by a uniform sphere of galaxies is proportional to the distance from the center of the sphere. The new general Yang-Mills field may give a field-theoretic explanation of the accelerated cosmic expansion. The predict...
Vacuum structure and string tension in Yang-Mills dimeron ensembles
Zimmermann, Falk; Muller-Preussker, Michael
2012-01-01
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. In particular, we examine the extent to which these ensembles capture topological and confinement properties of the Yang-Mills vacuum. This further allows us to test the classic picture of meron-induced quark confinement as triggered by dimeron dissociation. At small bare couplings, spacial, topological-charge and color correlations among the dimerons generate a short-range order which screens topological charges. With increasing coupling this order weakens rapidly, however, in part because the dimerons gradually dissociate into their meron constituents. Monitoring confinement properties by evaluating Wilson-loop expectation values, we find the growing disorder due to these progressively liberated merons to generate a finite and (with the coupling) increasing string tension. The short-distance behavior of the static quark...
Yang-Mills Instanton Sheaves with Arbitrary Topological Charges
Lai, Sheng-Hong; Lai, I-Hsun
2016-01-01
We use a set of ADHM 3-instanton data to systematically construct a class of SU(2) Yang-Mills instanton solutions with arbitrary topological charges. Moreover, by using the biquaternion calculation with biconjugation operation developed recently, these new ADHM data are used to construct a class of SL(2,C) Yang-Mills instanton sheaves on CP^3 with arbitrary topological charges k greater than 3. This result extends the previous construction of Yang-Mills 2-instanton sheaves to arbitrary higher k-instanton sheaves.
The Parisi-Sourlas Mechanism in Yang-Mills Theory?
Magpantay, J A
2000-01-01
The Parisi-Sourlas mechanism is exhibited in pure Yang-Mills theory. Using the new scalar degrees of freedom derived from the non-linear gauge condition, we show that the non-perturbative sector of Yang-Mills theory is equivalent to a 4D O(1,3) sigma model in a random field. We then show that the leading term of this equivalent theory is invariant under supersymmetry transformations where (x^{2}+\\thetabar\\theta) is unchanged. This leads to dimensional reduction proving the equivalence of the non-perturbative sector of Yang-Mills theory to a 2D O(1,3) sigma model.
Noncommutative Yang-Mills in IIB Matrix Model
Aoki, H; Iso, S; Kawai, H; Kitazawa, Y; Tada, T
2000-01-01
We show that twisted reduced models can be interpreted as noncommutative Yang-Mills theory. Based upon this correspondence, we obtain noncommutative Yang-Mills theory with D-brane backgrounds in IIB matrix model. We propose that IIB matrix model with D-brane backgrounds serve as a concrete definition of noncommutative Yang-Mills. We investigate D-instanton solutions as local excitations on D3-branes. When instantons overlap, their interaction can be well described in gauge theory and AdS/CFT correspondence. We show that IIB matrix model gives us the consistent potential with IIB supergravity when they are well separated.
Particle motion in a Yang-Mills field Wong's equations and spin one-half analogues
Van Holten, J W
1995-01-01
A complete, straightforward and natural Lagrangian description is given for the classical non-relativistic dynamics of a particle with colour or internal symmetry degrees of freedom moving in a background Yang-Mills field. This provides a new simple Lagrangian formalism for Wong's equations for spinless particles, and presents also their generalisation, in gauge covariant form, for spin-\\frack particles, within a complete Lagrangian formalism.
Cylindrically symmetric Einstein-Yang-Mills-Higgs gauge configurations.
Mondaini, R. P.
1985-02-01
Two solutions are obtained for coupled Einstein-Yang-Mills-Higgs fields with cylindrical symmetry and rigid rotation. The Higgs fields are responsible for the creation of singularities and infinite energy densities at the cylinder's axis.
Gravity as the square of Yang-Mills?
Borsten, L
2016-01-01
In these lectures we review how the symmetries of gravitational theories may be regarded as originating from those of "Yang-Mills squared". We begin by motivating the idea that certain aspects of gravitational theories can be captured by the product, in some sense, of two distinct Yang-Mills theories, particularly in the context of scattering amplitudes. We then introduce a concrete dictionary for the covariant fields of (super)gravity in terms of the product of two (super) Yang-Mills theories. The dictionary implies that the symmetries of each (super) Yang-Mills factor generate the symmetries of the corresponding (super)gravity theory: general covariance, $p$-form gauge invariance, local Lorentz invariance, local supersymmetry, R-symmetry and U-duality.
A QCD Model Using Generalized Yang-Mills Theory
Institute of Scientific and Technical Information of China (English)
WANG Dian-Fu; SONG He-Shan; KOU Li-Na
2007-01-01
Generalized Yang-Mills theory has a covariant derivative,which contains both vector and scalar gauge bosons.Based on this theory,we construct a strong interaction model by using the group U(4).By using this U(4)generalized Yang-Mills model,we also obtain a gauge potential solution,which can be used to explain the asymptotic behavior and color confinement.
Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory
Kokenyesi, Zoltan; Szabo, Richard J
2016-01-01
We derive the analog of the large $N$ Gross-Taylor holomorphic string expansion for the refinement of $q$-deformed $U(N)$ Yang-Mills theory on a compact oriented Riemann surface. The derivation combines Schur-Weyl duality for quantum groups with the Etingof-Kirillov theory of generalized quantum characters which are related to Macdonald polynomials. In the unrefined limit we reproduce the chiral expansion of $q$-deformed Yang-Mills theory derived by de Haro, Ramgoolam and Torrielli. In the classical limit $q=1$, the expansion defines a new $\\beta$-deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit $\\beta=1$ to the orbifold Euler characteristics of Hurwitz spaces of holomorphic maps. We discuss the geometrical meaning of our expansions in relation to quantum spectral curves and $\\beta$-ensembles of matrix models arising in refined topological string theory.
On maximally supersymmetric Yang-Mills theories
Movshev, M
2004-01-01
We consider ten-dimensional supersymmetric Yang-Mills theory (10D SUSY YM theory) and its dimensional reductions, in particular, BFSS and IKKT models. We formulate these theories using algebraic techniques based on application of differential graded Lie algebras and associative algebras as well as of more general objects, L_{\\infty}- and A_{\\infty}- algebras. We show that using pure spinor formulation of 10D SUSY YM theory equations of motion and isotwistor formalism one can interpret these equations as Maurer-Cartan equations for some differential Lie algebra. This statement can be used to write BV action functional of 10D SUSY YM theory in Chern-Simons form. The differential Lie algebra we constructed is closely related to differential associative algebra Omega of (0, k)-forms on some supermanifold; the Lie algebra is tensor product of Omega and matrix algebra . We construct several other algebras that are quasiisomorphic to Omega and, therefore, also can be used to give BV formulation of 10D SUSY YM theory...
Curving Yang-Mills-Higgs Gauge Theories
Kotov, Alexei
2015-01-01
Established fundamental physics can be described by fields, which are maps. The source of such a map is space-time, which can be curved due to gravity. The map itself needs to be curved in its gauge field part so as to describe interaction forces like those mediated by photons and gluons. In the present article, we permit non-zero curvature also on the internal space, the target of the field map. The action functional and the symmetries are constructed in such a way that they reduce to those of standard Yang-Mills-Higgs (YMH) gauge theories precisely when the curvature on the target of the fields is turned off. For curved targets one obtains a new theory, a curved YMH gauge theory. It realizes in a mathematically consistent manner an old wish in the community: replacing structures constants by functions depending on the scalars of the theory. In addition, we provide a simple 4d toy model, where the gauge symmetry is abelian, but turning off the gauge fields, no rigid symmetry remains---another possible manife...
Generalisation of the Yang-Mills Theory
Savvidy, George
2015-01-01
We suggest an extension of the gauge principle which includes tensor gauge fields. In this extension of the Yang-Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The proposed extension is essentially based on the extension of the Poincar\\'e algebra and the existence of an appropriate transversal representations. The invariant Lagrangian is expressed in terms of new higher-rank field strength tensors. It does not contain higher derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with a dimensionless coupling constant. We calculated the scattering amplitudes of non-Abelian tensor gauge bosons at tree level, as well as their one-loop contribution into the Callan-Symanzik beta function. This contribution is negative and corresponds to the asymptotically free theory. Considering the contribution of tensorgluons of all spins into the beta function we found that it is leading to the theo...
Yang-Mills-Vlasov system in the temporal gauge. Systeme de Yang-Mills-Vlasov en jauge temporelle
Energy Technology Data Exchange (ETDEWEB)
Choquet-Bruhat, Y.; Noutchegueme, N. (Paris-6 Univ., 75 (FR))
1991-01-01
We prove a local in time existence theorem of a solution of the Cauchy problem for the Yang-Mills-Vlasov integrodifferential system. Such equations govern the evolution of plasmas, for instance of quarks and gluons (quagmas), where non abelian gauge fields and Yang-Mills charges replace the usual electromagnetic field and electric charge. We work with the temporal gauge and use functional spaces with appropriate weight on the momenta, but no fall off is required in the space direction.
Deconfinement in Yang-Mills theory through toroidal compactification with deformation
Simic, Dusan
2010-01-01
We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double- trace deformation of toroidally compactified Yang-Mills theory on R2 \\times S1_L \\times S1_{\\beta}. At large N, fixed-L, and arbitrary {\\beta}, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N, small L and a range of {\\beta}, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak regarding the magnetic comp...
Yelnykov, O V
2005-01-01
This thesis addresses three topics: calculation of the invariant measure for the pure Yang-Mills configuration space in (3 + 1) dimensions, Hamiltonian analysis of the pure Chern-Simons theory on the noncommutative plane and noncommutative quantum mechanics in the presence of singular potentials. In Chapter 1 we consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parameterized in terms of a matrix variable which facilitates the elimination of the gauge degrees of freedom. We develop an approximate calculation of the volume element on the gauge-invariant configuration space. We also make a rough estimate of the ratio of 0++ glueball mass and the square root of string tension by comparison with (2 + 1)-dimensional Yang-Mills theory. In Chapter 2 the Hamiltonian analysis of the pure Chern- Simons theory on the noncommutative plane is performed. We use the techniques of geometric quantization to show that the classical reduced phase space o...
Dark Matter from a Classically Scale-Invariant $SU(3)_X$
Karam, Alexandros
2016-01-01
In this work we study a classically scale-invariant extension of the Standard Model in which the dark matter and electroweak scales are generated through the Coleman-Weinberg mechanism. The extra $SU(3)_X$ gauge factor gets completely broken by the vevs of two scalar triplets. Out of the eight resulting massive vector bosons the three lightest are stable due to an intrinsic $Z_2\\times Z_2'$ discrete symmetry and can constitute dark matter candidates. We analyze the phenomenological viability of the predicted multi-Higgs sector imposing theoretical and experimental constraints. We perform a comprehensive analysis of the dark matter predictions of the model solving numerically the set of coupled Boltzmann equations involving all relevant dark matter processes and explore the direct detection prospects of the dark matter candidates.
Finite temperature and the Polyakov loop in the covariant variational approach to Yang-Mills Theory
Quandt, Markus; Reinhardt, Hugo
2017-03-01
We extend the covariant variational approach for Yang-Mills theory in Landau gauge to non-zero temperatures. Numerical solutions for the thermal propagators are presented and compared to high-precision lattice data. To study the deconfinement phase transition, we adapt the formalism to background gauge and compute the effective action of the Polyakov loop for the colour groups SU(2) and SU(3). Using the zero-temperature propagators as input, all parameters are fixed at T = 0 and we find a clear signal for a deconfinement phase transition at finite temperatures, which is second order for SU(2) and first order for SU(3). The critical temperatures obtained are in reasonable agreement with lattice data.
Covariant variational approach to Yang-Mills Theory: effective potential of the Polyakov loop
Quandt, Markus
2016-01-01
We compute the effective action of the Polyakov loop in SU(2) and SU(3) Yang-Mills theory using a previously developed covariant variational approach. The formalism is extended to background gauge and it is shown how to relate the low order Green's functions to the ones in Landau gauge studied earlier. The renormalization procedure is discussed. The self-consistent effective action is derived and evaluated using the numerical solution of the gap equation. We find a clear signal for a deconfinement phase transition at finite temperatures, which is second order for SU(2) and first order for SU(3). The critical temperatures obtained are in reasonable agreement with high precision lattice data.
Quantization Near Violent Singularities in Einstein-Yang-Mills Black Holes
Galtsov, D V
2001-01-01
Classical singularities inside black holes in the Einstein-Yang-Mills theory exhibit unusual features. Only for discrete values of the black hole mass one encounters singularities of the Schwarzschild type (timelike) and the Reissner-Nordstrom type (spacelike). For a generic mass the approach to singularity is not smooth: the metric oscillates with an infinitely growing amplitude and decreasing period. In spite of some similarity with the BKL oscillations, here the behavior is not chaotic. However the oscillation amplitude exceeds classical limits after few cycles, so the question arises how this behavior gets modified by quantum effects. We discuss this issue both in the framework of QFT and in the string theory.
Exact, Schwarzschild-like solution for Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Singleton, D.
1995-04-01
Exploiting the connection between general relativity and Yang-Mills theory an exact, Schwarzchild-like solution is given for an SU(N) gauge field coupled to a scalar field in the Bogomolny, Prasad, Sommerfield limit. The SU(2) solution is found using the second order Euler-Lagrange formalism, while the SU(N) generalization is given using the first order Bogomolny formalism. In analogy with the Schwarzschild solution of general relativity, these Yang-Mills solutions possess an event horizon with respect to the SU(N) charge. It is conjectured that this may be the confinement mechanism for QCD, since just as a Schwarzschild black hole will permanently confine anything which carries the charge of general relativity (mass-energy), so this Yang-Mills solution will confine any particle which carries the SU(N) charge.
Quantum Yang-Mills theory: an overview of a programme
Milsted, Ashley
2016-01-01
We present an overview of a programme to understand the low-energy physics of quantum Yang-Mills theory from a quantum-information perspective. Our setting is that of the hamiltonian formulation of pure Yang-Mills theory in the temporal gauge on the lattice. Firstly, inspired by recent constructions for $\\mathbb{Z}/2\\mathbb{Z}$ lattice gauge theory, in particular, Kitaev's toric code, we describe the gauge-invariant sector of hilbert space by introducing a primitive quantum gate: the quantum parallel transporter. We then develop a nonabelian generalisation of laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling RG fixed points. The resulting state acquires the structure of a tensor network, namely, a multiscale entanglement renormalisation ansatz, and allows for the efficient computation of local observables and Wilson loops. Various refinements of the tensor network are discussed leading to several generalisations. ...
A tree-level 3-point function in the su(3)-sector of planar N=4 SYM
Foda, Omar; Kostov, Ivan; Serban, Didina
2013-01-01
We classify the 3-point functions of local gauge-invariant single-trace operators in the scalar sector of planar N=4 supersymmetric Yang-Mills involving at least one su(3) operator. In the case of two su(3) and one su(2) operators, the tree-level 3-point function can be expressed in terms of scalar products of su(3) Bethe vectors. Moreover, if the second level Bethe roots of one of the su(3) operators is trivial (set to infinity), this 3-point function can be written in a determinant form. Using the determinant representation, we evaluate the structure constant in the semi-classical limit, when the number of roots goes to infinity.
Equivariance on Discrete Space and Yang-Mills-Higgs Model
Ikemori, Hitoshi; Matsui, Yoshimitsu; Otsu, Hideharu; Sato, Toshiro
2015-01-01
We introduce the basic equivariant quantity $Q$ in the gauge theory on the noncommutative descrete $Z_{2}$ space, which plays an important role for the equivariant dimensional reduction. If the gauge configuration of the ground state on the extra dimensional space is described by the equivariant $Q$, then the extra dimensional space is invisible. Especially, using the equivariance principle, we show that the Yang-Mills theory on $R^{2}\\times Z_{2}$ space is equivalent to the Yang-Mills-Higgs model on $R^{2}$ space. It can be said that this model is the simplest model of this type.
All tree amplitudes of supersymmetric Einstein-Yang-Mills theory
Adamo, Tim; Roehrig, Kai A; Skinner, David
2015-01-01
We present a new formula for all tree amplitudes in four dimensional supergravity coupled to super Yang-Mills. Like the Cachazo-He-Yuan formula, our expression is supported on solutions of the scattering equations, but with momenta written in terms of spinor helicity variables. Supersymmetry and parity are both manifest. In the pure gravity and pure Yang-Mills sectors, it reduces to the known twistor-string formulae. We show that the formula behaves correctly under factorization. We sketch how these amplitudes may be obtained from a four-dimensional (ambi)twistor string.
Field-dependent BRST transformations in Yang-Mills theory
Lavrov, Peter M
2013-01-01
We find an explicit form for the Jacobian of arbitrary field-dependent BRST transformations in Yang-Mills theory. For the functional-integral representation of the (gauge-fixed) Yang-Mills vacuum functional, such transformations merely amount to a precise change in the gauge-fixing functional. This proves the independence of the vacuum functional under any field-dependent BRST transformation. We also give a formula for the transformation parameter functional which generates a prescribed change of gauge and evaluate it for connecting two arbitrary R_xi gauges.
Field-dependent BRST transformations in Yang-Mills theory
Lavrov, Peter M.; Lechtenfeld, Olaf
2013-10-01
We find an explicit form for the Jacobian of arbitrary field-dependent BRST transformations in Yang-Mills theory. For the functional-integral representation of the (gauge-fixed) Yang-Mills vacuum functional, such transformations merely amount to a precise change in the gauge-fixing functional. This proves the independence of the vacuum functional under any field-dependent BRST transformation. We also give a formula for the transformation parameter functional which generates a prescribed change of gauge and evaluate it for connecting two arbitrary Rξ gauges.
Testing the Witten-Veneziano mechanism with the Yang-Mills gradient flow on the lattice
Cè, Marco; Engel, Georg P; Giusti, Leonardo
2014-01-01
We present a precise computation of the topological charge distribution in the $SU(3)$ Yang-Mills theory. It is carried out on the lattice with high statistics Monte Carlo simulations by employing the clover discretization of the field strength tensor combined with the Yang-Mills gradient flow. The flow equations are integrated numerically by a fourth-order structure-preserving Runge-Kutta method. We have performed simulations at four lattice spacings and several lattice sizes to remove with confidence the systematic errors in the second (topological susceptibility $\\chi_t^\\text{YM}$) and the fourth cumulant of the distribution. In the continuum we obtain the preliminary results $t_0^2\\chi_t^\\text{YM}=6.53(8)\\times 10^{-4}$ and the ratio between the fourth and the second cumulant $R=0.233(45)$. Our results disfavour the $\\theta$-behaviour of the vacuum energy predicted by dilute instanton models, while they are compatible with the expectation from the large-$N_c$ expansion.
Lagrangian multiplier and massive Yang-Mills fields
Energy Technology Data Exchange (ETDEWEB)
Li, Z.P.
1982-09-01
If we give appropriate constraint to the gauge invariant Lagrangian, the variation principle of the action convert to the variational problems with subsidiary condition. The effective Lagrangian which contains Lagrangian multiplier may have the mass term of the mesons. In that case we obtain naturally the massive Yang-Mills fields which was discussed by Nakanishi.
Eigenvalue spectrum of lattice N=4 super Yang-Mills
Weir, D.; Catterall, S.; Mehta, D. B.
We present preliminary results for the eigenvalue spectrum of four-dimensional ${\\cal N}=4$ super Yang-Mills theory on the lattice. In particular, by studying the the spectral density a measurement of the anomalous dimension is made and found to be consistent with zero.
Coset space dimensional reduction of Einstein-Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Chatzistavrakidis, A. [Institute of Nuclear Physics, NCSR Demokritos, 15310 Athens (Greece); Physics Department, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece); Manousselis, P. [Physics Department, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece); Department of Engineering Sciences, University of Patras, 26110 Patras (Greece); Prezas, N. [Theory Unit, Physics Department, 1211 Geneva (Switzerland); Zoupanos, G.
2008-04-15
In the present contribution we extend our previous work by considering the coset space dimensional reduction of higher-dimensional Einstein-Yang-Mills theories including scalar fluctuations as well as Kaluza-Klein excitations of the compactification metric and we describe the gravity-modified rules for the reduction of non-abelian gauge theories. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
Internal Structure of Einstein-Yang-Mills Black Holes
Donets, E. E.; Gal'tsov, D. V.; Zotov, M. Yu.
1996-01-01
It is shown that a generic black hole solution of the SU(2) Einstein-Yang-Mills equations develops a new type of an infinitely oscillating behavior near the singularity. Only for certain discrete values of the event horizon radius exceptional solutions exist, possessing an inner structure of the Schwarzschild or Reissner-Nordstrom type.
Internal Structure of Einstein-Yang-Mills Black Holes
Donets, E E; Zotov, M Yu
1996-01-01
Interior solutions for the SU(2) Einstein-Yang-Mills black holes are investigated. It is found that generically the metric does not possess inner Cauchy horizons and infinitely oscillates near the singularity. However, for certain discrete radii of the event horizon exceptional solutions exist with an inner structure of the Schwarzschild (n=1) or Reissner--Nordstrom (n=2,3,...) type.
5D Maximally Supersymmetric Yang-Mills on the Lattice
Joseph, Anosh
2016-01-01
We provide details of the lattice construction of five-dimensional maximally supersymmetric Yang-Mills theory. The lattice theory is supersymmetric, gauge invariant and free from spectrum doublers. Such a supersymmetric lattice formulation is interesting as it can be used for non-perturbative explorations of the five-dimensional theory, which has a known gravitational dual.
A nonperturbative method for the Yang Mills Lagrangian
Jora, Renata
2014-01-01
Using the properties of the partition function for a Yang Mills theory we compute simple relations among the renormalization constants. In the particular case of the background gauge field method we obtain that the all orders beta function for the gauge coupling constant contains only the first two orders coefficients different than zero and thus corresponds to the 't Hooft scheme.
Phase structure of lattice N=4 super Yang-Mills
DEFF Research Database (Denmark)
Catterall, Simon; Damgaard, Poul H.; DeGrand, Thomas;
2012-01-01
We make a first study of the phase diagram of four-dimensional N = 4 super Yang-Mills theory regulated on a space-time lattice. The lattice formulation we employ is both gauge invariant and retains at all lattice spacings one exactly preserved supersymmetry charge. Our numerical results are consi...
N=4 Supersymmetric Yang-Mills Theory on Orbifold-$T^4/{\\bf Z}_2$
Jinzenji, M; Jinzenji, Masao; Sasaki, Toru
2001-01-01
We derive the partition function of N=4 supersymmetric Yang-Mills theory on orbifold-$T^4/{\\bf Z}_2$. In classical geometry, K3 surface is constructed from the orbifold-$T^4/{\\bf Z}_2$. Along the same way as the orbifold construction, we construct the partition function of K3 surface from orbifold-$T^4/{\\bf Z}_2$. The partition function is given by the product of the contribution of the untwisted sector of $T^4/{\\bf Z}_2$, and that of the twisted sector of $T^4/{\\bf Z}_2$ i.e., ${\\cal O}(-2)$ curve blow-up formula.
Yang-Mills theory as bimetrical gravity: Polarization effects and finite-energy gluon clusters
Energy Technology Data Exchange (ETDEWEB)
Pavlovsky, Oleg V
2002-01-01
In this report a gravity representation of Yang-Mills theory is given. Using this approach, one obtains new information on solutions of classical YM theory. Singular solutions (black-hole-like solutions) of the YM equations are discussed in connection with bimetrical gravity. The behaviour of these solutions in a theory with a 'cosmological' Lambda-part is also investigated. A physical interpretation of such solutions is given. Using an effective field theory approach we try to show that quantum fluctuations and vacuum polarization effects lead to the generation of finite-energy objects in QCD.
Spinors, strings, integrable models, and decomposed Yang-Mills theory
Ioannidou, Theodora; Jiang, Ying; Niemi, Antti J.
2014-07-01
This paper deals with various interrelations between strings and surfaces in three-dimensional ambient space, two-dimensional integrable models, and two-dimensional and four-dimensional decomposed SU(2) Yang-Mills theories. Initially, a spinor version of the Frenet equation is introduced in order to describe the differential geometry of static three-dimensional stringlike structures. Then its relation to the structure of the su_(2) Lie algebra valued Maurer-Cartan one-form is presented, while by introducing time evolution of the string a Lax pair is obtained, as an integrability condition. In addition, it is shown how the Lax pair of the integrable nonlinear Schrödinger equation becomes embedded into the Lax pair of the time extended spinor Frenet equation, and it is described how a spinor-based projection operator formalism can be used to construct the conserved quantities, in the case of the nonlinear Schrödinger equation. Then the Lax pair structure of the time extended spinor Frenet equation is related to properties of flat connections in a two-dimensional decomposed SU(2) Yang-Mills theory. In addition, the connection between the decomposed Yang-Mills and the Gauß-Codazzi equation that describes surfaces in three-dimensional ambient space is presented. In that context the relation between isothermic surfaces and integrable models is discussed. Finally, the utility of the Cartan approach to differential geometry is considered. In particular, the similarities between the Cartan formalism and the structure of both two-dimensional and four-dimensional decomposed SU(2) Yang-Mills theories are discussed, while the description of two-dimensional integrable models as embedded structures in the four-dimensional decomposed SU(2) Yang-Mills theory are presented.
Exact momentum fluctuations of an accelerated quark in N=4 super Yang-Mills
Fiol, Bartomeu; Torrents, Genis
2013-01-01
In this work we consider a heavy quark moving with constant proper acceleration in the vacuum of any four dimensional conformal field theory. We argue that the two-point function of its momentum fluctuations is exactly captured by the Bremsstrahlung function that gives the total radiated power. For the particular case of N=4 SU(N) SYM this function is exactly known, so in this case we obtain an explicit expression for the momentum diffusion coefficient, and check that various limits of this result are reproduced by probe computations in AdS_5. Finally, we evaluate this transport coefficient for a heavy quark accelerated in the vacuum of N=4 SU(3) SYM, and comment on possible lessons of our results for the study of heavy quarks traversing the super Yang-Mills plasma.
Energy-momentum tensor on the lattice: non-perturbative renormalization in Yang--Mills theory
Giusti, Leonardo
2015-01-01
We construct an energy-momentum tensor on the lattice which satisfies the appropriate Ward Identities (WIs) and has the right trace anomaly in the continuum limit. It is defined by imposing suitable WIs associated to the Poincare` invariance of the continuum theory. These relations come forth when the length of the box in the temporal direction is finite, and they take a particularly simple form if the coordinate and the periodicity axes are not aligned. We implement the method for the SU(3) Yang--Mills theory discretized with the standard Wilson action in presence of shifted boundary conditions in the (short) temporal direction. By carrying out extensive numerical simulations, the renormalization constants of the traceless components of the tensor are determined with a precision of roughly half a percent for values of the bare coupling constant in the range 0<= g^2_0<=1.
Integrable open spin chain in super Yang-Mills and the plane-wave/SYM duality
Chen, Bin; Wang, Xiao-Jun; Wu, Yong-Shi
2004-02-01
We investigate the integrable structures in an Script N = 2 superconformal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the closed string sector, an integrable structure is inherited from its parent theory, Script N = 4 SYM. For the open string sector, the planar one-loop mixing matrix for gauge invariant holomorphic scalar operators is identified with the hamiltonian of an integrable SU(3) open spin chain. Using the K-matrix formalism we identify the integrable open-chain boundary conditions that correspond to string boundary conditions. The solutions to the algebraic Bethe ansatz equations (ABAE) with a few impurities are shown to recover the anomalous dimensions that exactly match the spectrum of free open string in the plane-wave background. We also discuss the properties of the solutions of ABAE beyond the BMN regime.
Integrable Open Spin Chain in Super Yang-Mills and the Plane-wave/SYM duality
Chen, B; Wu, Y S; Chen, Bin; Wang, Xiao-Jun; Wu, Yong-Shi
2004-01-01
We investigate the integrable structures in an N=2 superconfomal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the closed string sector, an integrable structure is inherited from its parent theory, N=4 SYM. For the open string sector, the planar one-loop mixing matrix for gauge invariant holomorphic operators is identified with the Hamiltonian of an integrable SU(3) open spin chain. Using the K-matrix formalism we identify the integrable open-chain boundary conditions that correspond to string boundary conditions. The solutions to the algebraic Bethe ansatz equations (ABAE) with a few impurities are shown to recover the anomalous dimensions that exactly match the spectrum of free open string in the plane-wave background. We also discuss the properties of the solutions of ABAE beyond the BMN regime.
Topological susceptibility in the SU(3) gauge theory
DEFF Research Database (Denmark)
Del Debbio, Luigi; Giusti, Leonardo; Pica, Claudio
2004-01-01
We compute the topological susceptibility for the SU(3) Yang--Mills theory by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3), which corresponds to chi=(191 +/- 5 MeV)^4 if F_K is used to se...
Towards a Loop Quantum Gravity and Yang-Mills unification
Energy Technology Data Exchange (ETDEWEB)
Alexander, Stephon, E-mail: stephonalexander@mac.com [Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755 (United States); Department of Physics and Astronomy, Haverford College, Haverford, PA 19041 (United States); Department of Physics, Princeton University, NJ 08544 (United States); Institute for Gravitation and the Cosmos, Department of Physics, Penn State, University Park, PA 16802 (United States); Marciano, Antonino [Department of Physics and Astronomy, Haverford College, Haverford, PA 19041 (United States); Department of Physics, Princeton University, NJ 08544 (United States); Tacchi, Ruggero Altair [Department of Physics, University of California, Davis, CA 95616 (United States)
2012-09-19
We propose a new method of unifying gravity and the Standard Model by introducing a spin-foam model. We realize a unification between an SU(2) Yang-Mills interaction and 3D general relativity by considering a constrained Spin(4){approx}SO(4) Plebanski action. The theory is quantized a la spin-foam by implementing the analogue of the simplicial constraints for the Spin(4) symmetry, providing a way to couple Yang-Mills fields to spin-foams. A natural 4D extension of the theory is introduced. We also present a way to recover 2-point correlation functions between the connections as a first way to implement scattering amplitudes between particle states, aiming to connect Loop Quantum Gravity to new physical predictions.
Emergent Yang-Mills Theories from Universal Extra Dimensions
Chkareuli, J L
2016-01-01
We study emergent Yang-Mills theories which could origin from universal extra dimensions. Particularly, some vector field potential terms or polynomial vector field constraints introduced into five-dimensional non-Abelian gauge theory is shown to lead to spontaneous violation of an underlying spacetime symmetry and generate vector pseudo-Goldstone modes as conventional 4D gauge boson candidates. As a special signature, apart from conventional gauge couplings, there appear an infinite number of the properly suppressed direct multi-boson (multi-photon in particular) interaction couplings in emergent Yang-Mills theories whose observation could shed light on their high-dimensional nature. Moreover, in these theories an internal symmetry is also appeared spontaneously broken to its diagonal subgroups. This breaking origins from the extra vector field components playing a role of some adjoint scalar field multiplet in the 4D spacetime. So, one naturally has the Higgs effect without a specially introduced scalar fie...
Spectroscopy of two dimensional N=2 Super Yang Mills theory
August, Daniel; Wipf, Andreas
2016-01-01
Albeit the standard model is the most successful model of particles physics, it still has some theoretical shortcomings, for instance the hierarchy problem, the absence of dark matter, etc. Supersymmetric extensions of the standard model could be a possible solution to these problems. One of the building blocks of these supersymmetric models are supersymmetric gauge theories. It is expected that they exhibit interesting features like confinement, chiral symmetry breaking, magnetic monopoles and the like. We present new results on N=2 Super Yang Mills theory in two dimensions. The lattice action is derived by a dimensional reduction of the N=1 Super Yang Mills theory in four dimensions. By preserving the R symmetry of the four dimensional model we can exploit Ward identities to fine tune our parameters of the model to obtain the chiral and supersymmetric continuum limit. This allows us to calculate the mass spectrum at the physical point and compare these results with effective field theories.
Einstein-Yang-Mills solitons towards new degrees of freedom
Galtsov, D V
1998-01-01
A recent progress in obtaining non-spherical and non-static solitons in the four-dimensional Einstein--Yang--Mills (EYM) theory is discussed, and a non-perturbative formulation of the stationary axisymmetric problem is attempted. First a 2D dilaton gravity model is derived for the spherically symmetric time-dependent configurations. Then a similar Euclidean representation is constructed for the stationary axisymmetric non-circular SU(2) EYM system using the (2+1)+1 reduction scheme suggested by Maeda, Sasaki, Nakamura and Miyama. The crucial role in this reduction is played by the extra terms entering the reduced Yang--Mills and Kaluza--Klein two-forms similarly to Chern--Simons terms in the theories with higher rank antisymmetric tensor fields. We also derive a simple 2D action describing static axisymmetric magnetic EYM configurations and discuss a possibility of existence of cylindrical EYM sphalerons.
Currents and anomalies in topological Yang-Mills theory
Dahmen, H. D.; Marculescu, S.; Szymanowski, L.
1992-09-01
The quantum properties of topological Yang-Mills theory are investigated in the light of the N = 2 supersymmetry observed in flat space. We construct a unique system of covariantly (partially) conserved currents which develop anomalies while preserving BRS invariance of the theory. In particular, the one-loop renormalized energy-momentum tensor is free of purely gravitational contributions and can be written as a BRS variation. We study the consequences of changing the renormalization prescriptions inherited from the N = 2 supersymmetry to those consistent with BRS. Most of our conclusions are verified by explicit calculations. As a byproduct we derive the formula of Atiyah, Hitchin and Singer for the dimension of the moduli space of self-dual Yang-Mills fields. Finally strong arguments are given that the full system of Donaldson polynomials and the quantum BRS current are not renormalized beyond one-loop.
BRST symmetric gaugeon formalism for Yang-Mills fields
Koseki, M; Endo, R
1995-01-01
Yokoyama's gaugeon formalism is knwon to admit q-number gauge transformation. We introduce BRST symmetries into the formalism for the Yang-Mills gauge field. Owing to the BRST symmetry, Yokoyama's physical subsidiary conditions are replaced by a single condition of the Kugo-Ojima type. Our physical subsidiary condition is invariant under the q-number gauge transformation. Thus, our physical subspace is gauge invariant.
Slavnov determinants, Yang-Mills structure constants, and discrete KP
Foda, O
2012-01-01
Using Slavnov's scalar product of a Bethe eigenstate and a generic state in closed XXZ spin-1/2 chains, with possibly twisted boundary conditions, we obtain determinant expressions for tree-level structure constants in 1-loop conformally-invariant sectors in various planar (super) Yang-Mills theories. When certain rapidity variables are allowed to be free rather than satisfy Bethe equations, these determinants become discrete KP tau-functions.
Induced mass in N=2 super Yang-Mills theories
Araújo-Diniz, S; Diniz, Sortelano A.; Piguet, Olivier
2003-01-01
The masses of the matter fields of N=2 Super-Yang-Mills theories can be defined as parameters of deformed supersymmetry transformations. The formulation used involves central charges for the matter fields. The explicit form of the deformed supersymmetry transformations and of the invariant Lagrangian in presence of the gauge supermultiplet are constructed. This works generalizes a former one, due to the same authors, which presented the free matter case.
Dynamical CP violation of the generalized Yang-Mills model
Institute of Scientific and Technical Information of China (English)
WANG Dian-Fu; SUN Xiao-Yu; CHANG Xiao-Jing
2011-01-01
Starting from the generalized Yang-Mills model which contains, besides the vector part Vμ, also a scalar part S and a pseudoscalar part P. It is shown, in terms of the Nambu-Jona-Lasinio (NJL) mechanism,that CP violation can be realized dynamically. The combination of the generalized Yang-MiUs model and the NJL mechanism provides a new way to explain CP violation.
Asymptotic freedom of Yang-Mills theory with gravity
Folkerts, Sarah; Pawlowski, Jan M
2011-01-01
We study the high energy behaviour of Yang-Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.
Asymptotic freedom of Yang-Mills theory with gravity
Energy Technology Data Exchange (ETDEWEB)
Folkerts, Sarah, E-mail: Sarah.Folkerts@physik.uni-muenchen.de [Institut f. Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); Litim, Daniel F. [Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH (United Kingdom); Pawlowski, Jan M. [Institut f. Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); ExtreMe Matter Inst. EMMI, GSI, Planckstr. 1, 64291 Darmstadt (Germany)
2012-03-19
We study the behaviour of Yang-Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.
The local renormalization of super-Yang-Mills theories
Gillioz, Marc
2016-01-01
We show how to consistently renormalize $\\mathcal{N} = 1$ and $\\mathcal{N} = 2$ super-Yang-Mills theories in flat space with a local (i.e. space-time-dependent) renormalization scale in a holomorphic scheme. The action gets enhanced by a term proportional to derivatives of the holomorphic coupling. In the $\\mathcal{N} = 2$ case, this new action is exact at all orders in perturbation theory.
Continuous Family of Einstein-Yang-Mills Wormholes
Donets, E E
1992-01-01
It is shown that for some particular value of the cosmological constant depending on the gauge coupling constant a continuous one-parameter family of Einstein-Yang-Mills wormholes exists which interpolates between the instanton and the gravitating meron solutions. In contradistinction with the previously known solutions the topological charge of these wormholes is not quantized. For all of them the contribution of gravity to the action exactly cancels that of the gauge field.
Regge trajectories in {N} = 2 supersymmetric Yang-Mills theory
Córdova, Clay
2016-09-01
We demonstrate that {N} = 2 supersymmetric non-Abelian gauge theories have towers of BPS particles obeying a Regge relation, J ˜ m 2, between their angular momenta, J, and their masses, m. For SU( N) Yang-Mills theories, we estimate the slope of these Regge trajectories using a non-relativistic quiver quantum mechanics model. Along the way, we also prove various structure theorems for the quiver moduli spaces that appear in the calculation.
A Curious Relation Between Gravity and Yang-Mills Theories
Baulieu, L
2000-01-01
We find that Euclidian or Minkowski gravity in d dimensions can be formally expressed as the restriction to a slice of a supersymmetric Yang-Mills theory in d+1 dimensions with SO(d+1), SO(d,1) or SO(d-1,2) internal symmetry. We suggest that renormalization effects in the bulk imply a contraction of the latter symmetry into the Poincare group ISO(d) or ISO(d-1,1).
New Results on N=4 SuperYang-Mills Theory
Baulieu, L; Baulieu, Laurent; Bossard, Guillaume
2005-01-01
The N=4 SuperYang--Mills theory is covariantly determined by a U(1) \\times SU(2) \\subset SL(2,R) \\times SU(2) internal symmetry and two scalar and one vector BRST topological symmetry operators. This determines an off-shell closed sector of N=4 SuperYang-Mills, with 6 generators, which is big enough to fully determine the theory, in a Lorentz covariant way. This reduced algebra derives from horizontality conditions in four dimensions. The horizontality conditions only depend on the geometry of the Yang-Mills fields. They also descend from a genuine horizontality condition in eight dimensions. In fact, the SL(2,R) symmetry is induced by a dimensional reduction from eight to seven dimensions, which establishes a ghost-antighost symmetry, while the SU(2) symmetry occurs by dimensional reduction from seven to four dimensions. When the four dimensional manifold is hyperKahler, one can perform a twist operation that defines the N=4 supersymmetry and its SL(2,H)\\sim SU(4) R-symmetry in flat space. (For defining a TQ...
Magnetic Yang-Mills Theory of the Gluon Plasma
Baker, M
2009-01-01
We propose magnetic SU(N) pure gauge theory as an effective field theory describing the long distance nonperturbative magnetic response of the deconfined phase of Yang-Mills theory. The magnetic non-Abelian Lagrangian, unlike that of electrodynamics where there is exact electromagnetic duality, is not known explicitly, but here we regard the magnetic SU(N) Yang-Mills Lagrangian as the leading term in the long distance effective gauge theory of the plasma phase. In this treatment, which is applicable for a range of temperatures in the interval T_c < T < 3 T_c accessible in heavy ion experiments, formation of the magnetic energy profile around a spatial Wilson loop in the deconfined phase parallels the formation of an electric flux tube in the confined phase. We use the effective theory to calculate spatial Wilson loops and the magnetic charge density induced in the plasma by the corresponding color electric current loops. These calculations suggest that the deconfined phase of Yang-Mills theory has the p...
New relations for Einstein-Yang-Mills amplitudes
Stieberger, Stephan; Taylor, Tomasz R.
2016-12-01
We obtain new relations between Einstein-Yang-Mills (EYM) amplitudes involving N gauge bosons plus a single graviton and pure Yang-Mills amplitudes involving N gauge bosons plus one additional vector boson inserted in a way typical for a gauge boson of a "spectator" group commuting with the group associated to original N gauge bosons. We show that such EYM amplitudes satisfy U(1) decoupling relations similar to Kleiss-Kuijf relations for Yang-Mills amplitudes. We consider a D-brane embedding of EYM amplitudes in the framework of disk amplitudes involving open and closed strings. A new set of monodromy relations is derived for mixed open-closed amplitudes with one closed string inserted on the disk world-sheet and a number of open strings at the boundary. These relations allow expressing the latter in terms of pure open string amplitudes and, in the field-theory limit, they yield the U(1) decoupling relations for EYM amplitudes.
Regular and chaotic classical dynamics in the U(5)-SU(3) quantum phase transition of the IBM
Macek, M
2012-01-01
We study the classical dynamics in a generic first-order quantum phase transition between the U(5) and SU(3) limits of the interacting boson model. The dynamics is chaotic, of H\\'enon-Heiles type, in the spherical phase and is regular, yet sensitive to local degeneracies, in the deformed phase. Both types of dynamics persist in the coexistence region resulting in a divided phase space.
Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Koekenyesi, Zoltan; Sinkovics, Annamaria [Institute of Theoretical Physics, MTA-ELTE Theoretical Research Group, Eoetvoes Lorand University, 1117, Budapest, Pazmany, s. 1/A (Hungary); Szabo, Richard J. [Heriot-Watt Univ., Edinburgh (United Kingdom). Dept. of Mathematics; Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom); The Higgs Centre for Theoretical Physics, Edinburgh (United Kingdom)
2016-11-15
We derive the analog of the large N Gross-Taylor holomorphic string expansion for the refinement of q-deformed U(N) Yang-Mills theory on a compact oriented Riemann surface. The derivation combines Schur-Weyl duality for quantum groups with the Etingof-Kirillov theory of generalized quantum characters which are related to Macdonald polynomials. In the unrefined limit we reproduce the chiral expansion of q-deformed Yang-Mills theory derived by de Haro, Ramgoolam and Torrielli. In the classical limit q = 1, the expansion defines a new β-deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit β = 1 to the orbifold Euler characteristics of Hurwitz spaces of holomorphic maps. We discuss the geometrical meaning of our expansions in relation to quantum spectral curves and β-ensembles of matrix models arising in refined topological string theory. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
A global solution of the Einstein-Yang-Mills equation on the conformal space
Institute of Scientific and Technical Information of China (English)
LU; Qikeng(陆启铿)
2002-01-01
The method used to construct the SU(2) Yang-Mills field on a compactified Minkowski space-M(which is equivalent to the conformal space) is generalized to construct an SU(N)(N > 2) Yang-Mills fieldFjκ on M. It is proved that both Fjκ and the invariant metric tensor gjκ of M satisfy the Einstein-Yang-Mills equation. The case of N →∞ is also discussed.
Transport coefficients in Yang-Mills theory and QCD
Energy Technology Data Exchange (ETDEWEB)
Strodthoff, Nils; Christiansen, Nicolai; Haas, Michael [Institut fuer Theoretische Physik, Heidelberg (Germany); Pawlowski, Jan M. [Institut fuer Theoretische Physik, Heidelberg (Germany); ExtreMe Matter Institute EMMI, Darmstadt (Germany)
2015-07-01
We calculate the shear viscosity over entropy density ratio η/s in Yang-Mills theory from the Kubo formula using an exact diagrammatic representation in terms of full propagators and vertices using gluon spectral functions as external input. We provide an analytic fit formula for the temperature dependence of η/s over the whole temperature range from a glueball resonance gas at low temperatures, to a high-temperature regime consistent with perturbative results. Subsequently we provide a first estimate for η/s in QCD.
Stabilizing Perturbative Yang-Mills Free Energy with Gribov Quantization
Fukushima, Kenji
2013-01-01
We evaluate the free energy of the Yang-Mills theory using the Gribov quantization that copes with non-perturbative resummation. The magnetic scale is automatically incorporated in the framework and we find it efficient to stabilize the perturbative expansion of the free energy. In the range of the temperature T=T_c~2T_c major uncertainty in our results comes from the non-perturbative running coupling that is adopted from the lattice simulation, while the convergence above 2T_c is impressively robust.
N=1 supersymmetric Yang-Mills theory on the lattice
Energy Technology Data Exchange (ETDEWEB)
Piemonte, Stefano
2015-04-08
Supersymmetry (SUSY) relates two classes of particles of our universe, bosons and fermions. SUSY is considered nowadays a fundamental development to explain many open questions about high energy physics. The N=1 super Yang-Mills (SYM) theory is a SUSY model that describes the interaction between gluons and their fermion superpartners called ''gluinos''. Monte Carlo simulations on the lattice are a powerful tool to explore the non-perturbative dynamics of this theory and to understand how supersymmetry emerges at low energy. This thesis presents new results and new simulations about the properties of N=1 SYM, in particular about the phase diagram at finite temperature.
Aspects of lattice N=4 supersymmetric Yang--Mills
Schaich, David
2015-01-01
Non-perturbative investigations of $\\mathcal N = 4$ supersymmetric Yang--Mills theory formulated on a space-time lattice have advanced rapidly in recent years. Large-scale numerical calculations are currently being carried out based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing. A recent development is the creation of an improved lattice action through a new procedure to regulate flat directions in a manner compatible with this supersymmetry, by modifying the moduli equations. In this proceedings I briefly summarize this new procedure and discuss the parameter space of the resulting improved action that is now being employed in numerical calculations.
Latest results from lattice N=4 supersymmetric Yang--Mills
Schaich, David; Damgaard, Poul H; Giedt, Joel
2016-01-01
We present some of the latest results from our numerical investigations of N=4 supersymmetric Yang--Mills theory formulated on a space-time lattice. Based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, we recently developed an improved lattice action that is now being employed in large-scale calculations. Here we update our studies of the static potential using this new action, also applying tree-level lattice perturbation theory to improve the analysis of the potential itself. Considering relatively weak couplings, we obtain results for the Coulomb coefficient that are consistent with continuum perturbation theory.
Yang-Mills Theories at High-Energy Accelerators
Sterman, George
2016-01-01
I'll begin with a brief review of the triumph of Yang-Mills theory at particle accelerators, a development that began some years after their historic paper. This story reached a culmination, or at least local extremum, with the discovery at the Large Hadron Collider of a Higgs-like scalar boson in 2012. The talk then proceeds to a slightly more technical level, discussing how we derive predictions from the gauge field theories of the Standard Model and its extensions for use at high energy accelerators.
Branes from Moyal Deformation Quantization of Generalized Yang Mills Theories
Castro, C
1999-01-01
It is shown that a Moyal deformation quantization of the SO(4k) Generalized Yang-Mills (GYM) theory action in D=4k dimensions, for spacetime independent field configurations, in the $\\hbar \\to 0$ limit, yields the Dolan-Tchrakian p-brane action after fixing the conformal and world volume reparametrization invariance, associated with the p-brane world volume dimension p+1=4k, embedded in a D=4k target spacetime background. The gauge fields/target spacetime coordinates correspondence is required but no large N limit is necessary.
Integrability in N=4 super Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Eden, B. [ITF and Spinoza Institute, University of Utrecht, Minnaertgebouw, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)
2008-10-15
We use the Bethe ansatz to calculate the cusp anomalous dimension in planar N=4 super Yang-Mills theory as an exact function of the coupling constant. The calculation allows us to fix the remaining ambiguities in the integrable system describing the spectrum of operators/string energy levels in the AdS/CFT correspondence. The cusp anomalous dimension is not affected by finite size effects, which in general remain ill-understood. We suggest a method for computing the lowest example of an anomalous dimension modified by such corrections.
Callan-Symanzik approach to infrared Yang-Mills theory
Directory of Open Access Journals (Sweden)
Weber Axel
2014-01-01
Full Text Available Dyson-Schwinger equations are the most common tool for the determination of the correlation functions of Landau gauge Yang-Mills theory in the continuum, in particular in the infrared regime. We shall argue that the use of Callan-Symanzik renormalization group equations has distinctive advantages over the Dyson-Schwinger equations, in particular for the vertex functions. We present a generalization of the infrared safe renormalization scheme proposed by Tissier and Wschebor in 2011. The comparison with the existing lattice data for the gluon and ghost propagators can be used to determine the most appropriate renormalization scheme.
Maximally supersymmetric Yang-Mills on the lattice
Schaich, David
2015-01-01
We summarize recent progress in lattice studies of four-dimensional N=4 supersymmetric Yang--Mills theory and present preliminary results from ongoing investigations. Our work is based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, and we review a new procedure to regulate flat directions by modifying the moduli equations in a manner compatible with this supersymmetry. This procedure defines an improved lattice action that we have begun to use in numerical calculations. We discuss some highlights of these investigations, including the static potential and an update on the question of a possible sign problem in the lattice theory.
Fate of Yang-Mills black hole in early Universe
Energy Technology Data Exchange (ETDEWEB)
Nakonieczny, Lukasz; Rogatko, Marek [Institute of Physics Maria Curie-Sklodowska University 20-031 Lublin, pl. Marii Curie-Sklodowskiej 1 (Poland)
2013-02-21
According to the Big Bang Theory as we go back in time the Universe becomes progressively hotter and denser. This leads us to believe that the early Universe was filled with hot plasma of elementary particles. Among many questions concerning this phase of history of the Universe there are questions of existence and fate of magnetic monopoles and primordial black holes. Static solution of Einstein-Yang-Mills system may be used as a toy model for such a black hole. Using methods of field theory we will show that its existence and regularity depend crucially on the presence of fermions around it.
A Curious Truncation of N=4 Yang-Mills
Basu, A; Sethi, S; Basu, Anirban; Sethi, Savdeep
2004-01-01
The coupling constant dependence of correlation functions of BPS operators in N=4 Yang-Mills can be expressed in terms of integrated correlation functions. We approximate these integrated correlators by using a truncated OPE expansion. This leads to differential equations for the coupling dependence. When applied to a particular sixteen point correlator, the coupling dependence we find agrees with the corresponding amplitude computed via the AdS/CFT correspondence. We conjecture that this truncation becomes exact in the large N and large 't Hooft coupling limit.
Super-Yang-Mills theories on S4 x R
Kim, Jungmin; Lee, Kimyeong; Park, Jaemo
2014-01-01
We construct super-Yang-Mills theories on S4 x R, S4 x S1 and S4 x interval with the field content of maximal SYM, coupled to boundary degrees in the last case. These theories provide building blocks of the `5d uplifts' of gauge theories on S4, obtained by compactifying the 6d (2,0) theory. We pay special attention to the N=2* theory on S4. We also explain how to construct maximal SYM on S5 x R, and clarify when SYM theories can be put on S^n x R.
Width of the confining string in Yang-Mills theory.
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.
Loop formulation of supersymmetric Yang-Mills quantum mechanics
Steinhauer, Kyle
2014-01-01
We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.
Picard-Fuchs Ordinary Differential Systems in $N = 2$ Supersymmetric Yang-Mills Theories
Ohta, Y
1999-01-01
In general, Picard-Fuchs systems in N=2 supersymmetric Yang-Mills theories are realized as a set of simultaneous partial differential equations. However, if the QCD scale parameter is used as unique independent variable instead of moduli, the resulting Picard-Fuchs systems are represented by a single ordinary differential equation (ODE) whose order coincides with the total number of independent periods. This paper discusses some properties of these Picard-Fuchs ODEs. In contrast with the usual Picard-Fuchs systems written in terms of moduli derivatives, there exists a Wronskian for this ordinary differential system and this Wronskian produces a new relation among periods, moduli and QCD scale parameter, which in the case of SU(2) is reminiscent of scaling relation of prepotential. On the other hand, in the case of the SU(3) theory, there are two kinds of ordinary differential equations, one of which is the equation directly constructed from periods and the other is derived from the SU(3) Picard-Fuchs equation...
Classical Higgs fields on gauge gluon bundles
Directory of Open Access Journals (Sweden)
Palese Marcella
2016-01-01
Full Text Available Classical Higgs fields and related canonical conserved quantities are defined by invariant variational problems on suitably defined gauge gluon bundles. We consider Lagrangian field theories which are assumed to be invariant with respect to the action of a gauge-natural group. As an illustrative example we exploit the ‘gluon Lagrangian’, i.e. a Yang-Mills Lagrangian on the (1, 1-order gauge-natural bundle of SU(3-principal connections. The kernel of the gauge-natural Jacobi morphism for such a Lagrangian, by inducing a reductive split structure, canonically defines a ‘gluon classical Higgs field’.
The Hilbert series of 3d N=2 Yang-Mills theories with vectorlike matter
Cremonesi, Stefano
2015-01-01
This paper presents a formula for the Hilbert series that counts gauge invariant chiral operators in 3d N=2 Yang-Mills theories with vectorlike matter and no Chern-Simons interactions. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background, which is determined by the Higgs mechanism. The sum over magnetic charges is restricted due to instanton effects that partially lift the classical Coulomb branch. The formalism is applied to unitary and symplectic gauge theories with fundamental matter, reproducing old results for the moduli space of vacua and the chiral ring, without resorting to any further effective superpotential on the moduli space.
Yang-Mills correlators across the deconfinement phase transition
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.
Yang-Mills correlators across the deconfinement phase transition
Reinosa, U; Tissier, M; Tresmontant, A
2016-01-01
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 dif...
Lifting the Gribov ambiguity in Yang-Mills theories
Serreau, Julien
2013-01-01
We report on the work presented in Phys. Lett. B712 (2012) 97, where a new one-parameter family of Landau gauges has been proposed for Yang-Mills theories, inspired by an analogy with disordered systems in condensed matter physics. This is based on a particular average over Gribov copies which avoids the Neuberger zero problem of the standard Fadeev-Popov construction. The proposed gauge fixing can be formulated as a local renormalizable field theory in four dimensions and is well-suited for analytical calculations. A remarkable feature is that, for what concerns the calculation of ghost and gauge field correlators, the gauged-fixed action is perturbatively equivalent to a simple massive extension of the Faddeev-Popov action. The renormalization group flow of the theory admits infrared safe trajectories, with no Landau pole. The one-loop calculations of Yang-Mills two-point correlators show remarkable agreement with lattice simulations all the way to the deep infrared.
Effective Lagrangian of SU(2) Yang-Mills Theory in the Presence of Fermions
Institute of Scientific and Technical Information of China (English)
FAN Ji-Yang; JIANG Ying; ZHU Zhong-Yuan
2002-01-01
We derive the one-loop effective action of SU(2) Yang Mills theory in the presence of fermions in the lowenergy limit. This result is presented by separating the topological degrees, which describe the non-Abelian monopolesfrom the dynamical degrees of the gauge potential and integrate out all the dynamical degrees and fermions in SU(2)Yang-Mills theory.
N=2 SYM Action as a BRST Exact Term, Topological Yang Mills and Instantons
Ulker, K
2003-01-01
By defining an extended BRST operator that includes the chiral part of N=2 global supersymmetry, it is shown that the full N=2 off-shell Super Yang Mills Action can be represented as an exact BRST term. The action written in this form suggests that the fields of the Topological Yang Mills theory can be defined in terms of composite fields of supersymmetry ghosts and N=2 fields in a natural way. Topological Yang Mills theory is obtained from the ordinary Euclidean N=2 SYM directly as field redefinitions without using twisting procedure. With the help of these results, relation between the recent instanton calculations in N=2 Super Yang Mills and Topological Yang Mills theories is also discussed.
Della Morte, Michele
2011-01-01
We make use of the global symmetries of the Yang-Mills theory on the lattice to design a new computational strategy for extracting glueball masses and matrix elements which achieves an exponential reduction of the statistical error with respect to standard techniques. By generalizing our previous work on the parity symmetry, the partition function of the theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations Z_N^3. Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. The strategy is implemented for the SU(3) Yang--Mills theory, and a full-fledged computation of the mass and multiplicity of the lightest glueball with vacuum quantum ...
Della Morte, Michele; Giusti, Leonardo
2011-05-01
We make use of the global symmetries of the Yang-Mills theory on the lattice to design a new computational strategy for extracting glueball masses and matrix elements which achieves an exponential reduction of the statistical error with respect to standard techniques. By generalizing our previous work on the parity symmetry, the partition function of the theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations Z N 3. Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. The strategy is implemented for the SU(3) Yang-Mills theory, and a full-fledged computation of the mass and multiplicity of the lightest glueball with vacuum quantum numbers is carried out at a lattice spacing of 0.17 fm.
Energy Technology Data Exchange (ETDEWEB)
Buisseret, F., E-mail: fabien.buisseret@umons.ac.be [Service de Physique Nucleaire et Subnucleaire, Universite de Mons-UMONS, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium); Haute Ecole Louvain en Hainaut (HELHa), Chaussee de Binche 159, B-7000 Mons (Belgium); Lacroix, G., E-mail: gwendolyn.lacroix@umons.ac.be [Service de Physique Nucleaire et Subnucleaire, Universite de Mons-UMONS, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)
2011-11-17
We discuss the dependence of pure Yang-Mills equation of state on the choice of gauge algebra. In the confined phase, we generalize to an arbitrary simple gauge algebra Meyer's proposal of modeling the Yang-Mills matter by an ideal glueball gas in which the high-lying glueball spectrum is approximated by a Hagedorn spectrum of closed-bosonic-string type. Such a formalism is undefined above the Hagedorn temperature, corresponding to the phase transition toward a deconfined state of matter in which gluons are the relevant degrees of freedom. Under the assumption that the renormalization scale of the running coupling is gauge-algebra independent, we discuss about how the behavior of thermodynamical quantities such as the trace anomaly should depend on the gauge algebra in both the confined and deconfined phase. The obtained results compare favorably with recent and accurate lattice data in the su(3) case and support the idea that the more the gauge algebra has generators, the more the phase transition is of first-order type.
Fluxes, Tadpoles and Holography for N=1 Super Yang Mills
Gómez, C; Resco, P; Gomez, Cesar; Montanez, Sergio; Resco, Pedro
2004-01-01
We study non perturbative superpotentials for N=1 super Yang Mills from the point of view of large $N$ dualities. Starting with open topological strings we work out the relation between the closed string sector dilaton tadpole, which appears in the annulus amplitude, and NSNS fluxes in the closed string dual on the resolved conifold. For the mirror closed string dual version on the deformed conifold we derive, for a non vanishing $G_{3}$ form, the $N$ supersymmetric vacua and the transformations of $G_{3}$ through domain walls. Finally, as an extension of Fischler Susskind mechanism we find a direct relation between the dilaton tadpole and the geometric warping factors induced by the gravitational backreaction of NSNS fluxes.
Step scaling and the Yang-Mills gradient flow
Lüscher, Martin
2014-01-01
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 Schr\\"odinger 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.
Chiral symmetry and the Yang--Mills gradient flow
Lüscher, Martin
2013-01-01
In the last few years, the Yang--Mills gradient flow was shown to be an attractive tool for non-perturbative studies of non-Abelian gauge theories. Here a simple extension of the flow to the quark fields in QCD is considered. As in the case of the pure-gauge gradient flow, the renormalizability of correlation functions involving local fields at positive flow times can be established using a representation through a local field theory in 4+1 dimensions. Applications of the extended flow in lattice QCD include non-perturbative renormalization and O(a) improvement as well as accurate calculations of the chiral condensate and of the pseudo-scalar decay constant in the chiral limit.
Lifting the Gribov ambiguity in Yang-Mills theories
Energy Technology Data Exchange (ETDEWEB)
Serreau, J., E-mail: serreau@apc.univ-paris7.fr [APC, AstroParticule et Cosmologie, Universite Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cite, 10, rue Alice Domon et Leonie Duquet, 75205 Paris Cedex 13 (France); Tissier, M. [LPTMC, Laboratoire de Physique Theorique de la Matiere Condensee, CNRS UMR 7600, Universite Pierre et Marie Curie, boite 121, 4 pl. Jussieu, 75252 Paris Cedex 05 (France)
2012-05-30
We propose a new one-parameter family of Landau gauges for Yang-Mills theories which can be formulated by means of functional integral methods and are thus well suited for analytic calculations, but which are free of Gribov ambiguities and avoid the Neuberger zero problem of the standard Faddeev-Popov construction. The resulting gauge-fixed theory is perturbatively renormalizable in four dimensions and, for what concerns the calculation of ghost and gauge field correlators, it reduces to a massive extension of the Faddeev-Popov action. We study the renormalization group flow of this theory at one-loop and show that it has no Landau pole in the infrared for some - including physically relevant - range of values of the renormalized parameters.
Lifting the Gribov ambiguity in Yang-Mills theories
Serreau, Julien
2012-01-01
We propose a new one-parameter family of Landau gauges for Yang-Mills theories which can be formulated by means of functional integral methods and are thus well suited for analytic calculations, but which are free of Gribov ambiguities and avoid the Neuberger zero problem of the standard Fadeev-Popov construction. The resulting gauge-fixed theory is perturbatively renormalizable in four dimensions and, for what concerns the calculation of ghost and gauge field correlators, it reduces to a massive extension of the Fadeev-Popov action. We study the renormalization group flow of this theory at one-loop and show that it has no Landau pole in the infrared for some - including physically relevant - range of values of the renormalized parameters.
Covariant gauges without Gribov ambiguities in Yang-Mills theories
Serreau, Julien; Tresmontant, Andréas
2013-01-01
We propose a formulation of a certain class of nonlinear covariant gauges as an extremization procedure that can be implemented on the lattice. At high energies, where the Gribov ambiguities can be ignored, this reduces to the Curci-Ferrari-Delbourgo-Jarvis gauges. We further propose a continuum formulation in terms of a local action which is free of Gribov ambiguities and avoids the Neuberger zero problem of the standard Faddeev-Popov construction. This involves an averaging over Gribov copies with a nonuniform weight, which introduces a new gauge-fixing parameter. We show that the proposed gauge-fixed action is perturbatively renormalizable in four dimensions and we provide explicit expressions of the renormalization factors at one loop. We discuss the possible implications of the present proposal for the calculation of Yang-Mills correlators.
Renormalization of the Yang-Mills spectral action
van Suijlekom, Walter D
2011-01-01
We prove renormalizability of the full spectral action for the Yang-Mills system on a flat 4-dimensional background manifold. Interpreting the spectral action as a higher-derivative gauge theory, a power-counting argument shows that it is superrenormalizable. We determine the counterterms at one-loop using zeta function regularization in a background field gauge and establish their gauge invariance. Consequently, the spectral action can be renormalized by a simple shift of the coefficients appearing in the asymptotic expansion of the spectral action. This manuscript provides more details than the shorter companion paper, where we have used a (formal) quantum action principle to arrive at gauge invariance of the counterterms. Here, we give in addition an explicit expression for the gauge propagator.
Perturbative study of Yang-Mills theory in the infrared
Siringo, Fabio
2015-01-01
Pure Yang-Mills SU(N) theory is studied in four dimensional space and Landau gauge by a double perturbative expansion based on a massive free-particle propagator. By dimensional regularization, all diverging mass terms cancel exactly in the double expansion, without the need to include mass counterterms that would spoil the symmetry of the original Lagrangian. The emerging perturbation theory is safe in the infrared and shares the same behaviour of the standard perturbation theory in the UV. At one-loop, Gluon and ghost propagators are found in excellent agreement with the data of lattice simulations and an infrared-safe running coupling is derived. A natural scale m=0.5-0.6 GeV is extracted from the data for N=3.
Cylindrically symmetric solitons in Einstein-Yang-Mills theory
Galtsov, D V; Davydov, Evgeny A.; Gal'tsov, Dmitri V.
2006-01-01
Recently new Einstein-Yang-Mills (EYM) soliton solutions were presented which describe superconducting strings with Kasner asymptotic (hep-th/0610183). Here we study the static cylindrically symmetric SU(2) EYM system in more detail. The ansatz for the gauge field corresponds to superposition of the azimuthal $B_\\phi$ and the longitudinal $B_z$ components of the color magnetic field. We derive sum rules relating data on the symmetry axis to asymptotic data and show that generic asymptotic structure of regular solutions is Kasner. Solutions starting with vacuum data on the axis generically are divergent. Regular solutions correspond to some bifurcation manifold in the space of parameters which has the low-energy limiting point corresponding to string solutions in flat space (with the divergent total energy) and the high-curvature point where gravity is crucial. Some analytical results are presented for the low energy limit, and numerical bifurcation curves are constructed in the gravitating case. Depending on ...
Yang-Mills Theory and the ABC Conjecture
He, Yang-Hui; Probst, Malte; Read, James
2016-01-01
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.
The leading term of the Yang-Mills free energy
Chatterjee, Sourav
2016-01-01
The construction of quantum Yang-Mills theories is a central open question in mathematical physics, famously posed as one of the millennium prize problems by the Clay Institute. Although huge strides were made in the Eighties, the problem has remained unsolved in dimensions three and four. This article makes a new contribution to this quest, by explicitly calculating the leading term of the free energy of three dimensional $U(N)$ lattice gauge theory for any $N$, as the lattice spacing tends to zero. This is a small step towards the complete solution of the above problem, since the main question can be rephrased as the problem of determining of the full asymptotics of the free energy, rather than only the leading term. The proof is based on a novel technique that avoids phase cell renormalization. The technique also yields a similar formula for the four dimensional theory, but only in the weak coupling limit.
Lifshitz black holes in Einstein-Yang-Mills theory
Devecioglu, Deniz Olgu
2014-01-01
We find that the four dimensional cosmological Einstein-Yang-Mills theory with $SU(2)$ gauge group admits Lifshitz spacetime as a base solution for the dynamical exponent $z>1$. Motivated by this, we next demonstrate numerically that the field equations admit black hole solutions which behave regularly on the horizon and at spatial infinity for different horizon topologies. The solutions depend on one parameter, the strength of the gauge field at the horizon, which is fine-tuned to capture the Lifshitz asymptotics at infinity. We also discuss the behavior of solutions and the change in Hawking temperature for black holes that are large or small with respect to the length scale $L$, which is itself fixed by the value of the cosmological constant.
Residual Confinement in High-Temperature Yang-Mills Theory
Maas, A; Gruter, B; Alkofer, R; Maas, Axel; Wambach, Jochen; Gruter, Burghard; Alkofer, Reinhard
2004-01-01
The infrared behavior of Landau gauge gluon and ghost propagators are investigated in Yang-Mills theory at non-vanishing temperatures. Self-consistent solutions are presented for temperatures below the presumed phase transition and in the infinite temperature limit. Gluon confinement is manifest in the infrared behavior of these propagators. As expected confinement prevails below the phase transition. In the infinite-temperature limit a qualitative change is observed: the chromoelectric sector exhibits a near-perturbative behavior while long-range chromomagnetic interactions, mediated by soft ghost modes, are still present. The latter behavior is in agreement with corresponding lattice results. It furthermore implies that part of the gluons are still confined.
Residual Confinement in High-Temperature Yang-Mills Theory
Maas, A.; Wambach, J.; Grüter, B.; Alkofer, R.
2005-01-01
The infrared behavior of Landau gauge gluon and ghost propagators are investigated in Yang-Mills theory at non-vanishing temperatures. Self-consistent solutions are presented for temperatures below the presumed phase transition and in the infinite temperature limit. Gluon confinement is manifest in the infrared behavior of these propagators. As expected confinement prevails below the phase transition. In the infinite-temperature limit a qualitative change is observed: the chromoelectric sector exhibits a near-perturbative behavior while long-range chromomagnetic interactions, mediated by soft ghost modes, are still present. The latter behavior is in agreement with corresponding lattice results. It furthermore implies that part of the gluons are still confined.
Thermal Yang-Mills theory in the Einstein universe
Avramidi, Ivan G.; Collopy, Samuel
2012-09-01
We study the stability of a non-Abelian chromomagnetic vacuum in Yang-Mills theory in Euclidean Einstein universe S1 × S3. We assume that the gauge group is a simple compact group G containing the group SU(2) as a subgroup and consider static covariantly constant gauge fields on S3 taking values in the adjoint representation of the group G and forming a representation of the group SU(2). We compute the heat kernel for the Laplacian acting on fields on S3 in an arbitrary representation of SU(2) and use this result to compute the heat kernels for the gluon and the ghost operators and the one-loop effective action. We show that the only configuration of the covariantly constant Yang-Mills background that is stable is the one that contains only spinor (fundamental) representations of the group SU(2); all other configurations contain negative modes and are unstable. For the stable configuration we compute the asymptotics of the effective action, the energy density, the entropy and the heat capacity in the limits of low/high temperature and small/large volume and show that the energy density has a non-trivial minimum at a finite value of the radius of the sphere S3. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.
Linde problem in Yang-Mills theory compactified on $\\mathbb{R}^2 \\times \\mathbb{T}^2$
Fraga, Eduardo S; Noronha, Jorge
2016-01-01
We investigate the perturbative expansion in $SU(3)$ Yang-Mills theory compactified on $\\mathbb{R}^2\\times \\mathbb{T}^2$ where the compact space is a torus $\\mathbb{T}^2= S^1_{\\beta}\\times S^1_{L}$, with $S^1_{\\beta}$ being a thermal circle with period $\\beta=1/T$ ($T$ is the temperature) while $S^1_L$ is a circle with length $L=1/\\Lambda$ where $\\Lambda$ is an energy scale. A Linde-type analysis indicates that perturbative calculations for the pressure in this theory break down already at order $\\mathcal{O}(g^2)$ due to the presence of a non-perturbative scale $\\sim g \\sqrt{T\\Lambda}$. We conjecture that a similar result should hold if the torus is replaced by any compact surface of genus one.
Yang-Mills theory in terms of gauge invariant dual variables
Diakonov, D
2002-01-01
Quantum Yang-Mills theory and the Wilson loop can be rewritten identically in terms of local gauge-invariant variables being directly related to the metric of the dual space. In this formulation, one reveals a hidden high local symmetry of the Yang-Mills theory, which mixes up fields with spins up to J=N for the SU(N) gauge group. In the simplest case of the SU(2) group the dual space seems to tend to the de Sitter space in the infrared region. This observation suggests a new mechanism of gauge-invariant mass generation in the Yang-Mills theory.
Neutrino Oscillation, Finite Self-Mass and General Yang-Mills Symmetry
Hsu, Jong-Ping
2016-01-01
The conservation of lepton number is assumed to be associated with a general Yang-Mills symmetry. New transformations involve (Lorentz) vector gauge functions and characteristic phase functions, and they form a group. General Yang-Mills fields are associated with new fourth-order equations and linear potentials. Lepton self-masses turn out to be finite and proportional to the inverse of lepton masses, which implies that neutrinos should have non-zero masses. Thus, general Yang-Mills symmetry could provide an understanding of neutrino oscillations and suggests that neutrinos with masses and very weak leptonic force may play a role in dark matter.
A Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry
Institute of Scientific and Technical Information of China (English)
WANG Dian-Fu; SONG He-Shan
2005-01-01
A generalized Yang-Mills model, which contains, besides the vector part Vμ, also a scalar part S, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of Nambu-Jona-Lasinio (NJL) mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills model. The combination of the generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.
Topological Susceptibility in the SU(3) Gauge Theory
Del Debbio, L; Pica, C; Debbio, Luigi Del; Giusti, Leonardo; Pica, Claudio
2006-01-01
We compute the topological susceptibility for the SU(3) Yang--Mills theory by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3), which corresponds to chi=(191 +/- 5 MeV)^4 if F_K is used to set the scale. Our result supports the Witten--Veneziano explanation for the large mass of the eta'.
Energy Technology Data Exchange (ETDEWEB)
Kneipp, Marco A.C. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Dept. de Fisica Teorica; Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas
2004-12-01
We review some recent developments on BPS string solutions and monopole confinement in the Higgs (or color) superconducting phase of N = 2 and N = 4 super Yang-Mills theories. In particular, the monopole magnetic fluxes are shown to be always integer linear combinations of string fluxes. Moreover, a bound for the threshold length of the string breaking is obtained. When the gauge group SU(N) is broken to Z{sub N}, the BPS string tension satisfies the Casimir scaling law. Furthermore, in the SU(3) case the string solutions are such that they allow the formation of a confining system with three monopoles. (author)
Gußmann, Alexander
2016-01-01
The existence of classical solutions of the Einstein-Yang-Mills-Higgs equations describing black holes inside 't Hooft-Polyakov magnetic monopoles implies that not all 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-Nordstr\\"om metric on the one hand and the "magnetic monopole black hole solutions" which can be interpreted as black holes inside 't Hooft-Polyakov magnetic monopoles described by a metric which is not of Reissner-Nordstr\\"om form on the other hand.) One can experimentally distinguish such black holes with same asymptotic characteristics but different ne...
Future applications of the Yang-Mills gradient flow in lattice QCD
Lüscher, Martin
2013-01-01
The Yang--Mills gradient flow has many interesting applications in lattice QCD. In this talk, some recent and possible future uses of the flow are discussed, emphasizing the underlying theoretical concepts rather than any computational aspects.
Mechanism by which spatially homogeneous Yang-Mills fields become stochastic
Energy Technology Data Exchange (ETDEWEB)
Avakyan, A.R.; Arutyunyan, S.G.; Baseyan, G.Z.
1982-11-20
A mechanical system with a nonzero angular momentum, corresponding to spatially homogeneous Yang-Mills fields, is analyzed. Numerical simulations have been carried out. A mechanism by which the fields become stochastic is found.
Non-perturbative Solutions to N=2 Supersymmetric Yang-Mills Theories Progress and Perspective
Ohta, Y
1999-01-01
This note reviews the progress on the low energy dynamics of N=2 supersymmetric Yang-Mills theories after the works of Seiberg and Witten. Specifically, the theory of prepotential for non-specialists is reviewed.
Kaehler transformations and the coupling of matter and Yang-Mills fields to supergravity
Energy Technology Data Exchange (ETDEWEB)
Binetruy, P.; Girardi, G.; Grimm, R.; Mueller, M.
1987-04-30
It is demonstrated that a geometric interpretation of Kaehler transformations in superspace allows to construct the full action for matter and Yang-Mills fields coupled to supergravity in a concise way, both in terms of superfields and component fields.
Classical glueballs in non-Abelian Born-Infeld theory
Galtsov, D V; Gal'tsov, Dmitri; Kerner, Richard
2000-01-01
It is shown that the Born-Infeld-type modification of the quadratic Yang-Mills action suggested by the superstring theory gives rise to classical particle-like solutions prohibited in the standard Yang-Mills theory. This becomes possible due to the scale invariance breaking by the Born-Infeld non-linearity. New classical glueballs are sphaleronic in nature and exhibit a striking similarity with the Bartnik-McKinnon solutions of the Yang-Mills theory coupled to gravity.
Static Spherically Symmetric Solutions of the SO(5) Einstein Yang-Mills Equations
Bartnik, Robert A.; Fisher, Mark; Oliynyk, Todd A.
2009-01-01
Globally regular (ie. asymptotically flat and regular interior), spherically symmetric and localised ("particle-like") solutions of the coupled Einstein Yang-Mills (EYM) equations with gauge group SU(2) have been known for more than 20 years, yet their properties are still not well understood. Spherically symmetric Yang--Mills fields are classified by a choice of isotropy generator and SO(5) is distinguished as the simplest model with a \\emph{non-Abelian} residual (little) group, $SU(2)\\times...
A U(4) QCD Model Using Generalized Yang-Mills Theory
Institute of Scientific and Technical Information of China (English)
WANG Dian-Fu; ZHONG Hai-Yang
2008-01-01
Generalized Yang-Mills theory has a covariant derivative which contains both vector and pseudoscalar gauge bosons.Based on this theory,we construct a U(4) strong interaction model By using this U(4) generalized Yang-Mills model,we obtain that mesons can be realized as the colorless pseudoscalar gauge bosons.We also obtain a gauge potential solution which can be used to explain the asymptotic behavior and color confinement.
An exploratory study of Yang-Mills three-point functions at non-zero temperature
Huber, Markus Q.
2017-03-01
Results for three-point functions of Landau gauge Yang-Mills theory at non-vanishing temperature are presented and compared to lattice results. It is found that the three-gluon vertex is enhanced for temperatures below the phase transition. At very low momenta it becomes negative for all temperatures. Furthermore, truncation effects in functional equations are discussed at the example of three-dimensional Yang-Mills theory for which a self-contained solution is presented.
An exploratory study of Yang-Mills three-point functions at non-zero temperature
Huber, Markus Q
2016-01-01
Results for three-point functions of Landau gauge Yang-Mills theory at non-vanishing temperature are presented and compared to lattice results. It is found that the three-gluon vertex is enhanced for temperatures below the phase transition. At very low momenta it becomes negative for all temperatures. Furthermore, truncation effects in functional equations are discussed at the example of three-dimensional Yang-Mills theory for which a self-contained solution is presented.
A Unified Field Theory of Gravity, Electromagnetism, and the Yang-Mills Gauge Field
Directory of Open Access Journals (Sweden)
Suhendro I.
2008-01-01
Full Text Available In this work, we attempt at constructing a comprehensive four-dimensional unified field theory of gravity, electromagnetism, and the non-Abelian Yang-Mills gauge field in which the gravitational, electromagnetic, and material spin fields are unified as intrinsic geometric objects of the space-time manifold S4 via the connection, with the general- ized non-Abelian Yang-Mills gauge field appearing in particular as a sub-field of the geometrized electromagnetic interaction.
Park, J S
1992-01-01
We re-examine the geometry and algebraic structure of BRST's of Topological Yang-Mills theory based on the universal bundle formalism of Atiyah and Singer. This enables us to find a natural generalization of the {\\it Russian formula and descent equations\\/}, which can be used as algebraic method to find the non-Abelian anomalies counterparts in Topological Yang-Mills theory. We suggest that the presence of the non-Abelian anomaly obstructs the proper definition of Donaldson's invariants.
Topological Quantization of Instantons in SU(2) Yang-Mills Theory
Institute of Scientific and Technical Information of China (English)
ZHONG Wo-Jun; DUAN Yi-Shi
2008-01-01
By decomposing SU(2) gauge potential in four-dimensional Euclidean SU(2) Yang-Mills theory in a new way,we find that the instanton number related to the isospin defects of a doublet order parameter can be topologically quantized by the Hopf index and Brouwer degree.It is also shown that the instanton number is just the sum of the topological charges of the isospin defects in the non-trivial sector of Yang-Mills theory.
Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic
Douglas, M R; Lukic, S; Reinbacher, R; Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene
2007-01-01
We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P^2. In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic.
One-dimensional structures behind twisted and untwisted super Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Baulieu, Laurent [CERN, Geneve (Switzerland). Theoretical Div.; Toppan, Francesco, E-mail: baulieu@lpthe.jussieu.f, E-mail: toppan@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
2010-07-01
We give a one-dimensional interpretation of the four-dimensional twisted N = 1 super Yang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N = 1 super Yang-Mills theory. (author)
Violation of the Weak Energy Condition by the Inflationary Yang-Mills Condensate
Institute of Scientific and Technical Information of China (English)
张杨
2002-01-01
Recent cosmic microwave background data favours a blueshifted primeval perturbation spectrum with an indexn＞1, which implies that the equation of state of dominant matter should be such that p + p＜0 during theinflationary expansion of the early universe. We study the quantum Yang-Mills condensate inflationary modeland find that this requirement can be satisfied by the effective quantum Yang-Mills condensate naturally in thestates with the negative dielectric constant.
Gravitational and Yang-Mills instantons in holographic RG flows
Gava, Edi; Narain, K S
2011-01-01
We study various holographic RG flow solutions involving warped asymptotically locally Euclidean (ALE) spaces of $A_{N-1}$ type. A two-dimensional RG flow from a UV (2,0) CFT to a (4,0) CFT in the IR is found in the context of (1,0) six dimensional supergravity, interpolating between $AdS_3\\times S^3/\\mathbb{Z}_N$ and $AdS_3\\times S^3$ geometries. We also find solutions involving non trivial gauge fields in the form of SU(2) Yang-Mills instantons on ALE spaces. Both flows are of vev type, driven by the vacuum expectation value of a (not exactly) marginal operator. RG flows in four dimensional field theories are studied in the type IIB and type I$'$ context. In type IIB theory, the flow interpolates between $AdS_5\\times S^5/\\mathbb{Z}_N$ and $AdS_5\\times S^5$ geometries. The field theory interpretation is that of an N=2 $SU(n)^N$ quiver gauge theory flowing to N=4 SU(n) gauge theory. In type I$'$ theory the solution describes an RG flow from N=2 quiver gauge theory with a product gauge group to N=2 gauge theor...
Two dimensional RG flows and Yang-Mills instantons
Gava, Edi; Narain, K S
2010-01-01
We study RG flow solutions in (1,0) six dimensional supergravity coupled to an anti-symmetric tensor and Yang-Mills multiplets corresponding to a semisimple group $G$. We turn on $G$ instanton gauge fields, with instanton number $N$, in the conformally flat part of the 6D metric. The solution interpolates between two (4,0) supersymmetric $AdS_3\\times S^3$ backgrounds with two different values of $AdS_3$ and $S^3$ radii and describes an RG flow in the dual 2D SCFT. For the single instanton case and $G=SU(2)$, there exist a consistent reduction ansatz to three dimensions, and the solution in this case can be interpreted as an uplifted 3D solution. Correspondingly, we present the solution in the framework of N=4 $(SU(2)\\ltimes \\mathbf{R}^3)^2$ three dimensional gauged supergravity. The flows studied here are of v.e.v. type, driven by a vacuum expectation value of a (not exactly) marginal operator of dimension two in the UV. We give an interpretation of the supergravity solution in terms of the D1/D5 system in ty...
Matrix models for 5d super Yang-Mills
Minahan, Joseph A
2016-01-01
In this contribution to the review 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...
Isotropy theorem for cosmological Yang-Mills theories
Cembranos, J A R; Jareño, S J Núñez
2012-01-01
We consider homogeneous non-abelian vector fields with general potential terms in an expanding universe. We find a mechanical analogy with a system of N interacting particles (with N the dimension of the gauge group) moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of a generalization of the virial theorem that for arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field. We consider also the case in which a gauge-fixing term is introduced in the action and show that the average equation of state does not depend on such a term. Finally, we extend the results to arbitrary background geometries and show that the average energy-momentum tensor of a rapidly evolving Yang-Mills fields is always isotropic and has the perfect fluid form for any locally inertial observer.
A novel renormalizable representation of the Yang-Mills theory
Dubin, A Yu
2007-01-01
For a generic gauge-invariant correlator _{A}, we reformulate the standard D=4 Yang-Mills theory as a renormalizable system of two interacting fields a_{\\mu} and B_{\\mu} which faithfully represent high- and low-energy degrees of freedom of the single gauge field A_{\\mu} in the original formulation. It opens a possibility to synthesize an infrared-nonsingular weak-coupling series, employed to integrate over a_{\\mu} for a given background B_{\\mu}, with qualitatively different methods. These methods are to be applied to evaluate the resulting (after the a_{\\mu}-integration) representation of _{A} in terms of gauge-invariant generically non-local low-energy observables, like Wilson loops. The latter observables are averaged over B_{\\mu} with respect to a gauge-invariant Wilsonean effective action S_{eff}[B]. To avoid a destructive dissipation between the high- and low-energy excitations, we implement a specific fine-tuning of the interaction between the pair of the fields: prior to the integration over B_{\\mu}, t...
Perturbations of the Yang-Mills field in the universe
Institute of Scientific and Technical Information of China (English)
Wen Zhao
2009-01-01
It has been suggested that the Yang-Mills (YM) field can be a kind of candidate for the inflationary field at high energy scales or dark energy at very low energy scales, which can naturally give the equation of state -1 <ω< 0 or ω<-1. We discuss the zero order and first order Einstein equations and YM field kinetic energy equations of the free YM field models. From the zero order equations, we find that ω+1 ∝α-2, from which it follows that the equation of state of the YM field always goes to - 1, independent of the initial conditions. By solving the first order Einstein equations and the YM field equations, we find that in the YM field inflationary models, the scale-invariant primordial perturbation power spectrum cannot be generated. Therefore, only using this kind of YM field is not enough to account for inflationary sources. However, as a kind of candidate for dark energy, the YM field has the 'sound speed' cs2 = -1/3 < 0, which makes the perturbation φ have a damping behavior at large scales. This provides a way to distinguish the YM field dark energy models from other kinds of models.
Magnetic Monopoles in the Einstein-Yang-Mills-Higgs System
Viet, N A; Viet, Nguyen Ai; Wali, Kameshwar C.
1995-01-01
We study the Yang-Mills-Higgs system within the framework of general relativity. In the static situation, using Bogomol'nyi type analysis, we derive a positive-definite energy functional which has a lower bound. Specializing to the gauge group $SU(2)$ and the t'Hooft-Polyakov ansatz for the gauge and Higgs fields, we seek static, spherically symmetric solutions to the coupled system of equations in both the isotropic and standard coordinate systems. In both cases, in the spontaneously broken symmetry situation, we find great simplications reducing the solutions of the coupled system to the solution of a single non-linear differential equation, different one in each case, but well-known in other contexts of physics. We find abelian and non-abelian monopole solutions with gravitational fields playing the role of Higgs fields in providing attraction that balances the repulsion due to the gauge fields. Numerical solutions indicate the possibility of blackhole horizons inside the monopoles enclosing the singularit...
Yang--Mills Glueballs as Closed Bosonic Strings
Dubovsky, Sergei
2016-01-01
We put forward the Axionic String Ansatz (ASA), which provides a unified description for the worldsheet dynamics of confining strings in pure Yang--Mills theory both in $D=3$ and $D=4$ space-time dimensions. The ASA is motivated by the excitation spectrum of long confining strings, as measured on a lattice, and by recently constructed integrable axionic non-critical string models. According to the ASA, pure gluodynamics in 3D is described by a non-critical bosonic string theory without any extra local worldsheet degrees of freedom. We argue that this assumption fixes the set of quantum numbers (spins, $P$- and $C$-parities) of almost all glueball states. We confront the resulting predictions with the properties of approximately $1^2+2^2+3^2+5^2=39$ lightest glueball states measured on a lattice and find a good agreement. On the other hand, the spectrum of low lying glueballs in 4D gluodynamics suggests the presence of a massive pseudoscalar mode on the string worldsheet, in agreement with the ASA and lattice ...
Yang-Mills glueballs as closed bosonic strings
Dubovsky, Sergei; Hernández-Chifflet, Guzmán
2017-02-01
We put forward the Axionic String Ansatz (ASA), which provides a unified description for the worldsheet dynamics of confining strings in pure Yang-Mills theory both in D = 3 and D = 4 space-time dimensions. The ASA is motivated by the excitation spectrum of long confining strings, as measured on a lattice, and by recently constructed integrable axionic non-critical string models. According to the ASA, pure gluodynamics in 3D is described by a non-critical bosonic string theory without any extra local worldsheet degrees of freedom. We argue that this assumption fixes the set of quantum numbers (spins, P-and C-parities) of almost all glueball states. We confront the resulting predictions with the properties of approximately 12 + 22 + 32 + 52 = 39 lightest glueball states measured on a lattice and find a good agreement. On the other hand, the spectrum of low lying glueballs in 4D gluodynamics suggests the presence of a massive pseudoscalar mode on the string worldsheet, in agreement with the ASA and lattice data for long strings.
Baker, M; Brambilla, Nora; Prosperi, G M; Zachariasen, F
1995-01-01
In this paper we express the velocity dependent, spin dependent heavy quark potential V_{q\\bar q} in QCD in terms of a Wilson Loop W(\\Gamma) determined by pure Yang Mills theory. We use an effective dual theory of long-distance Yang Mills theory to calculate W(\\Gamma) for large loops; i.e. for loops of size R > R_{FT}. (R_{FT} is the flux tube radius, fixed by the value of the Higgs (monopole) mass of the dual theory, which is a concrete realization of the Mandelstam 't Hooft dual superconductor mechanism of confinement). We replace W(\\Gamma) by W_{eff}(\\Gamma), given by a functional integral over the dual variables, which for R > R_{FT} can be evaluated by a semiclassical expansion, since the dual theory is weakly coupled at these distances. The classical approximation gives the leading contribution to W_{eff}(\\Gamma) and yields a velocity dependent heavy quark potential which for large R becomes linear in R, and which for small R approaches lowest order perturbative QCD. This latter fact means that these re...
Institute of Scientific and Technical Information of China (English)
WANG Dian-Fu; SUN Xiao-Yu; CHANG Xiao-Jing
2011-01-01
Starting from the generalized Yang-Mills model which contains, besides the vector part Vμ, also a scalar part S and a pseudoscalar part P. It is shown, in terms of the Nambu-Jona-Lasinio （NJL） mechanism, that CP violation can be realized dynamically. The
Doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group
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.
Transverse Momentum Broadening of a Fast Quark in a $\\N=4$ Yang Mills Plasma
Casalderrey-Solana, J; Casalderrey-Solana, Jorge; Teaney, Derek
2007-01-01
We compute the momentum broadening of a heavy fundamental charge propagating through a $\\mathcal{N}=4$ Yang Mills plasma at large t' Hooft coupling. We do this by expressing the medium modification of the probe's density matrix in terms of a Wilson loop averaged over the plasma. We then use the AdS/CFT correspondence to evaluate this loop, by identifying the dual semi-classical string solution. The calculation introduces the type ``1'' and type ``2'' fields of the thermal field theory and associates the corresponding sources with the two boundaries of the AdS space containing a black hole. The transverse fluctuations of the endpoints of the string determine $\\kappa_T = \\sqrt{\\gamma \\lambda} T^3 \\pi$ -- the mean squared momentum transfer per unit time. ($\\gamma$ is the lorentz gamma factor of the quark.) The result reproduces previous results for the diffusion coefficient of a heavy quark. We compare our results with previous AdS/CFT calculations of $\\hat{q}$.
Transverse momentum broadening of a fast quark in a Script N = 4 Yang-Mills plasma
Casalderrey-Solana, Jorge; Teaney, Derek
2007-04-01
We compute the momentum broadening of a heavy fundamental charge propagating through a Script N = 4 Yang Mills plasma at large t' Hooft coupling. We do this by expressing the medium modification of the probe's density matrix in terms of a Wilson loop averaged over the plasma. We then use the AdS/CFT correspondence to evaluate this loop, by identifying the dual semi-classical string solution. The calculation introduces the type ``1'' and type ``2'' fields of the thermal field theory and associates the corresponding sources with the two boundaries of the AdS space containing a black hole. The transverse fluctuations of the endpoints of the string determine κT = (γλ)1/2T3π—the mean squared momentum transfer per unit time. (γ is the Lorentz gamma factor of the quark.) The result reproduces previous results for the diffusion coefficient of a heavy quark. We compare our results with previous AdS/CFT calculations of hat q.
Quantum Vacua of 2d Maximally Supersymmetric Yang-Mills Theory
Koloğlu, Murat
2016-01-01
We analyze the classical and quantum vacua of 2d $\\mathcal{N}=(8,8)$ 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 $\\mathbb{R}^8$. We claim that the IR limit of the $SU(N)$ theory in the superselection sector labeled $M \\pmod{N}$ --- identified with the internal dynamics of $(M,N)$-string bound states of Type IIB string theory --- is described by the symmetric orbifold $\\mathcal{N}=(8,8)$ sigma model into $(\\mathbb{R}^8)^{D-1}/\\mathbb{S}_D$ 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 $\\mathbb{Z}$-valued generalized electric flux and an independent $\\mathbb{Z}_N$-valued 't Hooft flux...
Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function
Tsukiji, Hidekazu; Kunihiro, Teiji; Ohnishi, Akira; Takahashi, Toru T
2016-01-01
We investigate possible entropy production in Yang-Mills (YM) field theory by using a quantum distribution function called Husimi function $f_{\\rm H}(A, E, t)$ for YM field, which is given by a coarse graining of Wigner function and non-negative. We calculate the Husimi-Wehrl (HW) entropy $S_{\\rm HW}(t)=-{\\rm Tr}f_H \\log f_H$ defined as an integral over the phase-space, for which two adaptations of the test-particle method are used combined with Monte-Carlo method. We utilize the semiclassical approximation to obtain the time evolution of the distribution functions of the YM field, which is known to show a chaotic behavior in the classical limit. We also make a simplification of the multi-dimensional phase-space integrals by making a product ansatz for the Husimi function, which is found to give a 10-20 per cent over estimate of the HW entropy for a quantum system with a few degrees of freedom. We show that the quantum YM theory does exhibit the entropy production, and that the entropy production rate agrees ...
Note on Nonlinear Schr\\"odinger Equation, KdV Equation and 2D Topological Yang-Mills-Higgs Theory
Nian, Jun
2016-01-01
In this paper we discuss the relation between the (1+1)D nonlinear Schr\\"odinger equation and the KdV equation. By applying the boson/vortex duality, we can map the classical nonlinear Schr\\"odinger equation into the classical KdV equation in the small coupling limit, which corresponds to the UV regime of the theory. At quantum level, the two theories satisfy the Bethe Ansatz equations of the spin-$\\frac{1}{2}$ XXX chain and the XXZ chain in the continuous limit respectively. Combining these relations with the dualities discussed previously in the literature, we propose a duality web in the UV regime among the nonlinear Schr\\"odinger equation, the KdV equation and the 2D $\\mathcal{N}=(2,2)^*$ topological Yang-Mills-Higgs theory.
Field-dependent BRST-antiBRST transformations in Yang-Mills and Gribov-Zwanziger theories
Moshin, Pavel Yu.; Reshetnyak, Alexander A.
2014-11-01
We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet λa, a=1,2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang-Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang-Mills vacuum functional, special field-dependent BRST-antiBRST transformations, with sa-potential parameters λa=saΛ induced by a finite even-valued functional Λ and by the anticommuting generators sa of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary Rξ-like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional h, given in the Landau gauge, and being an additive extension of the Yang-Mills action by the Gribov horizon functional in the Gribov-Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST-antiBRST transformations to the case of general gauge theories and present an ansatz for such transformations. introduction of finite BRST-antiBRST transformations, being polynomial in powers of a constant Sp(2)-doublet of Grassmann-odd parameters λa and leaving the quantum action of the Yang-Mills theory invariant to all orders in λa; definition of finite field-dependent BRST-antiBRST transformations, being polynomial in powers of an Sp(2)-doublet of Grassmann-odd functionals λa(ϕ) depending on the classical Yang-Mills fields, the ghost
Confinement, Holonomy and Correlated Instanton-Dyon Ensemble I: SU(2) Yang-Mills Theory
Lopez-Ruiz, Miguel Angel; Liao, Jinfeng
2016-01-01
The mechanism of confinement in Yang-Mills theories remains a challenge to our understanding of nonperturbative gauge dynamics. While it is widely perceived that confinement may arise from chromo-magnetically charged gauge configurations with nontrivial topology, it is not clear what types of configurations could do that and how, in pure Yang-Mills and QCD-like (non-supersymmetric) theories. Recently a promising approach has emerged, based on statistical ensembles of dyons/anti-dyons that are constituents of instanton/anti-instanton solutions with nontrivial holonomy where the holonomy plays a vital role as an effective "Higgsing" mechanism. We report a thorough numerical investigation of the confinement dynamics in SU(2) Yang-Mills theory by constructing such a statistical ensemble of correlated instanton-dyons.
Maximally Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A maximally generalized Yang-Mills model, which contains, besides the vector part Vμ, also an axial-vector part Aμ, a scalar part S, a pseudoscalar part P, and a tensor part Tμv, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of the Nambu-Jona-Lasinio mechanism, that the gauge symmetry breaking can be realized dynamically in the maximally generalized Yang-Mills model. The combination of the maximally generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.
The global existence of Yang-Mills fields on curved space-times
Ghanem, Sari
2013-01-01
This is an introductory chapter in a series in which we take a systematic study of the Yang-Mills equations on curved space-times. In this first, we provide standard material that consists in writing the proof of the global existence of Yang-Mills fields on arbitrary curved space-times using the Klainerman-Rodnianski parametrix combined with suitable Gr\\"onwall type inequalities. While the Chru\\'sciel-Shatah argument requires a simultaneous control of the $L^{\\infty}_{loc}$ and the $H^{2}_{loc}$ norms of the Yang-Mills curvature, we can get away by controlling only the $H^{1}_{loc}$ norm instead, and write a new gauge independent proof on arbitrary, fixed, sufficiently smooth, globally hyperbolic, curved 4-dimensional Lorentzian manifolds. This manuscript is written in an expository way in order to provide notes to Master's level students willing to learn mathematical General Relativity.
Nonsymmetric unified theory of gravitation, electromagnetism and Yang-Mills field
Energy Technology Data Exchange (ETDEWEB)
Ragusa, S [Departamento de Fisica e Informatica, Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, CP 369, 13560-970 Sao Carlos, SP (Brazil)
2002-12-07
The recently studied new variation of Einstein's metric nonsymmetric unified field theory of gravitation and electromagnetism is enlarged to include the Yang-Mills field theory. It is shown that the antisymmetric part of the metric tensor, now a 2x2 matrix, can be made to describe both a field obeying Maxwell's equations and a field obeying Yang-Mills's field equations in the flat space linear approximation, thereby making its identification with the sum of a generalized electromagnetic and isotopic field strength tensors a possibly consistent procedure. The theory is shown to be free of unphysical ghost-negative energy radiative modes even when expanded on a curved Riemannian background. The Einstein-Maxwell-Yang-Mills theory is contained in the first approximation of the field equations on a curved general relativity background.
Gauge-covariant decomposition and magnetic monopole for G(2) Yang-Mills field
Matsudo, Ryutaro
2016-01-01
We give a gauge-covariant decomposition of the Yang-Mills field with an exceptional gauge group $G(2)$, which extends the field decomposition invented by Cho, Duan-Ge, and Faddeev-Niemi for the $SU(N)$ Yang-Mills field. As an application of the decomposition, we derive a new expression of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of $G(2)$. The resulting new form is used to define gauge-invariant magnetic monopoles in the $G(2)$ Yang-Mills theory. Moreover, we obtain the quantization condition to be satisfied by the resulting magnetic charge. The method given in this paper is general enough to be applicable to any semi-simple Lie group other than $SU(N)$ and $G(2)$.
Yang-Mills Solutions and Dyons on Cylinders over Coset Spaces with Sasakian Structure
Tormählen, Maike
2014-01-01
We present solutions of the Yang-Mills equation on cylinders $\\mathbb R\\times G/H$ over coset spaces with Sasakian structure and odd dimension $2m+1$. The gauge potential is assumed to be $SU(m)$-equivariant, parametrized by two real, scalar-valued functions. Yang-Mills theory with torsion in this setup reduces to the Newtonian mechanics of a point particle moving in $\\mathbb R^2$ under the influence of an inverted potential. We analyze the critical points of this potential and present an analytic as well as several numerical finite-action solutions. Apart from the Yang-Mills solutions that constitute $SU(m)$-equivariant instanton configurations, we construct periodic sphaleron solutions on $S^1\\times G/H$ and dyon solutions on $i\\mathbb R\\times G/H$.
Spatially compact solutions and stabilization in Einstein-Yang-Mills-Higgs theories.
Forgács, Péter; Reuillon, Sébastien
2005-08-01
New solutions to the static, spherically symmetric Einstein-Yang-Mills-Higgs equations with the Higgs field in the triplet (doublet) representation are presented. They form continuous families parametrized by alpha = M(W)/M(Pl) [M(W) (M(Pl)) denoting the W boson (the Planck) mass]. The corresponding space-times are regular and have spatially compact sections. A particularly interesting class with the Yang-Mills amplitude being nodeless is exhibited and is shown to be linearly stable with respect to spherically symmetric perturbations. For some solutions with nodes of the Yang-Mills amplitude a new stabilization phenomenon is found, according to which their unstable modes disappear as alpha increases (for the triplet) or decreases (for the doublet).
Explicit Derivation of Yang-Mills Self-Dual Solutions on non-Commutative Harmonic Space
Belhaj, A; Sahraoui, E L; Saidi, E H
2001-01-01
We develop the noncommutative harmonic space (NHS) analysis to study the problem of solving the non-linear constraint eqs of noncommutative Yang-Mills self-duality in four-dimensions. We show that this space, denoted also as NHS($\\eta,\\theta$), has two SU(2) isovector deformations $\\eta^{(ij)}$ and $\\theta^{(ij)}$ parametrising respectively two noncommutative harmonic subspaces NHS($\\eta,0$) and NHS($0,\\theta$) used to study the self-dual and anti self-dual noncommutative Yang-Mills solutions. We formulate the Yang-Mills self-dual constraint eqs on NHS($\\eta,0$) by extending the idea of harmonic analyticity to linearize them. Then we give a perturbative self-dual solution recovering the ordinary one. Finally we present the explicit computation of an exact self-dual solution.
Gauge field spectrum in massive Yang-Mills theory with Lorentz violation
Santos, T R S; Tomaz, A A
2016-01-01
The spectrum of the massive CPT-odd Yang-Mills propagator with Lorentz violation is performed at tree-level. The modification is due to mass terms generated by the exigence of multiplicative renormalizability of Yang-Mills theory with Lorentz violation. The causality analysis is performed from group and front velocities for both, spacelike and timelike background tensors. It is show that, by demanding causality, it is always possible to define a physical sector for the gauge propagator. Hence, it is expected that the model is also unitary, if one takes the Faddeev-Popov ghost into account.
Quantum Metamorphosis of Conformal Transformation in D3-Brane Yang-Mills Theory
Jevicki, A; Yoneya, T
1998-01-01
We show how the linear special conformal transformation in four-dimensional N=4 super Yang-Mills theory is metamorphosed into the nonlinear and field-dependent transformation for the collective coordinates of Dirichlet 3-branes, which agrees with the transformation law for the space-time coordinates in the anti-de Sitter (AdS) space-time. Our result provides a new and strong support for the conjectured relation between AdS supergravity and super conformal Yang-Mills theory (SYM). Furthermore, our work sheds elucidating light on the nature of the AdS/SYM correspondence.
Superspace gauge fixing in Yang-Mills matter-coupled conformal supergravity
Kugo, Taichiro; Yokokura, Ryo; Yoshioka, Koichi
2016-09-01
In D=4, N=1 conformal superspace, the Yang-Mills matter-coupled supergravity system is constructed where the Yang-Mills gauge interaction is introduced by extending the superconformal group to include the Kähler isometry group of chiral matter fields. There are two gauge-fixing procedures to get to the component Poincaré supergravity: one via the superconformal component formalism and the other via the Poincaré superspace formalism. These two types of superconformal gauge-fixing conditions are analyzed in detail and their correspondence is clarified.
Yang-Mills gauge fields conserving symmetry algebra of Dirac equation in homogeneous space
Breev, A I
2014-01-01
We consider the Dirac equation with external Yang-Mills gauge field in a homogeneous space with invariant metric. The Yang-Mills fields for which the motion group of the space serves as symmetry group of the Dirac equation are found by comparison of the Dirac equation with a invariant matrix differential operator of the first order. General constructions are illustrated by the example of de Sitter space. The basis of eigenfunctions and corresponding spectrum are obtained for the Dirac equation in the space $\\mathbb{R}^2 \\times \\mathbb{S}^2$ in the framework of the noncommutative integration method.
Model of Polyakov duality: String field theory Hamiltonians from Yang-Mills theories
Periwal, Vipul
2000-08-01
Polyakov has conjectured that Yang-Mills theory should be equivalent to a noncritical string theory. I point out, based on the work of Marchesini, Ishibashi, Kawai and collaborators, and Jevicki and Rodrigues, that the loop operator of the Yang-Mills theory is the temporal gauge string field theory Hamiltonian of a noncritical string theory. The consistency condition of the string interpretation is the zig-zag symmetry emphasized by Polyakov. I explicitly show how this works for the one-plaquette model, providing a consistent direct string interpretation of the unitary matrix model for the first time.
Plane wave matrix theory vs. N=4 D=4 super Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Kim, N. [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, 14476 Golm (Germany)
2004-06-01
A mass deformed, supersymmetric, Yang-Mills quantum mechanics has been introduced recently as the matrix model of M-theory on plane-wave backgrounds. Here we point out that the massive matrix model can be obtained as a dimensional reduction of N=4, D=4 Super Yang-Mills theory on S{sup 3}. The hamiltonian of the matrix model can be matched with the dilatation operator of the conformal field theory, and we discuss how they behave in the perturbative computations. (Abstract Copyright [2004], Wiley Periodicals, Inc.)
Fifty Years of Yang-Mills Theory and my Contribution to it
Jackiw, Roman W
2004-01-01
On the fiftieth anniversary of Yang-Mills theory, I review the contribution to its understanding by my collaborators and me. Contents: 1.Gauge Theories and Quantum Anomalies; 2.Mathematical Connections; 3. Gauge Field Dynamics other than Yang-Mills; 4. Gauge Formalism for General Relativity Variables; A. Christoffel connection as a gauge potential, B. Gravitational Chern-Simons term from gauge theory Chern-Simons term, C. Coordinate transformations in general relativity and gauge theory, (i) Response to changes in coordinates (ii) Invariant fields and constants of motion. References.
Perturbative running of the twisted Yang-Mills coupling in the gradient flow scheme
Bribian, Eduardo I
2016-01-01
We report on our ongoing computation of the perturbative running of the Yang-Mills coupling using gradient flow techniques. In particular, we use the gradient flow method with twisted boundary conditions to perform a perturbative expansion of the expectation value of the Yang-Mills energy density up to fourth order in the coupling at finite flow time. We regularise the resulting integrals using dimensional regularisation, and reproduce the universal coefficient of the 1/{\\epsilon} term in the relation between bare and renormalised couplings. The computation of the finite part leading to a determination of the {\\Lambda} parameter in this scheme is underway.
The Configuration Space of Low-dimensional Yang-Mills Theories
Pause, T
1998-01-01
We discuss the construction of the physical configuration space for Yang-Mills quantum mechanics and Yang-Mills theory on a cylinder. We explicitly eliminate the redundant degrees of freedom by either fixing a gauge or introducing gauge invariant variables. Both methods are shown to be equivalent if the Gribov problem is treated properly and the necessary boundary identifications on the Gribov horizon are performed. In addition, we analyze the significance of non-generic configurations and clarify the relation between the Gribov problem and coordinate singularities.
Integrable amplitude deformations for N =4 super Yang-Mills and ABJM theory
Bargheer, Till; Huang, Yu-Tin; Loebbert, Florian; Yamazaki, Masahito
2015-01-01
We study Yangian-invariant deformations of scattering amplitudes in 4d N =4 super Yang-Mills theory and 3d N =6 Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. In particular, we obtain the deformed Graßmannian integral for 4d N =4 supersymmetric Yang-Mills theory, both in momentum and momentum-twistor space. For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We investigate general deformations of on-shell diagrams, and find the deformed Graßmannian integral for this theory. We furthermore introduce the algebraic R-matrix construction of deformed Yangian invariants for ABJM theory.
Self-Dual Yang-Mills and the Hamiltonian Structures of Integrable Systems
Schiff, J
1992-01-01
In recent years it has been shown that many, and possibly all, integrable systems can be obtained by dimensional reduction of self-dual Yang-Mills. I show how the integrable systems obtained this way naturally inherit bihamiltonian structure. I also present a simple, gauge-invariant formulation of the self-dual Yang-Mills hierarchy proposed by several authors, and I discuss the notion of gauge equivalence of integrable systems that arises from the gauge invariance of the self-duality equations (and their hierarchy); this notion of gauge equivalence may well be large enough to unify the many diverse existing notions.
Invariants from classical field theory
Diaz, Rafael
2007-01-01
We introduce a method that generates invariant functions from classical field theories depending on external parameters. We apply our method to several field theories such as abelian BF, Chern-Simons and 2-dimensional Yang-Mills theory.
2PI Effective Action and Evolution Equations of N = 4 super Yang-Mills
Smolic, Jelena
2011-01-01
We employ nPI effective action techniques to study N = 4 super Yang-Mills, and write down the 2PI effective action of the theory. We also supply the evolution equations of two-point correlators within the theory.
Two-loop Feynman Diagrams in Yang-Mills Theory from Bosonic String Amplitudes
Körs, B; Kors, Boris; Schmidt, Michael G.
2000-01-01
We present intermediate results of an ongoing investigation which attempts a generalization of the well known one-loop Bern Kosower rules of Yang-Mills theory to higher loop orders. We set up a general procedure to extract the field theoretical limit of bosonic open string diagrams, based on the sewing construction of higher loop world sheets. It is tested with one- and two-loop scalar field theory, as well as one-loop and two-loop vacuum Yang-Mills diagrams, reproducing earlier results. It is then applied to two-loop two-point Yang-Mills diagrams in order to extract universal renormalization coefficients that can be compared to field theory. While developing numerous technical tools to compute the relevant contributions, we hit upon important conceptual questions: Do string diagrams reproduce Yang-Mills Feynman diagrams in a certain preferred gauge? Do they employ a certain preferred renormalization scheme? Are four gluon vertices related to three gluon vertices? Unfortunately, our investigations remained in...
Eigenvalue spectrum of lattice $\\mathcal{N}=4$ super Yang-Mills
Weir, David J; Mehta, Dhagash
2013-01-01
We present preliminary results for the eigenvalue spectrum of four-dimensional ${\\cal N}=4$ super Yang-Mills theory on the lattice. In particular, by studying the the spectral density a measurement of the anomalous dimension is made and found to be consistent with zero.
Microscopic- versus Effective Coupling in N=2 Yang-Mills With Four Flavours
Sachs, I; Sachs, Ivo; Weir, Billy
2000-01-01
We determine the instanton corrections to the effective coupling in SU(2), N=2 Yang-Mills theory with four flavours to all orders. Our analysis uses the S(2,Z)-invariant curve and the two instanton contribution obtained earlier to fix the higher order contributions uniquely.
Institute of Scientific and Technical Information of China (English)
WANG Dian-Fu
2008-01-01
In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Yang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.
2PI effective action and evolution equations of N=4 super Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Smolic, Jelena; Smolic, Milena [University of Amsterdam, Institute for Theoretical Physics, Amsterdam (Netherlands)
2012-08-15
We employ nPI effective action techniques to study N=4 super Yang-Mills, and write down the 2PI effective action of the theory to two-loop order in the symmetric phase. We also supply the evolution equations of two-point correlators within the theory. (orig.)
The complete one-loop spin chain for N=2 Super-Yang-Mills
Vecchia, P D
2004-01-01
We show that the complete planar one-loop mixing matrix of the N=2 Super Yang--Mills theory can be obtained from a reduction of that of the N=4 theory. For composite operators of scalar fields, this yields an anisotropic XXZ spin chain, whose spectrum of excitations displays a mass gap.
Generalized Riccati equations for self-dual Yang--Mills fields
Energy Technology Data Exchange (ETDEWEB)
Chau, L.; Yen, H.C.
1987-05-01
It is shown that although no Riccati equations in the strict sense are likely to exist for the self-dual Yang--Mills fields, certain ''generalized Riccati equations'' derivable from the Baecklund transformation do exist, and are capable of reproducing the linear system when a certain contraint is imposed.
Generalized WDVV equations for $F_4$ pure N=2 Super-Yang-Mills theory
Hoevenaars, L.K.; Kersten, P.H.M.; Martini, R.
2000-01-01
An associative algebra of holomorphic differential forms is constructed associated with pure N=2 Super-Yang-Mills theory for the Lie algebra $F_4$ . Existence and associativity of this algebra, combined with the general arguments in the work of Marshakov, Mironov and Morozov, proves that the prepote
Exact Solutions of the SU(2) Yang-Mills-Higgs Theory
Teh, R
2001-01-01
Some exact static solutions of the SU(2) Yang-Mills-Higgs theory are presented. These solutions do not satisfy the first order Bogomol'nyi equations, and do not possess finite energy. They are axially symmetric and could possibly represent monopoles and an antimonopole sitting on the z-axis.
The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces
Driver, Bruce K; Hall, Brian C; Kemp, Todd
2016-01-01
We prove the Makeenko-Migdal equation for two-dimensional Euclidean Yang-Mills theory on an arbitrary compact surface, possibly with boundary. In particular, we show that two of the proofs given by the first, third, and fourth authors for the plane case extend essentially without change to compact surfaces.
Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
DEFF Research Database (Denmark)
Caron Huot, Simon; He, Song
2013-01-01
We study the S-matrix of planar = 4 supersymmetric Yang-Mills theory when external momenta are restricted to a two-dimensional subspace of Minkowski space. We find significant simplifications and new, interesting structures for tree and loop amplitudes in two-dimensional kinematics, in particular...
The low-lying spectrum of N=1 supersymmetric Yang-Mills theory
Bergner, Georg; Montvay, Istvan; Muenster, Gernot; Piemonte, Stefano
2015-01-01
The spectrum of the lightest bound states in N=1 supersymmetric Yang-Mills theory with SU(2) gauge group, calculated on the lattice, is presented. The masses have first been extrapolated towards vanishing gluino mass and then to the continuum limit. The final picture is consistent with the formation of degenerate supermultiplets.
Challifour, John L.; Timko, Edward J.
2016-06-01
Using a Krein indefinite metric in Fock space, the Hamiltonian for cut-off models of canonically quantized Higgs-Yang-Mills fields interpolating between the Gupta-Bleuler-Feynman and Landau gauges is shown to be essentially maximal accretive and essentially Krein selfadjoint.
Freedom and confinement in lattice Yang-Mills theories. A case for divorce
Energy Technology Data Exchange (ETDEWEB)
Colangelo, P.; Cosmai, L.; Pellicoro, M.; Preparata, G.
1986-03-01
We present evidence that nonperturbative effects in lattice gauge theories do not obey at small coupling constant (large ..beta..) asymptotic scaling, but they rather behave as suggested by a recent result in continuum Yang-Mills theories. We also discuss the possible impact of these results on our understanding of QCD.
Existence of axially symmetric solutions in SU(2)-Yang-Mills and related theories
Hannibal, L; Hannibal, Ludger; Ossietzky, Carl von
1999-01-01
It is shown that the static axially symmetric solutions of SU(2) Einstein-Yang-Mills-Dilaton theory constructed by Kleihaus and Kunz are gauge-equivalent to two-parameter families of embedded abelian solutions, characterized by mass and magnetic dipole moment. The existence of other particle-like solutions is excluded.
Notes on equivalences and Higgs branches in N=2 supersymmetric Yang-Mills theory
Danielsson, U H; Danielsson, Ulf H; Stjernberg, Par
1996-01-01
In this paper we investigate how various equivalences between effective field theories of N=2 SUSY Yang-Mills theory with matter can be understood through Higgs breaking, i.e. by giving expectation values to squarks. We give explicit expressions for the flat directions for a wide class of examples.
Massive and mass-less Yang-Mills and gravitational fields
Veltman, M.J.G.; Dam, H. van
1970-01-01
Massive and mass-less Yang-Mills and gravitational fields are considered. It is found that there is a discrete difference between the zero-mass theories and the very small, but non-zero mass theories. In the case of gravitation, comparison of massive and mass-less theories with experiment, in partic
The Hamiltonian structure of Yang-Mills theories and instantons II
Bergvelt, M. J.; De Kerf, E. A.
1986-11-01
The formalism of constraints, reviewed in paper I, is applied to Yang-Mills theory to determine the physical phase space. This turns out to be the cotangent bundle of orbit space, the space of gauge inequivalent potentials. Self-dual configurations are not Hamiltonian with respect to the symplectic structure inherited from the general system.
Energy Technology Data Exchange (ETDEWEB)
Chau, L.L.
1983-01-01
Integrable properties, i.e., existence of linear systems, infinite number of conservation laws, Reimann-Hilbert transforms, affine Lie algebra of Kac-Moody, and Bianchi-Baecklund transformation, are discussed for the constraint equations of the supersymmetric Yang-Mills fields. For N greater than or equal to 3 these constraint equations give equations of motion of the fields. These equations of motion reduce to the ordinary Yang-Mills equations as the spinor and scalar fields are eliminated. These understandings provide a possible method to solve the full Yang-Mills equations. Connections with other non-linear systems are also discussed. 53 references.
Füzfa, A
2002-01-01
The general hamiltonian formalism for time-dependent Einstein-Yang-Mills equations is presented and then applied to the well studied case of spherically symmetric su(2)-valued Yang-Mills fields. Here, we focus on by far less known time dependent solutions of these equations, and especially on perturbations of Friedmann-Lemaitre homogeneous solutions. By analysing the hamiltonian constraints, we present numerical evidences that the non abelian Yang-Mills fields are more sensitive to inhomogeneity (at least in the expansion rate) than their scalar (inflaton) and abelian (Maxwell) counterparts. Interesting consequences on the process of gravitational instability are briefly outlined here and will be developped in a forthcoming paper.
Intermediate distance correlators in hot Yang-Mills theory
Laine, M; Vuorinen, A
2010-01-01
Lattice measurements of spatial correlation functions of the operators FF and FF-dual in thermal SU(3) gauge theory have revealed a clear difference between the two channels at "intermediate" distances, x ~ 1/(pi T). This is at odds with the AdS/CFT limit which predicts the results to coincide. On the other hand, an OPE analysis at short distances (x 1/(pi T)) as well as effective theory methods at long distances (x 1/(pi T)) suggest differences. Here we study the situation at intermediate distances by determining the time-averaged spatial correlators through a 2-loop computation. We do find unequal results, however the numerical disparity is small. Apart from theoretical issues, a future comparison of our results with time-averaged lattice measurements might also be of phenomenological interest in that understanding the convergence of the weak-coupling series at intermediate distances may bear on studies of the thermal broadening of heavy quarkonium resonances.
Thermodynamics and reference scale of SU(3) gauge theory from gradient flow on fine lattices
Kitazawa, Masakiyo; Hatsuda, Tetsuo; Iritani, Takumi; Itou, Etsuko; Suzuki, Hiroshi
2015-01-01
We study the parametrization of lattice spacing and thermodynamics of SU(3) gauge theory on the basis of the Yang-Mills gradient flow on fine lattices. The lattice spacing of the Wilson gauge action is determined over a wide range $6.3\\le\\beta\\le7.5$ with high accuracy. The measurements of the flow time and lattice spacing dependences of the expectation values of the energy-momentum tensor are performed on fine lattices.
Role of center vortices in chiral symmetry breaking in SU(3) gauge theory
2011-01-01
We study the behavior of the AsqTad quark propagator in Landau gauge on SU(3) Yang-Mills gauge configurations under the removal of center vortices. In SU(2) gauge theory, center vortices have been observed to generate chiral symmetry breaking and dominate the infrared behavior of the quark propagator. In contrast, we report a weak dependence on the vortex content of the gauge configurations, including the survival of dynamical mass generation on configurations with vanishing string tension.
Structure constants of planar N =4 Yang Mills at one loop
Alday, L F; Gava, E; Narain, K S; Alday, Luis F.; David, Justin R.; Gava, Edi
2005-01-01
We study structure constants of gauge invariant operators in planar N=4 Yang-Mills at one loop with the motivation of determining features of the string dual of weak coupling Yang-Mills. We derive a simple renormalization group invariant formula characterizing the corrections to structure constants of any primary operator in the planar limit. Applying this to the scalar SO(6) sector we find that the one loop corrections to structure constants of gauge invariant operators is determined by the one loop anomalous dimension Hamiltonian in this sector. We then evaluate the one loop corrections to structure constants for scalars with arbitrary number of derivatives in a given holomorphic direction. We find that the corrections can be characterized by suitable derivatives on the four point tree function of a massless scalar with quartic coupling. We show that individual diagrams violating conformal invariance can be combined together to restore it using a linear inhomogeneous partial differential equation satisfied ...
Numerical Hermitian Yang-Mills Connections and Vector Bundle Stability in Heterotic Theories
Anderson, Lara B; Karp, Robert L; Ovrut, Burt A
2010-01-01
A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.
Amplitude relations in heterotic string theory and Einstein-Yang-Mills
Schlotterer, Oliver
2016-01-01
We present all-multiplicity evidence that the tree-level S-matrix of gluons and gravitons in heterotic string theory can be reduced to color-ordered single-trace amplitudes of the gauge multiplet. Explicit amplitude relations are derived for up to three gravitons, up to two color traces and an arbitrary number of gluons in each case. The results are valid to all orders in the inverse string tension alpha' and generalize to the ten-dimensional superamplitudes which preserve 16 supercharges. Their field-theory limit results in an alternative proof of the recently discovered relations between Einstein-Yang-Mills amplitudes and those of pure Yang-Mills theory. Similarities and differences between the integrands of the Cachazo-He-Yuan formulae and the heterotic string are investigated.
Hedgehogs in Wilson loops and phase transition in SU(2) Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Belavin, V.A. [Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, RU-117259 Moscow (Russian Federation); Chernodub, M.N. [Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, RU-117259 Moscow (Russian Federation) and Department of Theoretical Physics, Uppsala University, P.O. Box 803, S-75108 Uppsala (Sweden)]. E-mail: maxim.chernodub@itep.ru; Kozlov, I.E. [Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, RU-117259 Moscow (Russian Federation); Faculty of Physics, Moscow State University, RU-119992 Moscow (Russian Federation)
2006-08-07
We suggest that the gauge-invariant hedgehog-like structures in the Wilson loops are physically interesting degrees of freedom in the Yang-Mills theory. The trajectories of these 'hedgehog loops' are closed curves corresponding to center-valued (untraced) Wilson loops and are characterized by the center charge and winding number. We show numerically in the SU(2) Yang-Mills theory that the density of hedgehog structures in the thermal Wilson-Polyakov line is very sensitive to the finite-temperature phase transition. The (additively normalized) hedgehog line density behaves like an order parameter: The density is almost independent of the temperature in the confinement phase and changes substantially as the system enters the deconfinement phase. In particular, our results suggest that the (static) hedgehog lines may be relevant degrees of freedom around the deconfinement transition and thus affect evolution of the quark-gluon plasma in high-energy heavy-ion collisions.
N=4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole
Huang, Xing
2014-01-01
We construct four-dimensional N=4 super-Yang-Mills theories on a conic sphere with various background R-symmetry gauge fields. We study free energy and supersymmetric Renyi entropy using heat kernel method as well as localization technique. We find that the universal contribution to the partition function in the free field limit is the same as that in the strong coupling limit, which implies that it may be protected by supersymmetry. Based on the fact that, the conic sphere can be conformally mapped to $S^1\\times H^3$ and the R-symmetry background fields can be supported by the R-charges of black hole, we propose that the holographic dual of these theories are five-dimensional, supersymmetric STU topological black holes. We demonstrate perfect agreement between N=4 super-Yang-Mills theories in the planar limit and the STU topological black holes.
The thermodynamics of quantum Yang-Mills theory theory and applications
Hofmann, Ralf
2016-01-01
This latest edition enhances the material of the first edition with a derivation of the value of the action for each of the Harrington-Shepard calorons/anticalorons that are relevant for the emergence of the thermal ground state. Also included are discussions of the caloron center versus its periphery, the role of the thermal ground state in U(1) wave propagation, photonic particle-wave duality, and calculational intricacies and book-keeping related to one-loop scattering of massless modes in the deconfining phase of an SU(2) Yang-Mills theory. Moreover, a derivation of the temperature-redshift relation of the CMB in deconfining SU(2) Yang-Mills thermodynamics and its application to explaining an apparent early re-ionization of the Universe are given. Finally, a mechanism of mass generation for cosmic neutrinos is proposed.
Hedgehogs in Wilson loops and phase transition in SU(2) Yang-Mills theory
Belavin, V A; Kozlov, I E
2006-01-01
We suggest that the gauge-invariant hedgehogs-like structures in the Wilson loops are physically interesting degrees of freedom in the Yang-Mills theory. The trajectories of these hedgehogs are closed curves which correspond to center-valued (untraced) Wilson loops and are characterized by the center charge and by the winding number. We show numerically in SU(2) Yang-Mills theory that the density of the hedgehogs in the thermal Wilson-Polyakov line is very sensitive to the finite temperature phase transition. The (additively normalized) hedgehog density behaves as an order parameter: the density is almost independent of the temperature in the confinement phase and changes substantially as the system gets into the deconfinement phase. Our results suggest in particular that the (static) hedgehogs may be relevant degrees of freedom around the deconfinement transition, and thus affect evolution of the quark-gluon plasma in high-energy heavy ion collisions.
On the spherically symmetric Einstein-Yang-Mills-Higgs equations in Bondi coordinates
Tadmon, Calvin
2012-01-01
We revisit and generalize, to the Einstein-Yang-Mills-Higgs system, previous results of D. Christodoulou and D. Chae concerning global solutions for the Einstein-scalar field and the Einstein-Maxwell-Higgs equations. The novelty of the present work is twofold. For one thing the assumption on the self-interaction potential is improved. For another thing explanation is furnished why the solutions obtained here and those proved by Chae for the Einstein-Maxwell-Higgs decay more slowly than those established by Christodoulou in the case of self-gravitating scalar fields. Actually this latter phenomenon stems from the non-vanishing local charge in Einstein-Maxwell-Higgs and Einstein-Yang-Mills-Higgs models.
Renormalization aspects of N = 1 Super Yang-Mills theory in the Wess-Zumino gauge
Energy Technology Data Exchange (ETDEWEB)
Capri, M.A.L.; Granado, D.R.; Guimaraes, M.S.; Justo, I.F.; Sorella, S.P.; Vercauteren, D. [UERJ-Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Instituto de Fisica, Maracana, Rio de Janeiro (Brazil); Mihaila, L. [Karlsruhe Institute of Technology (KIT), Institut fuer Theoretische Teilchenphysik, Karlsruhe (Germany)
2014-04-15
The renormalization of N = 1 Super Yang-Mills theory is analyzed in the Wess-Zumino gauge, employing the Landau condition. An all-orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field, and gluino renormalization. The nonrenormalization theorem of the gluon-ghost-antighost vertex in the Landau gauge is shown to remain valid in N = 1 Super Yang-Mills. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino. These features are explicitly checked through a three-loop calculation. (orig.)
Infrared Behaviour of Landau Gauge Yang-Mills Theory with a Fundamentally Charged Scalar Field
Fister, Leonard
2010-01-01
The infrared behaviour of the n-point functions of a Yang-Mills theory with a charged scalar field in the fundamental representation of SU(N) is studied in the formalism of Dyson-Schwinger equations. Assuming a stable skeleton expansion solutions in form of power laws for the Green functions are obtained. For a massless scalar field the uniform limit is sufficient to describe the infrared scaling behaviour of vertices. Not taking into account a possible Higgs-phase it turns out that kinematic singularities play an important role for the scaling solutions of massive scalars. On a qualitative level scalar Yang-Mills theory yields similar scaling solutions as recently obtained for QCD.
Some Comments on the String Singularity of the Yang-Mills-Higgs Theory
Lim, Kok-Geng; Teh, Rosy
2010-07-01
We are going to make use of the regulated polar angle which had been introduced by Boulware et al.. to show that in the SU(2) Yang-Mills-Higgs theory when the magnetic monopole is carried by the gauge field, the Higgs field does not carry the monopole and vice versa. In the Yang-Mills-Higgs theory, our solution shows that when the parameter ɛ ≠ 0, the monopole is carried by the gauge field and there is a string singularity in the gauge field. When the parameter ɛ → 0, the monopole is transferred from the gauge field to the Higgs field and the string singularity disappeared. The solution is only singular at the origin, that is at r = 0 as it becomes the Wu-Yang monopole.
Topics In N = 4 Yang-mills And The Self-dual String
Basu, A
2005-01-01
We analyze some systematics of the coupling constant dependence of correlators in N = 4 Yang- Mills, which is the world-volume theory on D3-branes. We use the fact that the operator Ot that generates infinitesimal changes of the coupling constant in this theory sits in the same supermultiplet as the superconformal currents. We show how superconformal current Ward identities determine a class of terms in the operator product expansion of Ot with any other operator. In certain cases, this leads to constraints on the coupling dependence of correlation functions in N = 4 Yang-Mills. As an application, we demonstrate the exact non-renormalization of two and certain three-point correlation functions of BPS operators. We next approximate these integrated correlators by using a truncated OPE expansion. This leads to differential equations for the coupling dependence. When applied to a particular sixteen point correlator, the coupling dependence we find agrees with the corresponding amplitude computed via the Ad...
Numerical Hermitian Yang-Mills connections and vector bundle stability in heterotic theories
Anderson, Lara B.; Braun, Volker; Karp, Robert L.; Ovrut, Burt A.
2010-06-01
A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.
Amplitude relations in heterotic string theory and Einstein-Yang-Mills
Schlotterer, Oliver
2016-11-01
We present all-multiplicity evidence that the tree-level S-matrix of gluons and gravitons in heterotic string theory can be reduced to color-ordered single-trace amplitudes of the gauge multiplet. Explicit amplitude relations are derived for up to three gravitons, up to two color traces and an arbitrary number of gluons in each case. The results are valid to all orders in the inverse string tension α' and generalize to the ten-dimensional superamplitudes which preserve 16 supercharges. Their field-theory limit results in an alternative proof of the recently discovered relations between Einstein-Yang-Mills amplitudes and those of pure Yang-Mills theory. Similarities and differences between the integrands of the Cachazo-He-Yuan formulae and the heterotic string are investigated.
Transport properties of N=4 supersymmetric Yang-Mills theory at finite coupling
Benincasa, P; Benincasa, Paolo; Buchel, Alex
2006-01-01
Gauge theory-string theory duality describes strongly coupled N=4 supersymmetric SU(n) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-n N=4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation for the shear and the sound wave lowest quasinormal modes in the leading order alpha'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the alpha'-corrected nonextremal black branes in string theory.
On the sign problem in 2D lattice super Yang--Mills
Catterall, Simon; Joseph, Anosh; Mehta, Dhagash
2011-01-01
In recent years a new class of supersymmetric lattice theories have been proposed which retain one or more exact supersymmetries for non-zero lattice spacing. Recently there has been some controversy in the literature concerning whether these theories suffer from a sign problem. In this paper we address this issue by conducting simulations of the N=(2, 2) and N=(8, 8) supersymmetric Yang--Mills theories in two dimensions for the U(N) theories with N=2,3,4, using the new twisted lattice formulations. Our results provide evidence that these theories do not suffer from a sign problem in the continuum limit. These results thus boost confidence that the new lattice formulations can be used successfully to explore non-perturbative aspects of four-dimensional N=4 supersymmetric Yang--Mills theory.
Light Dilaton at Fixed Points and Ultra Light Scale Super Yang Mills
DEFF Research Database (Denmark)
Antipin, Oleg; Mojaza, Matin; Sannino, Francesco
2012-01-01
We investigate the infrared dynamics of a nonsupersymmetric SU(X) gauge theory featuring an adjoint fermion, Nf Dirac flavors and an Higgs-like complex Nf x Nf scalar which is a gauge singlet. We first establish the existence of an infrared stable perturbative fixed point and then investigate...... the spectrum near this point. We demonstrate that this theory naturally features a light scalar degree of freedom to be identified with the dilaton and elucidate its physical properties. We compute the spectrum and demonstrate that at low energy the nonperturbative part of the spectrum of the theory is the one...... of pure supersymmetric Yang-Mills. We can therefore determine the exact nonperturbative fermion condensate and deduce relevant properties of the nonperturbative spectrum of the theory. We also show that the intrinsic scale of super Yang-Mills is exponentially smaller than the scale associated...
Yang-Mills equation for the nuclear geometrical collective model connexion
Sparks, N.; Rosensteel, G.
2017-01-01
The Bohr-Mottelson collective model of rotations and quadrupole vibrations is a foundational model in nuclear structure physics. A modern formulation using differential geometry of bundles builds on this legacy collective model to allow a deformation-dependent interaction between rotational and vortical degrees of freedom. The interaction is described by the bundle connexion. This article reports the Yang-Mills equation for the connexion. For a class of solutions to the Yang-Mills equation, the differential geometric collective model attains agreement between experiment and theory for the moments of inertia of deformed isotopes. More generally, the differential geometric framework applies to models of emergent phenomena in which two interacting sets of degrees of freedom must be unified.
Correspondence between Einstein-Yang-Mills-Lorentz systems and dynamical torsion models
Cembranos, Jose A R
2016-01-01
In the framework of Einstein-Yang-Mills theories, we study the gauge Lorentz group and establish a particular equivalence between this case and a certain class of theories with torsion within Riemann-Cartan space-times. This relation is specially useful in order to simplify the problem of finding exact solutions to the Einstein-Yang-Mills equations. Solutions for non-vanishing torsion with rotation and reflection symmetries are presented by the explicit use of this correspondence. Although these solutions were found in previous literature by a different approach, our method provides an alternative way to obtain them and it may be used in future research to find other exact solutions within this theory.
The gluino-glue particle and relevant scales for the simulations of supersymmetric Yang-Mills theory
Bergner, Georg; Münster, Gernot; Sandbrink, Dirk; Özugurel, Umut D
2012-01-01
Supersymmetric Yang-Mills theory is in several respects different from QCD and pure Yang-Mills theory. Therefore, a reinvestigation of the scales, at which finite size effects and lattice artifacts become relevant, is necessary. Both, finite size effects and lattice artifacts, induce a breaking of supersymmetry. In view of the unexpected mass gap between bosonic and fermionic particles an estimation of these effects is essential.
Implementing the Gribov-Zwanziger framework in N=1 Super Yang-Mills in the Landau gauge
Capri, M A L; Guimaraes, M S; Justo, I F; Palhares, L F; Sorella, S P; Vercauteren, D
2014-01-01
The Gribov-Zwanziger framework accounting for the existence of Gribov copies is extended to N=1 Super Yang--Mills theories quantized in the Landau gauge. We show that the restriction of the domain of integration in the Euclidean functional integral to the first Gribov horizon can be implemented in a way to recover non-perturbative features of N=1 Super Yang--Mills theories, namely: the existence of the gluino condensate as well as the vanishing of the vacuum energy.
Spontaneous breaking of color in N=1 Super Yang-Mills theory without matter
Diakonov, D; Diakonov, Dmitri; Petrov, Victor
2002-01-01
We argue that in the pure N=1 Super Yang-Mills theory gauge symmetry is spontaneously broken to the maximal Abelian subgroup. In particular, colored gluino condensate is nonzero. It invalidates, in a subtle way, the so-called strong-coupling instanton calculation of the (normal) gluino condensate and resolves the long-standing paradox why its value does not agree with that obtained by other methods.
Solutions to Yang-Mills field equations in eight dimensions and the last Hopf map
Energy Technology Data Exchange (ETDEWEB)
Grossman, B.; Kephart, T.W.; Stasheff, J.D.
1984-12-01
The authors show that the Hopf map S/sup 15/->S/sup 7/ S/sup 8/ admits a sourceless, topologically non-trivial gauge field. This result is cast in the form of a solution to eight dimensional Euclidean Yang-Mills field equations with topological charge Q=1. This solution is Spin (9) symmetric and leads to a new generalized duality condition FandF=+-(FandF)sup(*).
Coupling of Yang-Mills to N = 4, d = 4 supergravity
Bergshoeff, E.; Koh, I.G.; Sezgin, E.
1985-01-01
We couple N = 4, d = 4 supersymmetric Yang-Mills theory to supergravity. The scalars of the theory parametrize the coset (SO(n,6)/[SO(n)Ã—SO(6)])Ã—(SU(1,1)/U(1)). Keeping the composite local SO(n)Ã—SO(6)Ã—U(1) invariance intact, we gauge an (n + 6) parameter subgroup of SO(n,6) which is either (i) S
Geometry of the gauge algebra in noncommutative Yang-Mills theory
Lizzi, Fedele; Zampini, Alessandro; Szabo, Richard J.
2001-08-01
A detailed description of the infinite-dimensional Lie algebra of star-gauge transformations in non-commutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra u(∞), and of the C*-algebra of compact operators on a quantum mechanical Hilbert space. The spacetime and string interpretations are also elucidated.
Geometry of the Gauge Algebra in Noncommutative Yang-Mills Theory
Lizzi, F; Zampini, A
2001-01-01
A detailed description of the infinite-dimensional Lie algebra of star-gauge transformations in noncommutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra, and of the algebra of compact operators on a quantum mechanical Hilbert space. The spacetime and string interpretations are also elucidated.
Supersymmetry algebra and BPS states of super Yang-Mills theories on noncommutative tori
Konechny, Anatoly; Schwarz, Albert
1999-04-01
We consider 10-dimensional super Yang-Mills theory with topological terms compactified on a noncommutative torus. We calculate supersymmetry algebra and derive BPS energy spectra from it. The cases of d-dimensional tori with d=2,3,4 are considered in full detail. SO(d,d,Z)-invariance of the BPS spectrum and relation of new results to the previous work in this direction are discussed.
Coupled equations for K\\"ahler metrics and Yang-Mills connections
Alvarez-Consul, Luis; Garcia-Prada, Oscar
2011-01-01
We study equations on a principal bundle over a compact complex manifold coupling connections on the bundle with K\\"ahler structures in the base. These equations generalize the conditions of constant scalar curvature for a K\\"ahler metric and Hermite-Yang-Mills for a connection. We provide a moment map interpretation of the equations and study obstructions for the existence of solutions, generalizing the Futaki invariant, Mabuchi functional and geodesic stability. We finish by giving some examples of solutions.
Einstein and Yang-Mills theories in hyperbolic form without gauge-fixing
Abrahams, A M; Choquet-Bruhat, Y; York, J W
1995-01-01
The evolution of physical and gauge degrees of freedom in the Einstein and Yang-Mills theories are separated in a gauge-invariant manner. We show that the equations of motion of these theories can always be written in flux-conservative first-order symmetric hyperbolic form. This dynamical form is ideal for global analysis, analytic approximation methods such as gauge-invariant perturbation theory, and numerical solution.
5D maximally supersymmetric Yang-Mills in 4D superspace. Applications
Energy Technology Data Exchange (ETDEWEB)
McGarrie, Moritz
2013-03-15
We reformulate 5D maximally supersymmetric Yang-Mills in 4D Superspace, for a manifold with boundaries. We emphasise certain features and conventions necessary to allow for supersymmetric model building applications. Finally we apply the holographic interpretation of a slice of AdS and show how to generate Dirac soft masses between external source fields, as well as kinetic mixing, as a boundary effective action.
On the string actions for the generalized two-dimensional Yang-Mills theories
Sugawara, Y
1996-01-01
We study the structures of partition functions of the large N generalized two-dimensional Yang-Mills theories (gYM_2) by recasting the higher Casimirs. We clarify the appropriate interpretations of them and try to extend the Cordes-Moore-Ramgoolam's topological string model describing the ordinary YM_2 \\cite{CMR} to those describing gYM_2. The concept of ''deformed gravitational descendants'' will be introduced for this purpose.
A solution to the non-linear equations of D=10 super Yang-Mills theory
Mafra, Carlos R
2015-01-01
In this letter, we present a formal solution to the non-linear field equations of ten-dimensional super Yang--Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher mass dimensions are defined and their equations of motion spelled out.
Power-law mass inflation in Einstein-Yang-Mills-Higgs black holes
Galtsov, D V
1997-01-01
Analytical formulas are presented describing a generic singularity inside the static spherically symmetric black holes in the SU(2) Einstein-Yang-Mills-Higgs theories with triplet or doublet Higgs field. The singularity is spacelike and exhibits a `power-low mass inflation'. Alternatively this asymptotic may be interpreted as a pointlike singularity with a non-vanishing shear in the Kantowski-Sachs anisotropic cosmology.
Bassetto, A; Torrielli, A; Vian, F
2005-01-01
We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.
Infrared Safe Observables in ${\\cal N}=4$ Super Yang-Mills Theory
Bork, L V; Vartanov, G S; Zhiboedov, A V
2009-01-01
The infrared structure of MHV gluon amplitudes in ${\\cal N}=4$ super Yang-Mills theory is considered in the next-to-leading order of PT. Explicit cancelation of the infrared divergencies in properly defined cross-sections is demonstrated. The remaining finite parts for some inclusive differential cross-sections are calculated analytically. In general, contrary to the virtual corrections, they do not reveal any simple structure.
Statistical mechanics for dilatations in N=4 super Yang--Mills theory
Sochichiu, C
2006-01-01
Matrix model describing the anomalous dimensions of composite operators in $\\mathcal{N}=4$ super Yang--Mills up to one-loop level theory is considered at finite temperature. We compute the thermal effective action for this model, which we define as the log of the partition function restricted to the states of given length and spin. The result is obtained in the limits of high and low temperature.
Relating Gribov-Zwanziger theory and Yang-Mills theory in Batalin-Vilkovisky formalism
Upadhyay, Sudhaker
2011-01-01
We consider the BRST invariant Gribov-Zwanziger theory with appropriate horizon term in Batalin-Vilkovisky formalism. The usual infinitesimal BRST transformation is generalized by considering the parameter finite and field dependent. We show that such finite field dependent BRST transformation with suitable choice of finite parameter relates the generating functional of Gribov-Zwanziger theory to that of the Yang-Mills theory.
Superspace Formulation of N=4 Super Yang-Mills Theory with a Central Charge
Saito, J
2005-01-01
A superspace formulation using superconnections and supercurvatures is specifically constructed for N=4 extended super Yang-Mills theory with a central charge in four dimensions, first proposed by Sohnius, Stelle and West long ago. We find that the constraints, almost uniquely derived from the possible spin structure of the multiplet, can be algebraically solved which results in an off-shell supersymmetric formulation of the theory on the superspace.
Emergence of Yang Mills theory from the Non-Abelian Nambu Model
Escobar, C A
2016-01-01
The equivalence between the Non-Abelian Nambu model (NANM) and Yang Mills theory is proved, after demanding the Gauss laws at some initial time to the first one. Thereby, the Lorentz violation encoded into the constraint that defines the NANM is physically unobservable. As result, the Goldstone bosons in the NANM arising from the spontaneous symmetry breaking can be identified as the standard gauge fields.
Canonical simulations of supersymmetric SU(N) Yang-Mills quantum mechanics
Bergner, Georg; Wenger, Urs
2015-01-01
The fermion loop formulation naturally separates partition functions into their canonical sectors. Here we discuss various strategies to make use of this for supersymmetric SU(N) Yang-Mills quantum mechanics obtained from dimensional reduction in various dimensions and present numerical results for the separate canonical sectors with fixed fermion numbers. We comment on potential problems due to the sign of the contributions from the fermions and due to flat directions.
An instability of hyperbolic space under the Yang-Mills flow
Energy Technology Data Exchange (ETDEWEB)
Gegenberg, Jack; Day, Andrew C.; Liu, Haitao; Seahra, Sanjeev S. [Department of Mathematics and Statistics, University of New Brunswick Fredericton, New Brunswick, E3B 5A3 (Canada)
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 of 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.
Pitts, J Brian
2016-01-01
Classical and quantum field theory provide not only realistic examples of extant notions of empirical equivalence, but also new notions of empirical equivalence, both modal and occurrent. A simple but modern gravitational case goes back to the 1890s, but there has been apparently total neglect of the simplest relativistic analog, with the result that an erroneous claim has taken root that Special Relativity could not have accommodated gravity even if there were no bending of light. The fairly recent acceptance of nonzero neutrino masses shows that widely neglected possibilities for nonzero particle masses have sometimes been vindicated. In the electromagnetic case, there is permanent underdetermination at the classical and quantum levels between Maxwell's theory and the one-parameter family of Proca's electromagnetisms with massive photons, which approximate Maxwell's theory in the limit of zero photon mass. While Yang-Mills theories display similar approximate equivalence classically, quantization typically ...
The Confinement Mechanism in Yang-Mills Theory?
Magpantay, J A
1999-01-01
Using the recently proposed non-linear gauge condition, we show the area law behavior of the Wilson loop and the linear dependence of the instantaneous gluon propagator. The field configurations responsible for confinement are those in the non-linear sector of the gauge-fixing condition (the linear sector being the Coulomb gauge). The non-linear sector is actually composed of "Gribov horizons" on the surfaces parallel to the Coulomb surface. In this sector, the gauge field can be expressed in terms of a scalar field and a new vector field. The effective dynamics of the scalar field suggests non-perturbative effects. This was confirmed by showing that all spherically symmetric (in 4-D Euclidean) scalar fields are classical solutions and averaging these solutions using a qaussian distribution (thereby treating these fields as random) lead to confinement. In essence the confinement mechanism is not quantum mechanical in nature but simply a statistical treatment of classical spherically symmetric fields on the "h...
Directory of Open Access Journals (Sweden)
Pedro Romano-Aportela
2011-01-01
Full Text Available Se analizan las interacciones electromagnéticas y nucleares débiles utilizando el principio fundamental de simetría en espacios abstractos denominados teoría de campos de Yang-Mills, también conocidos como campos de norma (gauge fields y el mecanismo de Higgs. Los campos de norma actúan como mediadores de las interacciones, cuyo alcance está determinado de manera directa por la masa. Por este motivo los campos de norma se unen al mecanismo de Higgs que genera masa a los portadores de las interacciones, manteniendo la teoría invariante bajo una transformación de norma. Esto se logra a través de un rompimiento espontaneo de simetría para finalmente aplicar esta metodología con la finalidad de unificar las teorías de las interacciones considerando el modelo estándar de Weinberg-Salam.The electromagnetic and weak nuclear interactions are analyzed using the fundamental principle of symmetry in abstract spaces named theory of Yang-Mills fields, also known as gauge fields, and Higgs's mechanism. Gauge fields are mediators of interactions, whose scope is determined directly by the mass. For this reason, gauge fields are joined with the Higgs mechanism that generates mass to the interaction carriers, maintaining the invariant theory under a gauge transformation. This is achieved through spontaneous symmetry breaking to finally applying this methodology in order to unify the theories of interactions considering the Weinberg-Salam standard model.
Topological susceptibility in the SU(3) random vortex world-surface model
Engelhardt, M
2008-01-01
The topological charge is constructed for SU(3) center vortex world-surfaces composed of elementary squares on a hypercubic lattice. In distinction to the SU(2) case investigated previously, it is necessary to devise a proper treatment of the color structure at vortex branchings, which arise in the SU(3) case, but not for SU(2). The construction is used to evaluate the topological susceptibility in the random vortex world-surface model of infrared Yang-Mills dynamics. Results for the topological susceptibility are reported as a function of temperature, including both the confined as well as the deconfined phase.
On the absence of black hole event horizons: a test of De Sitter Yang-Mills Theory
Andersen, Timothy D
2014-01-01
De Sitter Quantum Gravity is a Yang-Mills theory based on the de Sitter or SO(4,1) group and a promising candidate for a quantum theory of gravity. In this paper, an exact, static, spherically symmetric solution of the classical equations is derived. I show that when the Schwarzchild radius to distance ratio is at post-Newtonian order the theory agrees with general relativity for all parameters but that, once the ratio becomes closer to unity, they differ. At the Schwarzchild radius from a black hole singularity, general relativity predicts an event horizon, which has become a controversial topic in quantum gravity because of information preservation issues. In the De Sitter theory I show, however, that time-like escape paths exist for any mass black hole until the singularity itself is reached. Since an event horizon has never been directly observed and there is currently no observation on which the two theories disagree, this provides a powerful test of the De Sitter theory.
Reformulations of the Yang-Mills theory toward quark confinement and mass gap
Energy Technology Data Exchange (ETDEWEB)
Kondo, Kei-Ichi; Shinohara, Toru [Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522 (Japan); Kato, Seikou [Fukui National College of Technology, Sabae 916-8507 (Japan); Shibata, Akihiro [Computing Research Center, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801 (Japan)
2016-01-22
We propose the reformulations of the SU (N) Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the SU (N) Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulations can be combined with the SU (N) extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the SU (N) Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole with the stability group U (N− 1). This suggests the non-Abelian dual superconductivity picture for quark confinement. This should be compared with the maximal option: the restricted field is Abelian and involves only the Abelian magnetic monopoles with the stability group U(1){sup N−1}, just like the Abelian projection. We give some applications of this reformulation, e.g., the stability for the homogeneous chromomagnetic condensation of the Savvidy type, the large N treatment for deriving the dimensional transmutation and understanding the mass gap, and also the numerical simulations on a lattice which are given by Dr. Shibata in a subsequent talk.
Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
Caporaso, N; Griguolo, L; Pasquetti, S; Seminara, D; Szabó, R J
2006-01-01
We study the relations between two-dimensional Yang-Mills theory on the torus, topological string theory on a Calabi-Yau threefold whose local geometry is the sum of two line bundles over the torus, and Chern-Simons theory on torus bundles. The chiral partition function of the Yang-Mills gauge theory in the large N limit is shown to coincide with the topological string amplitude computed by topological vertex techniques. We use Yang-Mills theory as an efficient tool for the computation of Gromov-Witten invariants and derive explicitly their relation with Hurwitz numbers of the torus. We calculate the Gopakumar-Vafa invariants, whose integrality gives a non-trivial confirmation of the conjectured nonperturbative relation between two-dimensional Yang-Mills theory and topological string theory. We also demonstrate how the gauge theory leads to a simple combinatorial solution for the Donaldson-Thomas theory of the Calabi-Yau background. We match the instanton representation of Yang-Mills theory on the torus with ...
N=4 Supersymmetric Yang-Mills Theory on a Kaehler Surface
Dijkgraaf, R; Schroers, B J
1998-01-01
We study N=4 supersymmetric Yang-Mills theory on a Kaehler manifold with $b_2^+ \\geq 3$. Adding suitable perturbations we show that the partition function of the N=4 theory is the sum of contributions from two branches: (i) instantons, (ii) a special class of Seiberg-Witten monopoles. We determine the partition function for the theories with gauge group SU(2) and SO(3), using S-duality. This leads us to a formula for the Euler characteristic of the moduli space of instantons.
Fifty years of Yang-Mills Theories: a phenomenological point of view
De Rújula, Alvaro
2005-01-01
On the occasion of the celebration of the first half-century of Yang--Mills theories, I am contributing a personal recollection of how the subject, in its early times, confronted physical reality, that is, its "phenomenology". There is nothing original in this work, except, perhaps, my own points of view. But I hope that the older practitioners of the field will find here grounds for nostalgia, or good reasons to disagree with me. Younger addicts may learn that history does not resemble at all what is reflected in current textbooks: it was orders of magnitude more fascinating.
Local integrands for two-loop all-plus Yang-Mills amplitudes
Badger, Simon; Peraro, Tiziano
2016-01-01
We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4-2epsilon dimensions.
Gluon scattering in N=4 super-Yang-Mills theory fromweak to strong coupling
Energy Technology Data Exchange (ETDEWEB)
Dixon, Lance J.; /SLAC
2008-03-25
I describe some recent developments in the understanding of gluon scattering amplitudes in N = 4 super-Yang-Mills theory in the large-N{sub c} limit. These amplitudes can be computed to high orders in the weak coupling expansion, and also now at strong coupling using the AdS/CFT correspondence. They hold the promise of being solvable to all orders in the gauge coupling, with the help of techniques based on integrability. They are intimately related to expectation values for polygonal Wilson loops composed of light-like segments.
BPS Equations in Omega-deformed N=4 Super Yang-Mills Theory
Ito, Katsushi; Nakajima, Hiroaki; Sasaki, Shin
2015-01-01
We study supersymmetry of N=4 super Yang-Mills theory in four dimensions deformed in the Omega-background. We take the Nekrasov-Shatashvili limit of the background so that two-dimensional super Poincare symmetry is recovered. We compute the deformed central charge of the superalgebra and study the 1/2 and 1/4 BPS states. We obtain the Omega-deformed 1/2 and 1/4 BPS dyon equations from the deformed supersymmetry transformation and the Bogomol'nyi completion of the energy.
Twisted N=4 Super Yang-Mills Theory in Omega-background
Ito, Katsushi; Sasaki, Shin
2013-01-01
We study the twisted N=4 super Yang-Mills theories in the Omega-background with the constant R-symmetry Wilson line gauge field. Based on the classification of topological twists of N=4 supersymmetry (the half, the Vafa-Witten and the Marcus twists), we construct the deformed off-shell supersymmetry associated with the scalar supercharges for these twists. We find that the Omega-deformed action is written in the exact form with respect to the scalar supercharges as in the undeformed case.
Coupled equations for K\\"ahler metrics and Yang-Mills connections (Thesis)
Garcia-Fernandez, Mario
2011-01-01
We study equations on a principal bundle over a compact complex manifold coupling connections on the bundle with K\\"ahler structures in the base. These equations generalize the conditions of constant scalar curvature for a K\\"ahler metric and Hermite-Yang-Mills for a connection. We provide a moment map interpretation of the equations and study obstructions for the existence of solutions, generalizing the Futaki character and the Mabuchi K-energy. We explain their relationship to the algebro-geometric moduli problem for pairs consisting of a polarized variety and a holomorphic vector bundle.
Global solutions of Yang-Mills equations on anti-de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Choquet-Bruhat, Y. (Paris Univ. (France). Mecanique Relativiste)
1989-12-01
Anti-de Sitter spacetime is a C{sup {infinity}} manifold diffeomorphic to R{sup 4}, endowed with a C{sup {infinity}} metric of hyperbolic signature. However this spacetime is not globally hyperbolic, and the known results about the solution of the Cauchy problem for wave equations on Lorentzian manifolds do not apply, even for a small interval of time and even for linear equations. We prove the global existence of a solution of the Cauchy problem for the Yang-Mills-Higgs equations on anti-de Sitter spacetime, under the condition that there is no radiation at timelike infinity, a condition that is explained mathematically. (author).
Goursat problem for the Yang-Mills-Vlasov system in temporal gauge
Directory of Open Access Journals (Sweden)
Marcel Dossa
2011-12-01
Full Text Available This article studies the characteristic Cauchy problem for the Yang-Mills-Vlasov (YMV system in temporal gauge, where the initial data are specified on two intersecting smooth characteristic hypersurfaces of Minkowski spacetime $(mathbb{R}^{4},eta $. Under a $mathcal{C}^{infty }$ hypothesis on the data, we solve the initial constraint problem and the evolution problem. Local in time existence and uniqueness results are established thanks to a suitable combination of the method of characteristics, Leray's Theory of hyperbolic systems and techniques developed by Choquet-Bruhat for ordinary spatial Cauchy problems related to (YMV systems.
Cut-and-join operators and N=4 super Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Brown, T.W. [DESY, Hamburg (Germany). Theory Group
2010-02-15
We show which multi-trace structures are compatible with the symmetrisation of local operators in N=4 super Yang-Mills when they are organised into representations of the global symmetry group. Cut-and-join operators give the non-planar expansion of correlation functions of these operators in the free theory. Using these techniques we find the 1/N corrections to the quarter-BPS operators which remain protected at weak coupling. We also present a new way of counting these chiral ring operators using the Weyl group S{sub N}. (orig.)
A Duality for Yang-Mills Moduli Spaces on Noncommutative Manifolds
Takai, H
2004-01-01
Studied are the moduli spaces of Yang-Mills connections on finitely generated projective modules associated with noncommutative flows. It is actually shown that they are homeomorphic to those on the dual modules associated with the dual noncommutative flows. Moreover the result is also affirmative in the case of multiflows. As an important application, computed are the moduli spaces of the instanton bundles over the noncommutative Euclidean 4-space with respect to the canonical action of space translations without using the ADHM-construction.
Global dynamics of a Yang-Mills field on an asymptotically hyperbolic space
Bizoń, Piotr
2014-01-01
We consider a spherically symmetric (purely magnetic) SU(2) Yang-Mills field propagating on an ultrastatic spacetime with two asymptotically hyperbolic regions connected by a throat of radius $\\alpha$. Static solutions in this model are shown to exhibit an interesting bifurcation pattern in the parameter $\\alpha$. We relate this pattern to the Morse index of the static solution with maximal energy. Using a hyperboloidal approach to the initial value problem, we describe the relaxation to the ground state solution for generic initial data and unstable static solutions for initial data of codimension one, two, and three.
Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields
Volkov, M S; Volkov, Mikhail S.; Galtsov, Dmitri V.
1999-01-01
We present a review of gravitating particle-like and black hole solutions with non-Abelian gauge fields. The emphasis is given to the description of the structure of the solutions and to the connection with the results of flat space soliton physics. We describe the Bartnik-McKinnon solitons and the non-Abelian black holes arising in the Einstein-Yang-Mills theory, and consider their various generalizations. These include axially symmetric and slowly rotating configurations, solutions with higher gauge groups, $\\Lambda$-term, dilaton, and higher curvature corrections. The stability issue is discussed as well. We also describe the gravitating generalizations for flat space monopoles, sphalerons, and Skyrmions.
Analytical self-dual solutions in a nonstandard Yang-Mills-Higgs scenario
Casana, R; da Hora, E; Santos, C dos
2013-01-01
We have found analytical self-dual solutions within the generalized Yang-Mills-Higgs model introduced in Phys. Rev. D 86, 085034 (2012). Such solutions are magnetic monopoles satisfying Bogomol'nyi-Prasad-Sommerfield (BPS) equations and usual finite energy boundary conditions. Moreover, the new solutions are classified in two different types according to their capability of recovering (or not) the usual 't Hooft--Polyakov monopole. Finally, we compare the profiles of the solutions we found with the standard ones, from which we comment about the main features exhibited by the new configurations.
On the Functional Renormalization Group approach for Yang-Mills fields
Lavrov, Peter M
2012-01-01
We explore the gauge dependence of the effective average action within the functional renormalization group (FRG) approach. It is shown that in the framework of standard definitions of FRG for the Yang-Mills theory, the effective average action remains gauge-dependent on-shell, independent on the use of truncation scheme. Furthermore, we propose a new formulation of the FRG, based on the use of composite operators. In this case one can provide on-shell gauge-invariance for the effective average action and universality of $S$-matrix.
On the functional renormalization group approach for Yang-Mills fields
Lavrov, Peter M.; Shapiro, Ilya L.
2013-06-01
We explore the gauge dependence of the effective average action within the functional renormalization group (FRG) approach. It is shown that in the framework of standard definitions of FRG for the Yang-Mills theory, the effective average action remains gauge-dependent on-shell, independent on the use of truncation scheme. Furthermore, we propose a new formulation of the FRG, based on the use of composite operators. In this case one can provide on-shell gauge-invariance for the effective average action and universality of S-matrix.
Wilson punctured network defects in 2D q-deformed Yang-Mills theory
Watanabe, Noriaki
2016-01-01
In the context of class S theories and 4D/2D duality relations there, we discuss the skein relations of general topological defects on the 2D side which are expected to be counterparts of composite surface-line operators in 4D class S theory. Such defects are geometrically interpreted as networks in a three dimensional space. We also propose a conjectural computational procedure for such defects in two dimensional SU(N) topological q-deformed Yang-Mills theory by interpreting it as a statistical mechanical system associated with ideal triangulations.
Renormalization aspects of N=1 Super Yang-Mills theory in the Wess-Zumino gauge
Capri, M A L; Guimaraes, M S; Justo, I F; Mihaila, L; Sorella, S P; Vercauteren, D
2014-01-01
The renormalization of N=1 Super Yang-Mills theory is analysed in the Wess-Zumino gauge, employing the Landau condition. An all orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field and gluino renormalization. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino, as explicitly shown through a three loop calculation.
Yang-Mills configurations from 3D Riemann-Cartan geometry
Mielke, E W; Hehl, F W
1994-01-01
Recently, the {\\it spacelike} part of the SU(2) Yang--Mills equations has been identified with geometrical objects of a three--dimensional space of constant Riemann--Cartan curvature. We give a concise derivation of this Ashtekar type (``inverse Kaluza--Klein") {\\it mapping} by employing a (3+1)--decomposition of {\\it Clifford algebra}--valued torsion and curvature two--forms. In the subcase of a mapping to purely axial 3D torsion, the corresponding Lagrangian consists of the translational and Lorentz {\\it Chern--Simons term} plus cosmological term and is therefore of purely topological origin.
From decay to complete breaking: pulling the strings in SU(2) Yang-Mills theory.
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.
't Hooft Loops, Electric Flux Sectors and Confinement in SU(2) Yang-Mills Theory
De Forcrand, Philippe; Forcrand, Philippe de; Smekal, Lorenz von
2002-01-01
We use 't Hooft loops of maximal size on finite lattices to calculate the free energy in the sectors of SU(2) Yang-Mills theory with fixed electric flux as a function of temperature and (spatial) volume. Our results provide evidence for the mass gap. The confinement of electric fluxes in the low temperature phase and their condensation in the high temperature phase are demonstrated. In a surprisingly large scaling window around criticality, the transition is quantitatively well described by universal exponents and amplitude ratios relating the properties of the two phases.
Towards the large N limit of pure Nu = 1 super Yang-Mills theory.
Maldacena, J; Nuñez, C
2001-01-22
We find the gravity solution corresponding to a large number of Neveu-Schwarz or D5-branes wrapped on a two sphere so that we have pure Nu = 1 super Yang-Mills in the IR. The supergravity solution is smooth, it shows confinement, and it breaks the U(1)(R) chiral symmetry in the appropriate way. When the gravity approximation is valid the masses of glueballs are comparable to the masses of Kaluza-Klein (KK) states on the 5-brane, but if we could quantize strings on this background it looks like we should be able to decouple the KK states.
Let's Twist Again: N=2 Super Yang Mills Theory Coupled To Matter
Maggiore, Nicola
2010-01-01
We give the twisted version of N=2 Super Yang Mills theory coupled to matter, including quantum fields, supersymmetry transformations, action and algebraic structure. We show that the whole action, coupled to matter, can be written as the variation of a nilpotent operator, modulo field equations. An extended Slavnov-Taylor identity, collecting gauge symmetry and supersymmetry, is written, which allows to define the web of algebraic constraints, in view of the algebraic renormalization and of the extension of the non-renormalization theorems holding for N=2 SYM theory without matter.
N=4 Supersymmetric Yang-Mills on S^3 in Plane Wave Matrix Model at Finite Temperature
Kitazawa, Yoshihisa
2008-01-01
We investigate the large N reduced model of gauge theory on a curved spacetime through the plane wave matrix model. We formally derive the action of the N=4 supersymmetric Yang-Mills theory on R \\times S^3 from the plane wave matrix model in the large N limit. Furthermore, we evaluate the effective action of the plane wave matrix model up to the two-loop level at finite temperature. We find that the effective action is consistent with the free energy of the N=4 supersymmetric Yang-Mills theory on S^3 at high temperature limit where the planar contributions dominate. We conclude that the plane wave matrix model can be used as a large N reduced model to investigate nonperturbative aspects of the N=4 supersymmetric Yang-Mills theory on R \\times S^3.
Twisted Superspace for N=D=2 Super BF and Yang-Mills with Dirac-K\\"ahler Fermion Mechanism
Kato, J; Uchida, Y; Kato, Junji; Kawamoto, Noboru; Uchida, Yukiya
2003-01-01
We propose a twisted D=N=2 superspace formalism. The relation between the twisted super charges including the BRST charge, vector and pseudo scalar super charges and the N=2 spinor super charges is established. We claim that this relation is essentially related with the Dirac-K\\"ahler fermion mechanism. We show that a fermionic bilinear form of twisted N=2 chiral and anti-chiral superfields is equivalent to the quantized version of BF theory with the Landau type gauge fixing while a bosonic bilinear form leads to the N=2 Wess-Zumino action. We then construct a Yang-Mills action described by the twisted N=2 chiral and vector superfields, and show that the action is equivalent to the twisted version of the D=N=2 super Yang-Mills action, previously obtained from the quantized generalized topological Yang-Mills action with instanton gauge fixing.
Mass Deformations of Super Yang-Mills Theories in D= 2+1, and Super-Membranes: A Note
Agarwal, Abhishek
2008-01-01
Mass deformations of supersymmetric Yang-Mills theories in three spacetime dimensions are considered. The gluons of the theories are made massive by the inclusion of a non-local gauge and Poincare invariant mass term due to Alexanian and Nair, while the matter fields are given standard Gaussian mass-terms. It is shown that the dimensional reduction of such mass deformed gauge theories defined on $R^3$ or $R\\times T^2$ produces matrix quantum mechanics with massive spectra. In particular, all known massive matrix quantum mechanical models obtained by the deformations of dimensional reductions of minimal super Yang-Mills theories in diverse dimensions are shown also to arise from the dimensional reductions of appropriate massive Yang-Mills theories in three spacetime dimensions. Explicit formulae for the gauge theory actions are provided.
Static Spherically Symmetric Solutions of the SO(5) Einstein Yang-Mills Equations
Bartnik, Robert A; Oliynyk, Todd A
2009-01-01
Globally regular (ie. asymptotically flat and regular interior), spherically symmetric and localised ("particle-like") solutions of the coupled Einstein Yang-Mills (EYM) equations with gauge group SU(2) have been known for more than 20 years, yet their properties are still not well understood. Spherically symmetric Yang--Mills fields are classified by a choice of isotropy generator and SO(5) is distinguished as the simplest model with a \\emph{non-Abelian} residual (little) group, $SU(2)\\times U(1)$, and which admits globally regular particle-like solutions. We exhibit an algebraic gauge condition which normalises the residual gauge freedom to a finite number of discrete symmetries. This generalises the well-known reduction to the real magnetic potential $w(r,t)$ in the original SU(2) YM model. Reformulating using gauge invariant polynomials dramatically simplifies the system and makes numerical search techniques feasible. We find three families of embedded SU(2) EYM equations within the SO(5) system, one of w...
A unified field theory II: Gravity interacting with a Yang-Mills and Higgs field
Gerhardt, Claus
2016-01-01
We quantize the interaction of gravity with a Yang-Mills and Higgs field using canonical quantization. Similar to the approach in a previous paper we discard the Wheeler-DeWitt equation and express the Hamilton constraint by the evolution equation of the mean curvature of the hypersurfaces in the foliation defined by the Hamiltonian setting. Expressing the time derivative of the mean curvature with the help of the Poisson brackets the canonical quantization of this equation leads to a wave equation in $Q=(0,\\infty)\\times \\cal{S}_o$, where $\\cal{S}_o$ is one of the Cauchy hypersurfaces in the Hamiltonian setting. The wave equation describes the interaction of an arbitrary Riemannian metric in $\\cal{S}_o$ and a given Yang-Mills and Higgs field. If the metric is complete $Q$ is globally hyperbolic. In case $\\cal{S}_o$ is compact we also prove a spectral resolution of the wave equation and establish sufficient conditions guaranteeing a mass gap.
Gravitating vortices, cosmic strings, and the K\\"ahler--Yang--Mills equations
Álvarez-Cónsul, Luis; García-Prada, Oscar
2015-01-01
In this work we study equations describing Abelian vortices on a Riemann surface with back reaction of the metric. The gravitating vortex equations are derived by dimensional reduction of the K\\"ahler--Yang--Mills equations on the product of the complex projective line with a Riemann surface, and inherit their moment map interpretation. Applying the general theory for the K\\"ahler--Yang--Mills equations, we give evidence of an analogue of the Donaldson--Uhlembeck--Yau Theorem for gravitating vortices --- commonly referred to as a Hitchin--Kobayashi correspondence. As a particular case of the gravitating vortex equations on $\\mathbb{P}^1$ we find the Einstein--Bogomol'nyi equations, whose solutions correspond to Nielsen--Olesen cosmic strings in the Bogomol'nyi phase. Using an existence theorem by Yisong Yang, our main result implies a Hitchin--Kobayashi correspondence for the Einstein--Bogomol'nyi equations. In particular, we prove a conjecture by Yang about the non-existence of cosmic strings on $\\mathbb{P}^...
Three-dimensional super Yang-Mills with compressible quark matter
Faedo, Antón F; Mateos, David; Pantelidou, Christiana; Tarrío, Javier
2015-01-01
We construct the gravity dual of three-dimensional, $SU(N_{\\textrm{c}})$ super Yang-Mills theory with $N_{\\textrm{f}}$ flavors of dynamical quarks in the presence of a non-zero quark density $N_{\\textrm{q}}$. The supergravity solutions include the backreaction of $N_{\\textrm{c}}$ color D2-branes and $N_{\\textrm{f}}$ flavor D6-branes with $N_{\\textrm{q}}$ units of electric flux on their worldvolume. For massless quarks, the solutions depend non-trivially only on the dimensionless combination $\\rho=N_{\\textrm{c}}^2 N_{\\textrm{q}} / \\lambda^2 N_{\\textrm{f}}^4$, with $\\lambda=g_{\\textrm{YM}}^2 N_{\\textrm{c}}$ the 't Hooft coupling, and describe renormalization group flows between the super Yang-Mills theory in the ultraviolet and a non-relativistic theory in the infrared. The latter is dual to a hyperscaling-violating, Lifshitz-like geometry with dynamical and hyperscaling-violating exponents $z=5$ and $\\theta=1$, respectively. If $\\rho \\ll 1$ then at intermediate energies there is also an approximate AdS$_4$ reg...
Gravity duals for the Coulomb branch of marginally deformed N=4 Yang-Mills
Hernández, R; Zoakos, D; Hernandez, Rafael; Sfetsos, Konstadinos; Zoakos, Dimitrios
2006-01-01
Supergravity backgrounds dual to a class of exactly marginal deformations of N supersymmetric Yang-Mills can be constructed through an SL(2,R) sequence of T-dualities and coordinate shifts. We apply this transformation to multicenter solutions and derive supergravity backgrounds describing the Coulomb branch of N=1 theories at strong 't Hooft coupling as marginal deformations of N=4 Yang-Mills. For concreteness we concentrate to cases with an SO(4)xSO(2) symmetry preserved by continuous distributions of D3-branes on a disc and on a three-dimensional spherical shell. We compute the expectation value of the Wilson loop operator and confirm the Coulombic behaviour of the heavy quark-antiquark potential in the conformal case. When the vev is turned on we find situations where a complete screening of the potential arises, as well as a confining regime where a linear or a logarithmic potential prevails depending on the ratio of the quark-antiquark separation to the typical vev scale. The spectra of massless excitat...
Thermodynamics of SU(2) quantum Yang-Mills theory and CMB anomalies
Hofmann, Ralf
2013-01-01
A brief review of effective SU(2) Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field $\\phi$, based on non-propagating (anti)selfdual field configurations of topological charge unity. We explain why the screening physics of an SU(2) photon is subject to an electric-magnetically dual interpretation. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB) determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2) Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2) photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planc...
Solving the Ghost-Gluon System of Yang-Mills Theory on GPUs
Hopfer, Markus; Haase, Gundolf
2012-01-01
We solve the ghost-gluon system of Yang-Mills theory using Graphics Processing Units (GPUs). Working in Landau gauge, we use the Dyson-Schwinger formalism for the mathematical description as this approach is well-suited to directly benefit from the computing power of the GPUs. With the help of a Chebyshev expansion for the dressing functions and a subsequent appliance of a Newton-Raphson method, the non-linear system of coupled integral equations is linearized. The resulting Newton matrix is generated in parallel using OpenMPI and CUDA(TM). Our results show, that it is possible to cut down the run time by two orders of magnitude as compared to a sequential version of the code. This makes the proposed techniques well-suited for Dyson-Schwinger calculations on more complicated systems where the Yang-Mills sector of QCD serves as a starting point. In addition, the computation of Schwinger functions using GPU devices is studied.
Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
Anber, Mohamed M; Teeple, Brett
2014-01-01
We study the phase structure of N=1 supersymmetric Yang-Mills theory on R^3XS^1, with massive gauginos, periodic around the S^1, with Sp(2N) (N>=2), Spin(N) (N>=5), G_2, F_4, E_6, E_7, E_8 gauge groups. As the gaugino mass m is increased, with S^1 size and strong coupling scale fixed, we find a first-order phase transition both for theories with and without a center. This semiclassically calculable transition is driven, as in SU(N) and G_2, arxiv.org/abs/1205.0290 and arxiv.org/abs/1212.1238, by a competition between monopole-instantons and exotic topological "molecules"---"neutral" or "magnetic" bions. We compute the trace of the Polyakov loop and its two-point correlator near the transition. We find a behavior similar to the one observed near the thermal deconfinement transition in the corresponding pure Yang-Mills (YM) theory in lattice studies (whenever available). Our results lend further support to the conjectured continuity, as a function of m, between the quantum phase transition studied here and the ...
Analytical approach to the D3-brane gravity dual for 3d Yang-Mills theory
Forkel, Hilmar
2015-01-01
The complexity of "top-down" string-dual candidates for strongly-coupled Yang-Mills theories and in particular for QCD almost always prohibits their exact analytical or even comprehensive numerical treatment. This impedes both a thorough quantitative analysis and the development of more realistic gravity duals. To mitigate these impediments, we devise an analytical approach to top-down duals on the basis of controlled, uniformly converging high-accuracy approximations for the normalizable string modes corresponding to gauge-theory states. We demonstrate the potential of this approach in Witten's dual for $3d$ Yang-Mills theory, i.e. in the near-horizon limit of non-extremal $D\\text{3}$-branes, compactified on $S^{1}$. We obtain accurate analytical approximations to the bulk modes which satisfy the boundary conditions exactly. On their basis, analytical results for masses, sizes, pole residues and correlation functions of glueball excitations are derived by spectral methods. These approximations can be systema...
Brihaye, Yves; Hartmann, Betti
2005-01-01
We construct solutions of an Einstein Yang Mills system including a cosmological constant in 4 + n spacetime dimensions, where the n-dimensional manifold associated with the extra dimensions is taken to be Ricci flat. Assuming the matter and metric fields to be independent of the n extra coordinates, a spherical symmetric ansatz for the fields leads to a set of coupled ordinary differential equations. We find that for n > 1 only solutions with either one non-zero Higgs field or with all Higgs fields constant and zero gauge field function (corresponding to a Wu Yang-type ansatz) exist. We give the analytic solutions available in this model. These are 'embedded' Abelian solutions with a diverging size of the manifold associated with the extra n dimensions. Depending on the choice of parameters, these latter solutions either represent naked singularities or they possess a single horizon. We also present solutions of the effective four-dimensional Einstein Yang Mills Higgs-dilaton model, where the higher-dimensional cosmological constant induces a Liouville-type potential. The solutions are non-Abelian solutions with diverging Higgs fields, which exist only up to a maximal value of the cosmological constant.
Aspects Of Yang-mills Theory: Solitons, Dualities And Spin Chains
Freyhult, L K
2004-01-01
One of the still big problems in the Standard Model of particle physics is the problem of confinement. Quarks or other coloured particles have never been observed in isolation. Quarks are only observed in colour neutral bound states. The strong interactions are described using a Yang-Mills theory. These type of theories exhibits asymptotic freedom, i.e. the coupling is weak at high energies. This means that the theory is perturbative at high energies only. Understanding quark confinement requires knowledge of the non perturbative regime. One attempt has been to identify the proper order parameters for describing the low energy limit and then to write down effective actions in terms of these order parameters. We discuss one possible scenario for confinement and the effective models constructed with this as inspiration. Further we discuss solitons in these models and their properties. Yang-Mills theory has also become important in the context of string theory. According to the AdS/CFT correspondence string theo...
Transport properties of N = 4 supersymmetric Yang-Mills theory at finite coupling
Energy Technology Data Exchange (ETDEWEB)
Benincasa, Paolo [Department of Applied Mathematics, University of Western Ontario, Middlesex College, London, ON, N6A 5B7 (Canada); Buchel, Alex [Department of Applied Mathematics, University of Western Ontario, Middlesex College, London, ON, N6A 5B7 (Canada); Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada)
2006-01-15
Gauge theory-string theory duality describes strongly coupled N = 4 supersymmetric SU(n{sub c}) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in the inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-n{sub c} N = 4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation of the shear and the sound wave lowest quasinormal modes in the leading order {alpha}'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the {alpha}'-corrected nonextremal black branes in string theory.
Transport properties of Script N = 4 supersymmetric Yang-Mills theory at finite coupling
Benincasa, Paolo; Buchel, Alex
2006-01-01
Gauge theory-string theory duality describes strongly coupled Script N = 4 supersymmetric SU(nc) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in the inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-nc Script N = 4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation of the shear and the sound wave lowest quasinormal modes in the leading order α'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the α'-corrected nonextremal black branes in string theory.
Continuum strong-coupling expansion of Yang-Mills theory: quark confinement and infra-red slavery
Energy Technology Data Exchange (ETDEWEB)
Mansfield, P. (Dept. of Mathematical Sciences, Univ. of Durham (United Kingdom))
1994-04-25
We solve Schroedinger'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. (orig.)
Tadmon, Calvin
2012-01-01
We show how to assign initial data for the characteristic Einstein-Yang-Mills-Higgs system on two intersecting smooth null hypersurfaces. We successfully adapt the hierarchical method set up by A. D. Rendall to solve the same problem for the Einstein equations in vacuum and with perfect fluid source. Unlike the work of Rendall, many delicate calculations and expressions are given in details so as to address, in a forthcoming work, the issue of global resolution of the characteristic initial value problem for the Einstein-Yang-Mills-Higgs system. The method obviously applies to the Einstein-Maxwell and the Einstein-scalar field models.
High energy behavior of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Bartels, Jochen; Hentschinski, Martin; Mischler, Anna-Maria [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Ewerz, Carlo [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; GSI Helmholtzzentrum fuer Schwerionenforschung, Darmstadt (Germany). ExtreMe Matter Institute EMMI; Bielefeld Univ. (Germany). Fakultaet fuer Physik; European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT), Villazzano (Italy)
2009-12-15
We study the high energy limit of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory for finite N{sub c}. We make use of the framework of perturbative resummation of large logarithms of the energy. More specifically, we apply the (extended) generalized leading logarithmic approximation. We find that the same conformally invariant two-to-four gluon vertex occurs as in non-supersymmetric Yang-Mills theory. As a new feature we find a direct coupling of the four-gluon t-channel state to the R-current impact factor. (orig.)
Kajantie, K; Vepsalainen, M; Vuorinen, Aleksi
2011-01-01
We use AdS/QCD duality to compute the finite temperature Green's function G(omega,k;T) of the shear operator T_12 for all omega,k in hot Yang-Mills theory. The goal is to assess how the existence of scales like the transition temperature and glueball masses affects the correlator computed in the scalefree conformal N=4 supersymmetric Yang-Mills theory. We observe sizeable effects for T close to T_c which rapidly disappear with increasing T. Quantitative agreement of these predictions with future lattice Monte Carlo data would suggest that QCD matter in this temperature range is strongly interacting.
Zhu, Yan
2013-01-01
In this PhD thesis, I will review recent progress in perturbative studies of energy momentum tensor correlators in high-temperature Yang-Mills theory. After briefly introducing the necessary tools and physical motivation, I proceed to discuss the machinery developed for the extraction of next-to-leading order Operator Product Expansions and thermal spectral functions and to introduce the results obtained in the bulk and shear channels of Yang-Mills theory. Particular emphasis is placed on the comparison of the results with recent lattice and gauge/gravity calculations, as well as on discussing their use in extracting the corresponding transport coefficients from Euclidean lattice data.
Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory
Energy Technology Data Exchange (ETDEWEB)
Dixon, Lance J.; /SLAC; Drummond, James M.; /CERN /Annecy, LAPTH; Henn, Johannes M.; /Humboldt U., Berlin /Princeton, Inst. Advanced Study
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 parameters 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.
Kleihaus, B
1999-01-01
We point out that the statements in [hep-th/9903063] concerning the regularity of static axially symmetric solutions in Yang-Mills-dilaton (YMD) [1] and Einstein-Yang-Mills(-dilaton) (EYMD) theory [2,3] are incorrect, and that the non-singular local gauge potential of the YMD solutions [4] is twice differentiable.
Thermodynamics of SU(2 quantum Yang-Mills theory and CMB anomalies
Directory of Open Access Journals (Sweden)
Hofmann Ralf
2014-04-01
Full Text Available A brief review of effective SU(2 Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field φ, based on non-propagating (antiselfdual field configurations of topological charge unity. We also discuss kinematic constraints on interacting propagating gauge fields implied by the according spatial coarse-graining, and we explain why the screening physics of an SU(2 photon is subject to an electric-magnetically dual interpretation. This argument relies on the fact that only (anticalorons of scale parameter ρ ∼ |φ|−1 contribute to the coarse-graining required for thermal-ground-state emergence at temperature T. Thus, use of the effective gauge coupling e in the (anticaloron action is justified, yielding the value ħ for the latter at almost all temperatures. As a consequence, the indeterministic transition of initial to final plane waves caused by an effective, pointlike vertex is fundamentally mediated in Euclidean time by a single (anticaloron being part of the thermal ground state. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2 Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2 photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planck collaboration. Finally, six relativistic polarisations residing in the SU(2 vector modes roughly match the number of degrees of freedom in cosmic neutrinos (Planck which would disqualify the latter as radiation. Indeed, if interpreted as single center
Yablon, Jay R.
2013-10-01
Evidence is summarized from four recent papers that baryons including protons and neutrons are magnetic monopoles of non-commuting Yang-Mills gauge theories: 1) Protons and neutrons are ``resonant cavities'' with binding energies determined strictly by the masses of the quarks they contain. This is proven true at parts-per million accuracy for each of the 2H, 3H,3He, 4He binding energies and the neutron minus proton mass difference. 2) Respectively, each free proton and neutron contains 7.64 MeV and 9.81 MeV of mass/energy used to confine its quarks. When these nucleons bind, some, never all, of this energy is released and the mass deficit goes into binding. The balance continues to confine quarks. 56Fe releases 99.8429% of this energy for binding, more than any other nuclide. 3) Once we consider the Fermi vev one also finds an entirely theoretical explanation of proton and neutron masses, which also connects within experimental errors to the CKM quark mixing angles. 4) A related GUT explains fermion generation replication based on generator loss during symmetry breaking, and answers Rabi's question ``who ordered this?'' 5) Nuclear physics is governed by combining Maxwell's two classical equations into one equation using non-commuting gauge fields in view of Dirac theory and Fermi-Dirac-Pauli Exclusion. 6) Atoms themselves are core magnetic charges (nucleons) paired with orbital electric charges (electrons and elusive neutrinos), with the periodic table itself revealing an electric/magnetic symmetry of Maxwell's equations often pondered but heretofore unrecognized for a century and a half.
Energy Technology Data Exchange (ETDEWEB)
Fargnoli, H.G.; Sampaio, Marcos; Nemes, M.C. [Federal University of Minas Gerais, ICEx, Physics Department, P.O. Box 702, Belo Horizonte, MG (Brazil); Hiller, B. [Coimbra University, Faculty of Science and Technology, Physics Department, Center of Computational Physics, Coimbra (Portugal); Baeta Scarpelli, A.P. [Setor Tecnico-Cientifico, Departamento de Policia Federal, Lapa, Sao Paulo (Brazil)
2011-05-15
We present both an ultraviolet and an infrared regularization independent analysis in a symmetry preserving framework for the N=1 Super Yang-Mills beta function to two loop order. We show explicitly that off-shell infrared divergences as well as the overall two loop ultraviolet divergence cancel out, whilst the beta function receives contributions of infrared modes. (orig.)
Krishnaswami, G.S.
2008-01-01
We consider large-N multi-matrix models whose action closely mimics that of Yang-Mills theory, including gauge-fixing and ghost terms. We show that the factorized Schwinger-Dyson loop equations, expressed in terms of the generating series of gluon and ghost correlations G( ), are quadratic equations
Kleihaus, B; Kunz, Jutta
1999-01-01
In [hep-th/9907222] Hannibal claims to exclude the existence of particle-like static axially symmetric non-abelian solutions in SU(2) Einstein-Yang-Mills-dilaton theory. His argument is based on the asymptotic behaviour of such solutions. Here we disprove his claim by giving explicitly the asymptotic form of non-abelian solutions with winding number n=2.
Charge-density waves in deconfining SU(2) Yang-Mills thermodynamics
Falquez, Carlos; Baumbach, Tilo
2011-01-01
At one-loop accuracy we compute, characterize, and discuss the dispersion laws for the three low-momentum branches of propagating longitudinal, electric U(1) fields in the effective theory for the deconfining phase of pure SU(2) Yang-Mills thermodynamics. With an electric-magnetically dual interpretation of SU(2)$_{\\tiny CMB}$ we argue that upon a breaking of plasma isotropy and homogeneity, introduced e.g. by a temperature gradient, the longitudinal modes could conspire to provide magnetic seed fields for magneto-hydrodynamical dynamos inside structures of galaxy, galaxy-cluster, and cosmological scales. Such a scenario ultimately links structure with seed-field formation. As judged from the present cosmological epoch, the maximally available coherent field strength of 10$^{-8}$\\,Gauss from SU(2)$_{\\tiny CMB}$ matches with the upper bound for cosmological present-day field strength derived from small-angle anisotropies of the cosmic microwave background.
Wilson Loop Area Law for 2D Yang-Mills in Generalized Axial Gauge
Nguyen, Timothy
2016-01-01
We prove that Wilson loop expectation values for arbitrary simple closed contours obey an area law up to second order in perturbative two-dimensional Yang-Mills theory. Our analysis occurs within a general family of axial-like gauges, which include and interpolate between holomorphic gauge and the Wu-Mandelstam-Liebrandt light cone gauge. Our methods make use of the homotopy invariance properties of iterated integrals of closed one-forms, which allows us to evaluate the nontrivial integrals occurring at second order. We close with a discussion on complex gauge-fixing and deformation of integration cycles for holomorphic path integrals to shed light on some of the quantum field-theoretic underpinnings of our results.
Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence
Kassandrov, Vladimir V.; Rizcallah, Joseph A.
We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, SL(2, ℂ) Yang-Mills and complex Maxwell fields, the latter produced by integer-valued electric charges (“elementary” for the Kerr-like congruences), can all be explicitly associated with any shear-free null geodesic congruence. Using twistor variables, we derive the general solution of the equations of the shear-free null geodesic congruence (as a modification of the Kerr theorem) and analyze the corresponding “particle-like” field distributions, with bounded singularities of the associated physical fields. These can be obtained in a straightforward algebraic way and exhibit nontrivial collective dynamics simulating physical interactions.
Yang-Mills Field from Quaternion Space Geometry, and its Klein-Gordon Representation
Directory of Open Access Journals (Sweden)
Yefremov A.
2007-07-01
Full Text Available Analysis of covariant derivatives of vectors in quaternion (Q- spaces performed using Q-unit spinor-splitting technique and use of SL(2C-invariance of quaternion multiplication reveals close connexion of Q-geometry objects and Yang-Mills (YM field principle characteristics. In particular, it is shown that Q-connexion (with quaternion non-metricity and related curvature of 4 dimensional (4D space-times with 3D Q-space sections are formally equivalent to respectively YM-field potential and strength, traditionally emerging from the minimal action assumption. Plausible links between YM field equation and Klein-Gordon equation, in particular via its known isomorphism with Duffin-Kemmer equation, are also discussed.
Dark energy as a fixed point of the Einstein Yang-Mills Higgs Equations
Rinaldi, Massimiliano
2015-01-01
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 a closed 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.
Gravitating Vortices, Cosmic Strings, and the Kähler-Yang-Mills Equations
Álvarez-Cónsul, Luis; Garcia-Fernandez, Mario; García-Prada, Oscar
2016-09-01
In this paper we construct new solutions of the Kähler-Yang-Mills equations, by applying dimensional reduction methods to the product of the complex projective line with a compact Riemann surface. The resulting equations, which we call gravitating vortex equations, describe abelian vortices on the Riemann surface with back reaction of the metric. As a particular case of these gravitating vortices on the Riemann sphere we find solutions of the Einstein-Bogomol'nyi equations, which physically correspond to Nielsen-Olesen cosmic strings in the Bogomol'nyi phase. We use this to provide a Geometric Invariant Theory interpretation of an existence result by Y. Yang for the Einstein-Bogomol'nyi equations, applying a criterion due to G. Székelyhidi.
Hydrodynamics of the Polyakov Line in SU$(N_c)$ Yang-Mills
Liu, Yizhuang; Zahed, Ismail
2015-01-01
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 $N_c=\\infty$. The stochastic relaxation of the eigenvalues of the Polyakov line out of 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.
Supersymmetric Yang Mills Fields and Black Holes ; In Ten Dimensional Unified Field Theory
Patwardhan, Ajay
2007-01-01
The Ten dimensional Unified field theory has a 4 dimensional Riemannian spacetime and six dimensional Calabi Yau space structure. The supersymmetric Yang Mills fields and black holes are solutions in these theories. The formation of primordial black holes in early universe, the collapse to singularity of stellar black holes, the Hawking evaporation of microscopic black holes in LHC are topics of observational and theoretical interest. The observation of gamma ray bursts and creation of spectrum of particles and radiation of dark and normal matter occur due to primordial and microscopic black holes. The approach to singularity in black hole interior solutions, require the Bogoliubov transforms of SUSY YM fields in black hole geometries; both during formation and in evaporation. The Hawking effect of radiating black holes is applicable for all the fields. Invariants can be defined to give the conditions for these processes.
Bassetto, A.; Nardelli, G.; Torrielli, A.
2002-10-01
Commutative Yang-Mills theories in 1+1 dimensions exhibit an interesting interplay between geometrical properties and U(N) gauge structures: in the exact expression of a Wilson loop with n windings a nontrivial scaling intertwines n and N. In the noncommutative case the interplay becomes tighter owing to the merging of space-time and ``internal'' symmetries in a larger gauge group U(∞). We perform an explicit perturbative calculation of such a loop up to O(g6) rather surprisingly, we find that in the contribution from the crossed graphs (the genuine noncommutative terms) the scaling we mentioned occurs for large n and N in the limit of maximal noncommutativity θ=∞. We present arguments in favor of the persistence of such a scaling at any perturbative order and succeed in summing the related perturbative series.
Confinement interpretation in a Yang-Mills + Higgs theory when considering Gribov's ambiguity
Justo, I F; Dudal, D; Gómez, A J; Guimaraes, M S; Sorella, S P; Vercauteren, D
2015-01-01
This work presents concisely the results obtained from the analysis of the two-point function of the gauge field in the $SU(2)$ and $SU(2)\\times U(1)$ gauge theories, in the Landau gauge, coupled to a scalar Higgs field in the fundamental or adjoint representation. Non-perturbative effects are considered by taking into account the Gribov ambiguity. In general, in both Yang-Mills models the gluon propagator has non-trivial contributions of physical and non-physical modes, which clearly depends on the group representation of the Higgs field. These results were presented during the Fourth Winter Workshop on Non-perturbative Quantum Field Theory, which took place in Sophia-Antipolis - France.
On super form factors of half-BPS operators in N=4 super Yang-Mills
Penante, Brenda; Travaglini, Gabriele; Wen, Congkao
2014-01-01
We compute form factors of half-BPS operators in N=4 super Yang-Mills dual to massive Kaluza-Klein modes in supergravity. These are appropriate supersymmetrisations T_k of the scalar operators Tr(\\phi^k) for any k, which for k=2 give the chiral part of the stress-tensor multiplet operator. Using harmonic superspace, we derive simple Ward identities for these form factors, which we then compute perturbatively at tree level and one loop. We propose a novel on-shell recursion relation which links form factors with different numbers of fields. Using this, we conjecture a general formula for the n-point MHV form factors of T_k for arbitrary k and n. Finally, we use supersymmetric generalised unitarity to derive compact expressions for all one-loop MHV form factors of T_k in terms of one-loop triangles and finite two-mass easy box functions.
Covariant variational approach to Yang-Mills theory: Effective potential of the Polyakov loop
Quandt, M.; Reinhardt, H.
2016-09-01
We compute the effective action of the Polyakov loop in S U (2 ) and S U (3 ) Yang-Mills theory using a previously developed covariant variational approach. The formalism is extended to background gauge and it is shown how to relate the low-order Green's functions to the ones in Landau gauge studied earlier. The renormalization procedure is discussed. The self-consistent effective action is derived and evaluated using the numerical solution of the gap equation. We find a clear signal for a deconfinement phase transition at finite temperatures, which is second order for S U (2 ) and first order for S U (3 ). The critical temperatures obtained are in reasonable agreement with high-precision lattice data.
Regge meets collinear in strongly-coupled $\\mathcal{N} = 4$ super Yang-Mills
Sprenger, Martin
2016-01-01
We revisit the calculation of the six-gluon remainder function in planar $\\mathcal{N} = 4$ 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 arXiv:1407.3766, 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.
The large $N$ limit of the topological susceptibility of Yang-Mills gauge theory
Cè, Marco; Giusti, Leonardo; Schaefer, Stefan
2016-01-01
We present a precise computation of the topological susceptibility $\\chi_{_\\mathrm{YM}}$ of SU$(N)$ Yang-Mills theory in the large $N$ limit. The computation is done on the lattice, using high-statistics Monte Carlo simulations with $N=3, 4, 5, 6$ and three different lattice spacings. Two major improvements make it possible to go to finer lattice spacing and larger $N$ compared to previous works. First, the topological charge is implemented through the gradient flow definition; and second, open boundary conditions in the time direction are employed in order to avoid the freezing of the topological charge. The results allow us to extrapolate the dimensionless quantity $t_0^2\\chi_{_\\mathrm{YM}}$ to the continuum and large $N$ limits with confidence. The accuracy of the final result represents a new quality in the verification of large $N$ scaling.
Einstein-Yang-Mills Black Hole Interiors Serious Problems But Simple Solution
Zotov, M Yu
1997-01-01
Recently, E. E. Donets, D. V. Galtsov, and the author have reported about the results of numerical and analytical investigation of the SU(2) Einstein-Yang-Mills (EYM) black hole interior solutions (gr-qc/9612067). It was shown that a generic interior solution develops a new type of an infinitely oscillating behavior with exponentially growing amplitude. Numerical data for three sequential oscillations were presented. The numerical integration technique was not discussed. Later P. Breitenlohner, G. Lavrelashvili, and D. Maison confirmed our main results (gr-qc/9703047). But they made some misleading statements, in particular, they claimed, discussing the oscillations, that ``as one performs the numerical integration one quickly runs into serious problems...'' so that ``it is practically impossible to follow more than one or two of them numerically'' because ``the numerical integration procedure breaks down''. It is shown here that trivial logarithmic substitutions and integration along the integral curve solve...
Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N
Morita, Takeshi; Wiseman, Toby; Withers, Benjamin
2014-01-01
Maximally supersymmetric (p+1)-dimensional Yang-Mills theory at large N and finite temperature, with possibly compact spatial directions, has a rich phase structure. Strongly coupled phases may have holographic descriptions as black branes in various string duality frames, or there may be no gravity dual. In this paper we provide tools in the gauge theory which give a simple and unified picture of the various strongly coupled phases, and transitions between them. Building on our previous work we consider the effective theory describing the moduli of the gauge theory, which can be computed precisely when it is weakly coupled far out on the Coulomb branch. Whilst for perturbation theory naive extrapolation from weak coupling to strong gives little information, for this moduli theory naive extrapolation from its weakly to its strongly coupled regime appears to encode a surprising amount of information about the various strongly coupled phases. We argue it encodes not only the parametric form of thermodynamic qua...
The Stringy Representation of the D>=3 Yang-Mills Theory
Dubin, A Yu
2001-01-01
I put forward the stringy representation of the 1/N strong coupling (SC) expansion for the regularized Wilson's loop-averages in the continuous D>=3 Yang-Mills theory (YM_{D}) with a sufficiently large bare coupling constant \\lambda>\\lambda_{cr} and a fixed ultraviolet cut off \\Lambda. The proposed representation is proved to provide with the confining solution of the Dyson-Schwinger chain of the judiciously regularized U(N) Loop equations. Building on the results obtained, we suggest the stringy pattern of the low-energy theory associated to the D=4 U(\\infty)=SU(\\infty) gauge theory in the standard \\lambda=>0 phase with the asymptotic freedom in the UV domain. A nontrivial test, to clarify whether the AdS/CFT correspondence conjecture may be indeed applicable to the large N pure YM_{4} theory in the \\lambda=>\\infty limit, is also discussed.
Noncommutative Yang-Mills-Higgs actions from derivation-based differential calculus
Cagnache, Eric; Wallet, Jean-Christophe
2008-01-01
Derivations of a (noncommutative) algebra can be used to construct various consistent differential calculi, the so-called derivation-based differential calculi. We apply this framework to the noncommutative Moyal algebras for which all the derivations are inner and analyse in detail the case where the derivation algebras generating the differential calculus are related to area preserving diffeomorphisms. The ordinary derivations corresponding to spatial dimensions are supplemented by additional derivations necessarely related to additional covariant coordinates. It is shown that these latter have a natural interpretation as Higgs fields when involved in gauge invariant actions built from the noncommutative curvature. The UV/IR mixing problem for (some of) the resulting Yang-Mills-Higgs models is discussed. A comparition to other noncommutative geometries already considered in the litterature is given.
Phase transitions of an anisotropic N=4 super Yang-Mills plasma via holography
Banks, Elliot
2016-07-01
Black hole solutions of type IIB supergravity were previously found that are dual to N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. In the zero temperature limit, these black holes approach a Liftshitz like scaling solution in the IR. It was recently shown that these black holes are unstable, and at low temperatures there is a new class of black hole solutions that are thermodynamically preferred. We extend this analysis, by considering consistent truncations of the Kaluza-Klein reduction of IIB supergravity on a five-sphere that preserves multiple scalar and U(1) gauge fields. We show that the previously constructed black holes become unstable at low temperatures, and construct new classes of exotic black hole solutions. We study the DC thermo-electric conductivity of these U(1) charged black holes, and find a diverging DC conductivity at zero temperature due to the divergence of the gauge field coupling.
Towards a Spin-foam unification of gravity, Yang-Mills interactions and matter fields
Alexander, Stephon; Tacchi, Ruggero Altair
2011-01-01
We propose a new method of unifying gravity and the Standard Model by introducing a spin-foam model. We realize a unification between an SU(2) Yang-Mills interaction and 3D general relativity by considering a Spin(4) Plebanski action. The theory is quantized a la spin-foam by implementing the analogue of the simplicial constraints for the broken phase of the Spin(4) symmetry. A natural 4D extension of the theory is shown. We also present a way to recover 2-point correlation functions between the connections as a first way to implement scattering amplitudes between particle states, aiming to connect Loop Quantum Gravity to new physical predictions.
Towards the spectrum of low-lying particles in supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Bergner, G. [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Montvay, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Muenster, G.; Oezugurel, U.D.; Sandbrink, D. [Muenster Univ. (Germany). Inst. fuer Theoretische Physik 1
2013-04-15
We present the current results of our simulations of N=1 supersymmetric Yang-Mills theory on a lattice. The masses of the gluino-glue particle, the a-{eta}', the a-f{sub 0} meson, and the scalar glueball are obtained at finer lattice spacing than before, and extrapolations towards vanishing gluino mass are made. The calculations employ different levels of stout smearing. The statistical accuracy as well as the control of finite size effects and lattice artefacts are better than in previous investigations. Taking the statistical and systematic uncertainties into account, the extrapolations towards vanishing gluino mass of the masses of the fermionic and bosonic states in our present calculations are consistent with the formation of degenerate supermultiplets.
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
Energy Technology Data Exchange (ETDEWEB)
Pereira, A.D. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Potsdam (Germany); UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); Sobreiro, R.F. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Sorella, S.P. [UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil)
2016-10-15
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi:10.1103/PhysRevD.92.045039. arXiv:1506.06995 [hepth], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions. (orig.)
Geometrodynamics of gauge fields on the geometry of Yang-Mills and gravitational gauge theories
Mielke, Eckehard W
2016-01-01
This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter t...
Itoh, K; Sawanaka, H; So, H; Ukita, N
2003-01-01
We present a lattice theory with an exact fermionic symmetry, which mixes the link and the fermionic variables. The staggered fermionic variables may be reconstructed into a Majorana fermion in the continuum limit. The gauge action has a novel structure. Though it is the ordinary plaquette action, two different couplings are assigned in the ``Ichimatsu pattern'' or the checkered pattern. In the naive continuum limit, the fermionic symmetry survives as a continuum (or an $O(a^0)$) symmetry. The transformation of the fermion is proportional to the field strength multiplied by the difference of the two gauge couplings in this limit. This work is an extension of our recently proposed cell model toward the realization of supersymmetric Yang-Mills theory on lattice.
A local and BRST-invariant Yang-Mills theory within the Gribov horizon
Capri, M A L; Fiorentini, D; Guimaraes, M S; Justo, I F; Pereira, A D; Mintz, B W; Palhares, L F; Sobreiro, R F; Sorella, S P
2016-01-01
We present a local setup for the recently introduced BRST-invariant formulation of Yang-Mills theories for linear covariant gauges that takes into account the existence of gauge copies \\`a la Gribov and Zwanziger. Through the convenient use of auxiliary fields, including one of the Stueckelberg type, it is shown that both the action and the associated nilpotent BRST operator can be put in local form. Direct consequences of this fully local and BRST-symmetric framework are drawn from its Ward identities: (i) an exact prediction for the longitudinal part of the gluon propagator in linear covariant gauges that is compatible with recent lattice results and (ii) a proof of the gauge-parameter independence of all correlation functions of local BRST-invariant operators.
Phase transitions of an anisotropic N=4 super Yang-Mills plasma via holography
Banks, Elliot
2016-01-01
Black hole solutions of type IIB supergravity were previously found that are dual to N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. In the zero temperature limit, these black holes approach a Liftshitz like scaling solution in the IR. It was recently shown that these black holes are unstable, and at low temperatures there is a new class of black hole solutions that are thermodynamically preferred. We extend this analysis, by considering consistent truncations of the Kaluza-Klein reduction of IIB supergravity on a five-sphere that preserves multiple scalar and $U(1)$ gauge fields. We show that the previously constructed black holes become unstable at low temperatures, and construct new classes of exotic black hole solutions. We study the DC thermo-electric conductivity of these $U(1)$ charged black holes, and find a diverging DC conductivity at zero temperature due to the divergence of the gauge field coupling.
Gravitating Vortices, Cosmic Strings, and the Kähler-Yang-Mills Equations
Álvarez-Cónsul, Luis; Garcia-Fernandez, Mario; García-Prada, Oscar
2017-04-01
In this paper we construct new solutions of the Kähler-Yang-Mills equations, by applying dimensional reduction methods to the product of the complex projective line with a compact Riemann surface. The resulting equations, which we call gravitating vortex equations, describe abelian vortices on the Riemann surface with back reaction of the metric. As a particular case of these gravitating vortices on the Riemann sphere we find solutions of the Einstein-Bogomol'nyi equations, which physically correspond to Nielsen-Olesen cosmic strings in the Bogomol'nyi phase. We use this to provide a Geometric Invariant Theory interpretation of an existence result by Y. Yang for the Einstein-Bogomol'nyi equations, applying a criterion due to G. Székelyhidi.
Equal-time two-point correlation functions in Coulomb gauge Yang-Mills theory
Campagnari, D; Reinhardt, H; Astorga, F; Schleifenbaum, W
2009-01-01
We apply a new functional perturbative approach to the calculation of the equal-time two-point correlation functions and the potential between static color charges to one-loop order in Coulomb gauge Yang-Mills theory. The functional approach proceeds through a solution of the Schroedinger equation for the vacuum wave functional to order g^2 and derives the equal-time correlation functions from a functional integral representation via new diagrammatic rules. We show that the results coincide with those obtained from the usual Lagrangian functional integral approach, extract the beta function and determine the anomalous dimensions of the equal-time gluon and ghost two-point functions and the static potential under the assumption of multiplicative renormalizability to all orders.
Stochastic Feynman Rules for Yang-Mills Theory on the Plane
Nguyen, Timothy
2016-01-01
We analyze quantum Yang-Mills theory on $\\mathbb{R}^2$ using a novel discretization method based on an algebraic analogue of stochastic calculus. Such an analogue involves working with "Gaussian" free fields whose covariance matrix is indefinite rather than positive definite. Specifically, we work with Lie-algebra valued fields on a lattice and exploit an approximate gauge-invariance that is restored when taking the continuum limit. This analysis is applied to show the equivalence between Wilson loop expectations computed using partial axial-gauge, complete axial-gauge, and the Migdal-Witten lattice formulation. As a consequence, we obtain intriguing Lie-theoretic identities involving heat kernels and iterated integrals.
The five-loop beta function of Yang-Mills theory with fermions
Herzog, F.; Ruijl, B.; Ueda, T.; Vermaseren, J. A. M.; Vogt, A.
2017-02-01
We have computed the five-loop corrections to the scale dependence of the renormalized coupling constant for Quantum Chromodynamics (QCD), its generalization to non-Abelian gauge theories with a simple compact Lie group, and for Quantum Electrodynamics (QED). Our analytical result, obtained using the background field method, infrared rearrangement via a new diagram-by-diagram implementation of the R* operation and the Forcer program for massless four-loop propagators, confirms the QCD and QED results obtained by only one group before. The numerical size of the five-loop corrections is briefly discussed in the standard overline{MS} scheme for QCD with n f flavours and for pure SU( N) Yang-Mills theory. Their effect in QCD is much smaller than the four-loop contributions, even at rather low scales.
Anti-self-dual Yang-Mills equations on noncommutative spacetime
Takasaki, K
2001-01-01
By replacing the ordinary product with the so called $\\star$-product, one can construct an analogue of the anti-self-dual Yang-Mills (ASDYM) equations on the noncommutative $\\bbR^4$. Many properties of the ordinary ASDYM equations turn out to be inherited by the $\\star$-product ASDYM equation. In particular, the twistorial interpretation of the ordinary ASDYM equations can be extended to the noncommutative $\\bbR^4$, from which one can also derive the fundamental strutures for integrability such as a zero-curvature representation, an associated linear system, the Riemann-Hilbert problem, etc. These properties are further preserved under dimensional reduction to the principal chiral field model and Hitchin's Higgs pair equations. However, some structures relying on finite dimensional linear algebra break down in the $\\star$-product analogues.
Lattice simulation of a center symmetric three dimensional effective theory for SU(2) Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Smith, Dominik
2010-11-17
We present lattice simulations of a center symmetric dimensionally reduced effective field theory for SU(2) Yang Mills which employ thermal Wilson lines and three-dimensional magnetic fields as fundamental degrees of freedom. The action is composed of a gauge invariant kinetic term, spatial gauge fields and a potential for theWilson line which includes a ''fuzzy'' bag term to generate non-perturbative fluctuations between Z(2) degenerate ground states. The model is studied in the limit where the gauge fields are set to zero as well as the full model with gauge fields. We confirm that, at moderately weak coupling, the ''fuzzy'' bag term leads to eigenvalue repulsion in a finite region above the deconfining phase transition which shrinks in the extreme weak-coupling limit. A non-trivial Z(N) symmetric vacuum arises in the confined phase. The effective potential for the Polyakov loop in the theory with gauge fields is extracted from the simulations including all modes of the loop as well as for cooled configurations where the hard modes have been averaged out. The former is found to exhibit a non-analytic contribution while the latter can be described by a mean-field like ansatz with quadratic and quartic terms, plus a Vandermonde potential which depends upon the location within the phase diagram. Other results include the exact location of the phase boundary in the plane spanned by the coupling parameters, correlation lengths of several operators in the magnetic and electric sectors and the spatial string tension. We also present results from simulations of the full 4D Yang-Mills theory and attempt to make a qualitative comparison to the 3D effective theory. (orig.)
`Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories
Raptis, Ioannis
2007-05-01
Certain pivotal results from various applications of Abstract Differential Geometry (ADG) to gravity and gauge theories are presently collected and used to argue that we already possess a geometrically (pre)quantized, second quantized and manifestly background spacetime manifold independent vacuum Einstein gravitational field dynamics. The arguments carry also mutatis mutandis to the case of free Yang-Mills theories, since from the ADG-theoretic perspective gravity is regarded as another gauge field theory. The powerful algebraico-categorical, sheaf cohomological conceptual and technical machinery of ADG is then employed, based on the fundamental ADG-theoretic conception of a field as a pair ({mathcal{E}},{mathcal{D}}) consisting of a vector sheaf {mathcal{E}} and an algebraic connection {mathcal{D}} acting categorically as a sheaf morphism on {mathcal{E}}'s local sections, to introduce a ‘universal’, because expressly functorial, field quantization scenario coined third quantization. Although third quantization is fully covariant, on intuitive and heuristic grounds alone it formally appears to follow a canonical route; albeit, in a purely algebraic and, in contradistinction to geometric (pre)quantization and (canonical) second quantization, manifestly background geometrical spacetime manifold independent fashion, as befits ADG. All in all, from the ADG-theoretic vantage, vacuum Einstein gravity and free Yang-Mills theories are regarded as external spacetime manifold unconstrained, third quantized, pure gauge field theories. The paper abounds with philosophical smatterings and speculative remarks about the potential import and significance of our results to current and future Quantum Gravity research. A postscript gives a brief account of this author's personal encounters with Rafael Sorkin and his work.
Propagation properties and condensate formation of the confined Yang-Mills field
Stingl, M.
1986-12-01
The dynamical generation of a pole in the self-energy of a Yang-Mills field-an extension of the Schwinger mechanism-establishes a link between the tendency of the field to form nonperturbative vacuum condensates and its ``noninterpolating'' property in the confining phase-the fact that it has no particles associated with it. The nonvanishing residue of such a pole-a parameter b4 of dimension (mass)4-on the one hand provides for a nonvanishing value of , a contribution to the ``gluon condensate.'' On the other hand, it implies a dominant nonperturbative form of the propagator that has no particle singularity on the real k2 axis; instead, it describes a quantized field whose elementary excitations are short lived. The dispersion law for these excitations is given and shows that they grow more particlelike (are asymptotically free) at large momenta, thus providing a qualitative description of the short-lived excitation at the origin of a gluon jet. At large k2, the nonperturbative propagator reproduces nonperturbative corrections derived from the operator-product expansion. Moreover, it is a solution to the Euclidean Dyson-Schwinger equation for the Yang-Mills field in the following sense: there exist nonperturbative three-vector vertices Γ3 and auxiliary ghost-ghost-vector vertices G3, satisfying all symmetry and invariance requirements, and in conjunction with which this propagator solves both the Euclidean Dyson-Schwinger equation through one-dressed-loop terms and the Γ3 Slavnov-Taylor identity up to perturbative corrections of order g2. The consistency conditions for this solution give b2=μ0 2exp[-(4π)2 /11g2] to this order, confirming the nonperturbative nature of the residue parameter, and providing a paradigm for the dynamical determination of condensates.
Dyon of a non-Abelian Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions
Navarro-Lerida, Francisco
2013-01-01
Dyons of an SO(5) Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions are presented. These solitons carry both magnetic and electric global charges. The SO(3)xSO(2) solutions are constructed numerically. These are Chern-Simons dyons, differing radically from Julia-Zee dyons. The Chern-Simons densities employed are defined in 3+1 dimensions, and they are the first two of the 'new' Chern-Simons densities introduced recently. They are defined in terms of both Yang-Mills fields and a 5-component isomultiplet Higgs. When two or more of these Chern-Simons densities are present in the Lagrangian, solutions with vanishing electric charge but nonvanishing electrostatic potential may exist.
Leble, Sergey
2011-01-01
One-dimensional Yang-Mills-Nahm models are considered from algebrogeometric points of view. A quasiclassical quantization of the models based on path integral and its zeta function representation in terms of a Green function diagonal for a heat equation with an elliptic potential is considered. The Green function diagonal and, hence, zeta function and its derivative are expressed via solutions of Hermit equation and, alternatively, by means of Its-Matveev formalism in terms of Riemann teta-functions. For the Nahm model, which field is represented via elliptic (lemniscate) integral by construction, one-loop quantum corrections to action are evaluated as the zeta function derivative in zero point in terms of a hyperelliptic integral. The alternative expression should help to link the representations and continue investigation of the Yang-Mills-Nahm models. Keywords: Nahm model, one-loop quantum corrections, zeta function, elliptic potential, hyperelliptic integral, Its-Matveev formula. MSC numbers: 81Q30, 35J10...
On the irrelevance of the Gribov issue in N=4 Super Yang-Mills in the Landau gauge
Capri, M A L; Justo, I F; Palhares, L F; Sorella, S P
2014-01-01
The issue of the Gribov copies is discussed in Euclidean N=4 Super Yang-Mills theory quantized in the Landau gauge. As a consequence of the absence of a renormalization group invariant scale, it turns out that it is not possible to attach a dynamical meaning to the Gribov parameter. This implies that, in N=4 Super Yang-Mills, there is no need for the restriction of the domain of integration in the functional integral to the Gribov region, and no non-perturbative dynamical scale is generated. This result is in agreement with the absence of a confining phase observed from the Coulomb behaviour of the Wilson loop evaluated through the AdS/CFT correspondence. The non-renormalization theorem of the gluon-ghost-antighost vertex of the Landau gauge is also explicitly checked till three loops.
Balakin, Alexander B; Zayats, Alexei E
2016-01-01
Alternative theories of gravity and their solutions are of considerable importance as 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, namely, 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 cosmol...
Directory of Open Access Journals (Sweden)
Suhendro I.
2008-01-01
Full Text Available In this work, we attempt at constructing a comprehensive four-dimensional unified field theory of gravity, electromagnetism, and the non-Abelian Yang-Mills gauge field in which the gravitational, electromagnetic, and material spin fields are unified as intrinsic geometric objects of the space-time manifold $S_4$ via the connection, with the generalized non-Abelian Yang-Mills gauge field appearing in particular as a sub-field of the geometrized electromagnetic interaction.
Energy Technology Data Exchange (ETDEWEB)
Narita, Makoto [Department of Mathematics, National Taiwan University, 1, Sec. 4, Roosevelt Rd., Taipei 106, Taiwan (China)
2006-12-21
We discuss the strong cosmic censorship conjecture for cosmological spacetimes in the Einstein-Yang-Mills-dilaton system. Locally rotational symmetric Bianchi I spacetimes are considered. We show local and global existence theorems for the system. Asymptotic behaviour for the spacetimes is also investigated. The curvature invariant is blowup at the initial singularities and the spacetimes are future geodesic complete. Thus, the strong cosmic censorship conjecture for the spacetimes holds.
Meng, K.; Li, J.
2016-10-01
We construct a new static black hole solution of Gauss-Bonnet massive gravity coupled to Maxwell and Yang-Mills fields in five dimensions. We calculate the thermodynamical quantities of the black hole and check the first law of black hole thermodynamics. Thermal stability of the black hole is explored in the context of both canonical and grand canonical ensembles. By identifying the cosmological constant as the pressure of the gravitational system, we study the phase transitions of the black hole.
Effect of Self-Interaction on Vacuum Energy for Yang-Mills System in Kaluza-Klein Theory
Shiraishi, Kiyoshi
2015-01-01
We calculate the vacuum energy for Yang--Mills (YM) system in the background space-time $M^4 \\times S^3$, taking the effect of self-interaction of the YM fields into account. The compactification scale obtained by Candelas--Weinberg mechanism becomes large if the YM coupling is large. The case with an extra space $S^3/Z_2$ is also considered, and it is shown that the vacuum associated with broken gauge symmetry is unstable.
${\\cal N}=4$ Supersymmetric Yang-Mills Theory on Orbifold-$T^4\\/{\\bf Z}_$2 Higher Rank Case
Jinzenji, M; Jinzenji, Masao; Sasaki, Toru
2001-01-01
We derive the partition function of ${\\cal N}=4$ supersymmetric Yang-Mills theory on orbifold-$T^4/{\\bf Z}_2$ for SU(N). We generalize our previous work for SU(2) to the SU(N) case. These partition functions can be factorized into product of bulk contribution of quotient space $T^4/{\\bf Z}_2$ and of blow-up formula including $A_{N-1}$ theta functions with level N.
Plane-wave matrix theory from N=4 super-Yang-Mills on RxS{sup 3}
Energy Technology Data Exchange (ETDEWEB)
Kim, Nakwoo E-mail: kim@aei.mpg.de; Klose, Thomas E-mail: thklose@aei.mpg.de; Plefka, Jan E-mail: plefka@aei.mpg.de
2003-11-03
Recently a mass deformation of the maximally supersymmetric Yang-Mills quantum mechanics has been constructed from the supermembrane action in eleven-dimensional plane-wave backgrounds. However, the origin of this plane-wave matrix theory in terms of a compactification of a higher-dimensional super-Yang-Mills model has remained obscure. In this paper we study the Kaluza-Klein reduction of D=4, N=4 super-Yang-Mills theory on a round three-sphere, and demonstrate that the plane-wave matrix theory arises through a consistent truncation to the lowest lying modes. We further explore the relation between the dilatation operator of the conformal field theory and the Hamiltonian of the quantum mechanics through perturbative calculations up to two-loop order. In particular, we find that the one-loop anomalous dimensions of pure scalar operators are completely captured by the plane-wave matrix theory. At two-loop level this property ceases to exist.
Keller, Jochen
2008-01-01
The thesis is considering aspects of SU(2) Yang-Mills thermodynamics in its deconfining high-temperature phase. We calculate the two-point correlation function of the energy density of the photon in a thermalized gas, at first in the conventional U(1) gauge theory, followed by a calculation, where the photon is identified with the massless gauge mode in deconfining SU(2) Yang-Mills thermodynamics. Apart from the fact, that this calculation is interesting from a technical point of view, we can consider several aspects of phenomenological relevance. Since we interpret the two-point correlator of energy density as a measure for the energy transfer, and thus for the electromagnetic interaction of microscopic objects, such as atoms immersed into a photon gas, we are able to give an explanation for the unexpected stability of cold, innergalactic clouds consisting of atomic hydrogen. Subsequently, we evaluate the spatial string tension in deconfining SU(2) Yang-Mills thermodynamics, which can be regarded as measure ...
Yang-Mills theory for semidirect products G x g{sup *} and its instantons
Energy Technology Data Exchange (ETDEWEB)
Ruiz Ruiz, F. [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2015-07-15
Yang-Mills theory with a symmetry algebra that is the semidirect product h x h* defined by the coadjoint action of a Lie algebra h on its dual h* is studied. The gauge group is the semidirect product G{sub h} x h*, a noncompact group given by the coadjoint action on h* of the Lie group G{sub h} of h* For h simple, a method to construct the self-antiself dual instantons of the theory and their gauge nonequivalent deformations is presented. Every G{sub h} x h* instanton has an embedded G{sub h} instanton with the same instanton charge, in terms of which the construction is realized. As an example, h = su(2) and instanton charge one is considered. The gauge group is in this case SU(2) x R{sup 3}. Explicit expressions for the selfdual connection, the zero modes and the metric and complex structures of the moduli space are given. (orig.)
Towards a string bit formulation of N=4 super Yang-Mills
Alday, L F; Gava, E; Narain, K S; Alday, Luis F.; David, Justin R.; Gava, Edi
2006-01-01
We show that planar cal N=4 Yang-Mills theory at zero 't Hooft coupling can be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We show that these oscillators can serve as world-sheet variables, the string bits, of a discretized string. There is a one to one correspondence between the on shell gauge invariant words of the free Y-M theory and the states in the oscillators' Hilbert space, obeying a local gauge and cyclicity constraints. The planar two-point functions and the three-point functions of all gauge invariant words are obtained by the simple delta-function overlap of the corresponding discrete string world sheet. At first order in the 't Hooft coupling, i.e. at one-loop in the Y-M theory, the logarithmic corrections of the planar two-point and the three-point functions can be incorporated by nearest neighbour interactions among the discretized string bits. In the SU(2) sub-sector we show that the one-loop corrections to the structure constants can be uniquely determined by the ...
Doubled Lattice Chern-Simons-Yang-Mills Theories with Discrete Gauge Group
Caspar, Stephan; Olesen, Therkel Z; Vlasii, Nadiia D; Wiese, Uwe-Jens
2016-01-01
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 pha...
A Tree-level Unitary Noncompact Weyl-Einstein-Yang-Mills Model
Dengiz, Suat
2016-01-01
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 constant curvature vacuum. The model is unitary in de Si...
SU(2) Dirac-Yang-Mills quantum mechanics of spatially constant quark and gluon fields
Pavel, H -P
2011-01-01
The quantum mechanics of spatially constant SU(2) Yang-Mills- and Dirac-fields minimally coupled to each other is investigated as the strong coupling limit of 2-color-QCD. Using a canonical transformation of the quark and gluon fields, which Abelianises the Gauss law constraints to be implemented, the corresponding unconstrained Hamiltonian and total angular momentum are derived. In the same way as this reduces the colored spin-1 gluons to unconstrained colorless spin-0 and spin-2 gluons, it reduces the colored spin-1/2 quarks to unconstrained colorless spin-0 and spin-1 quarks. These however continue to satisfy anti-commutation relations and hence the Pauli-exclusion principle. The obtained unconstrained Hamiltonian is then rewritten into a form, which separates the rotational from the scalar degrees of freedom. In this form the low-energy spectrum can be obtained with high accuracy. As an illustrative example, the spin-0 energy-spectrum of the quark-gluon system is calculated for massless quarks of one flav...
Gauge coupling field, currents, anomalies and N = 1 super-Yang-Mills effective actions
Ambrosetti, Nicola; Arnold, Daniel; Derendinger, Jean-Pierre; Hartong, Jelle
2017-02-01
Working with a gauge coupling field in a linear superfield, we construct effective Lagrangians for N = 1 super-Yang-Mills theory fully compatible with the expected all-order behavior or physical quantities. Using the one-loop dependence on its ultraviolet cutoff and anomaly matching or cancellation of R and dilatation anomalies, we obtain the Wilsonian effective Lagrangian. With similar anomaly matching or cancellation methods, we derive the effective action for gaugino condensates, as a function of the real coupling field. Both effective actions lead to a derivation of the NSVZ β function from algebraic arguments only. The extension of results to N = 2 theories or to matter systems is briefly considered. The main tool for the discussion of anomalies is a generic supercurrent structure with 16B +16F operators (the S multiplet), which we derive using superspace identities and field equations for a fully general gauge theory Lagrangian with the linear gauge coupling superfield, and with various U(1)R currents. As a byproduct, we show under which conditions the S multiplet can be improved to contain the Callan-Coleman-Jackiw energy-momentum tensor whose trace measures the breaking of scale invariance.
On spinors, strings, integrable models and decomposed Yang-Mills theory
Ioannidou, Theodora; Niemi, Antti J
2014-01-01
This paper deals with various interrelations between strings and surfaces in three dimensional ambient space, two dimensional integrable models and two dimensional and four dimensional decomposed SU(2) Yang-Mills theories. Initially, a spinor version of the Frenet equation is introduced in order to describe the differential geometry of static three dimensional string-like structures. Then its relation to the structure of the su(2) Lie algebra valued Maurer-Cartan one-form is presented; while by introducing time evolution of the string a Lax pair is obtained, as an integrability condition. In addition, it is show how the Lax pair of the integrable nonlinear Schroedinger equation becomes embedded into the Lax pair of the time extended spinor Frenet equation and it is described how a spinor based projection operator formalism can be used to construct the conserved quantities, in the case of the nonlinear Schroedinger equation. Then the Lax pair structure of the time extended spinor Frenet equation is related to ...
Gauge Coupling Field, Currents, Anomalies and N=1 Super-Yang-Mills Effective Actions
Ambrosetti, Nicola; Derendinger, Jean-Pierre; Hartog, Jelle
2016-01-01
Working with a gauge coupling field in a linear superfield, we construct effective Lagrangians for N=1 super-Yang-Mills theory fully compatible with the expected all-order behaviour or physical quantities. Using the one-loop dependence on its ultraviolet cutoff and anomaly matching or cancellation of R and dilatation anomalies, we obtain the Wilsonian effective Lagrangian. With similar anomaly matching or cancellation methods, we derive the effective action for gaugino condensates, as a function of the real coupling field. Both effective actions lead to a derivation of the NSVZ beta function from algebraic arguments only. The extension of results to N=2 theories or to matter systems is briefly considered. The main tool for the discussion of anomalies is a generic supercurrent structure with 16_B+16_F operators (the S multiplet), which we derive using superspace identities and field equations for a fully general gauge theory Lagrangian with the linear gauge coupling superfield, and with various U(1)_R currents...
Einstein-Yang-Mills Isolated Horizons Phase Space, Mechanics, Hair and Conjectures
Corichi, A; Sudarsky, D; Corichi, Alejandro; Nucamendi, Ulises; Sudarsky, Daniel
2000-01-01
The concept of "Isolated Horizon" has been recently used to provide a fullHamiltonian treatment of black holes. It has been applied successfully to thecases of {\\it non-rotating}, {\\it non-distorted} black holes in EinsteinVacuum, Einstein-Maxwell and Einstein-Maxwell-Dilaton Theories. In this note,it is investigated the extent to which the framework can be generalized to thecase of non-Abelian gauge theories where `hairy black holes' are known toexist. It is found that this extension is indeed possible, despite the factthat in general, there is no `canonical normalization' yielding a preferredHorizon Mass. In particular the zeroth and first laws are established for allnormalizations. Colored static spherically symmetric black hole solutions tothe Einstein-Yang-Mills equations are considered from this perspective. Acanonical formula for the Horizon Mass of such black holes is found. Thisanalysis is used to obtain nontrivial relations between the masses of thecolored black holes and the regular solitonic solut...
Analytical study of Yang-Mills theory in the infrared from first principles
Siringo, Fabio
2015-01-01
Pure Yang-Mills SU(N) theory is studied in the Landau gauge and four dimensional space. While leaving the original Lagrangian unmodified, a double perturbative expansion is devised, based on a massive free-particle propagator. In dimensional regularization, all diverging mass terms cancel exactly in the double expansion, without the need to include mass counterterms that would spoil the symmetry of the Lagrangian. No free parameters are included that were not in the original theory, yielding a fully analytical approach from first principles. The expansion is safe in the infrared and is equivalent to the standard perturbation theory in the UV. At one-loop, explicit analytical expressions are given for the propagators and the running coupling and are found in excellent agreement with the data of lattice simulations. A universal scaling property is predicted for the inverse propagators and shown to be satisfied by the lattice data. Higher loops are found to be negligible in the infrared below 300 MeV where the c...
Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N
Morita, Takeshi; Shiba, Shotaro; Wiseman, Toby; Withers, Benjamin
2015-07-01
Maximally supersymmetric ( p + 1)-dimensional Yang-Mills theory at large N and finite temperature, with possibly compact spatial directions, has a rich phase structure. Strongly coupled phases may have holographic descriptions as black branes in various string duality frames, or there may be no gravity dual. In this paper we provide tools in the gauge theory which give a simple and unified picture of the various strongly coupled phases, and transitions between them. Building on our previous work we consider the effective theory describing the moduli of the gauge theory, which can be computed precisely when it is weakly coupled far out on the Coulomb branch. Whilst for perturbation theory naive extrapolation from weak coupling to strong gives little information, for this moduli theory naive extrapolation from its weakly to its strongly coupled regime appears to encode a surprising amount of information about the various strongly coupled phases. We argue it encodes not only the parametric form of thermodynamic quantities for these strongly coupled phases, but also certain transcendental factors with a geometric origin, and allows one to deduce transitions between the phases. We emphasise it also gives predictions for the behaviour of other observables in these phases.
The Gauge String Solution of the D>=3 Yang-Mills Loop Equations
Dubin, A Yu
2001-01-01
I adapt the Gauge String, representing the strong coupling (SC) expansion in the continuous D>=3 Yang-Mills theory (YM_{D}) with a sufficiently large bare coupling constant \\lambda>\\lambda_{cr} and a fixed ultraviolet cut off \\Lambda, to the analysis of the regularized Wilson's loop-averages. When generalized to describe the fat (rather than infinitely thin) flux-tubes, the pattern of thus modified U(N) Gauge String is proved to be consistent with the chain of the judiciously regularized U(N) Loop equations. In particular, we reveal the dimensional reduction YM_{D}=>YM_{2}, taking place in the extreme SC limit \\lambda=>\\infty, and compare it with the implications of the AdS/CFT correspondence conjecture. On the other hand, for the loop-averages associated to the sufficiently large minimal areas, the proposed stringy pattern is supposed to be in the one infrared universality class (provided the loops are without zig-zag backtrackings) with the novel implementation of the noncritical D-dimensional Nambu-Goto st...
The Yang-Mills Vacuum Wave Functional in 2+1 Dimensions
Krug, Sebastian
2014-01-01
We investigate Yang-Mills theory in 2+1 dimensions in the Schroedinger representation. The Schroedinger picture is interesting because it is well suited to explore properties of the vacuum state in the non-perturbative regime. Yet, not much analytical work has been done on this subject, and even the topic of perturbation theory in the Schroedinger representation is not well developed, especially in the case of gauge theories. In a paper by Hatfield [Phys.Lett.B 147, 435 (1984)] the vacuum wave functional for SU(2) theory was computed to O(e). In the non-perturbative regime, the most sophisticated analytical approach has been developed by Karabali et al. in a series of papers (see [Nucl.Phys.B 824, 387 (2010)] and references therein). This thesis aims to put perturbation theory in the Schroedinger representation on more solid ground by computing the vacuum wave functional for a general gauge group SU$(N_c)$ up to O$(e^2)$, utilizing modifications of these two methods. This is important since it provides us wit...
Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
Ferrari, Frank
2003-04-01
We study the physics of N=1 super Yang-Mills theory with the gauge group U(N) and one adjoint Higgs field, by using the recently derived exact effective superpotentials. Interesting phenomena occur for some special values of the Higgs potential couplings. We find critical points with massless glueballs and/or massless monopoles, confinement without a mass gap, and tensionless domain walls. We describe the transitions between regimes with different patterns of gauge symmetry breaking, or, in the matrix model language, between solutions with a different number of cuts. The standard large N expansion is singular near the critical points, with domain wall tensions scaling as a fractional power of N. We argue that the critical points are four-dimensional analogues of the Kazakov critical points that are commonly found in low dimensional matrix integrals. We define a double scaling limit that yields the exact tension of BPS two-branes in the resulting N=1, four-dimensional noncritical string theory. D-brane states can be deformed continuously into closed string solitonic states, and vice versa, along paths that go over regions where the string coupling is strong.
Script N = 4 Super Yang Mills at Finite Density: the Naked Truth
Evans, Nick; Hockings, James
2002-07-01
We study Script N = 4 super Yang Mills theory at finite U(1)R charge density (and temperature) using the AdS/CFT Correspondence. The ten dimensional backgrounds around spinning D3 brane configurations split into two classes of solution. One class describe spinning black branes and have previously been extensively studied, and interpreted, in a thermodynamic context, as the deconfined high density phase of the dual field theory. The other class have naked singularities and in the supersymmetric limit are known to correspond to multi-centre solutions describing the field theory in the Coulomb phase. We provide evidence that the non-supersymmetric members of this class represent naked, spinning D-brane distributions describing the Coulomb branch at finite density. At a critical density a phase transition occurs to a spinning black brane representing the deconfined phase where the Higgs vevs have evaporated. We perform a free energy calculation to determine the phase diagram of the Coulomb branch at finite temperature and density.
Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
Ferrari, F
2003-01-01
We study the physics of N=1 super Yang-Mills theory with gauge group U(Nc) and one adjoint Higgs field, by using the recently derived exact effective superpotentials. Interesting phenomena occur for some special values of the Higgs potential couplings. We find critical points with massless glueballs and/or massless monopoles, confinement without a mass gap, and tensionless domain walls. We describe the transitions between regimes with different patterns of gauge symmetry breaking, or, in the matrix model language, between solutions with a different number of cuts. The standard large Nc expansion is singular near the critical points, with domain walls tensions scaling as a fractional power of Nc. We argue that the critical points are four dimensional analogues of the Kazakov critical points that are commonly found in low dimensional matrix integrals. We define a double scaling limit that yields the exact tension of BPS two-branes in the resulting N=1, four dimensional non-critical string theory. D-brane states...
Magnetic monopole solutions in a modified Einstein-Yang-Mills-Higgs system
Ai Viet, Nguyen; Wali, Kameshwar C.
1995-02-01
We study the Yang-Mills-Higgs system within the framework of general relativity with an unconventional coupling of the scalar field to gravity. In the static situation, using a Bogomol'nyi-type analysis, we derive a positive-definite energy functional with a lower bound that is attained when the Bogomolnyi conditions are satisfied. Specializing to the gauge group SU(2) and the 't Hooft-Polyakov ansatz for the gauge and Higgs fields, we seek static, spherically symmetric solutions to the coupled system of equations together with Bogomol'nyi conditions. In both the isotropic and standard coordinate systems, in the spontaneously broken symmetry situation, we find great simplifications reducing the solutions of the coupled system to the solution of a single nonlinear differential equation, different one in each case, but well known in other contexts of physics. We find Abelian and non-Abelian monopole solutions with gravitational fields playing the role of Higgs fields in providing attraction that balances the repulsion due to the gague fields. These solutions in general have naked singularities at the origin. But as solutions we also find extreme Reissner-Nordström black holes as well as a new non-Abelian monopole solution that has a horizon enclosing the singularity.
N=4 Super Yang Mills at Finite Density the Naked Truth
Evans, N; Evans, Nick; Hockings, James
2002-01-01
We study N=4 super Yang Mills theory at finite U(1)_R charge density (and temperature) using the AdS/CFT Correspondence. The ten dimensional backgrounds around spinning D3 brane configurations split into two classes of solution. One class describe spinning black holes and have previously been extensively studied, and interpreted, in a thermodynamic context, as the deconfined high density phase of the dual field theory. The other class have naked singularities and in the supersymmetric limit are known to correspond to multi-centre solutions describing the field theory in the Coulomb phase. We provide evidence that the non-supersymmetric members of this class represent naked, spinning D-brane distributions describing the Coulomb branch at finite density. At a critical density a phase transition occurs to a spinning black hole representing the deconfined phase where the higgs vevs have evaporated. We perform a free energy calculation to determine the phase diagram of the Coulomb branch at finite temperature and ...
Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
Bork, L V; Vartanov, G S; Zhiboedov, A V
2009-01-01
In this paper we give all the details of the calculation that we presented in our previous paper ArXiv:0908.0387 where the infrared structure of the MHV gluon amplitudes in the planar limit for ${\\cal N}=4$ super Yang-Mills theory was considered in the next-to-leading order of perturbation theory. Explicit cancellation of the infrared divergencies in properly defined inclusive cross-sections is demonstrated first in a toy model example of "conformal QED" and then in the real ${\\cal N}=4$ SYM theory. We give the full-length details both for the calculation of the real emission and for the diagrams with splitting in initial and final states. The finite parts for some inclusive differential cross-sections are presented in an analytical form. In general, contrary to the virtual corrections, they do not reveal any simple structure. An example of the finite part containing just the log functions is presented. The dependence of inclusive cross-section on the external scale related to the definition of asymptotic sta...
Hamiltonian Approach to 1+1 dimensional Yang-Mills theory in Coulomb gauge
Reinhardt, H
2008-01-01
We study the Hamiltonian approach to 1+1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss' law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss' law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schroedinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the ...
Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
Kamata, Norihiko
2016-01-01
We study several types of tree-level improvement in the Yang-Mills gradient flow method in order to reduce the lattice discretization errors in line with a reference [Fodor et al., arXiv:1406.0827]. The tree-level $\\mathcal{O}(a^2)$ improvement can be achieved in a simple manner, where an appropriate weighted average is computed between two definitions of the action density $\\langle E(t)\\rangle$ measured at every flow time $t$. We further develop the idea of achieving the tree-level $\\mathcal{O}(a^4)$ improvement. For testing our proposal, we present numerical results of $\\langle E(t)\\rangle$ obtained on gauge configurations generated with the Wilson and Iwasaki gauge actions at three lattice spacings ($a\\approx 0.1, 0.07$ and 0.05 fm). Our results show that tree-level improved flows significantly eliminate the discretization corrections in the relatively small-$t$ regime. To demonstrate the feasibility of our proposal, we also study the scaling behavior of the dimensionless combinations of the $\\Lambda_{\\ove...
On Yang--Mills Theories with Chiral Matter at Strong Coupling
Energy Technology Data Exchange (ETDEWEB)
Shifman, M.; /Minnesota U., Theor. Phys. Inst. /Saclay, SPhT; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept.
2008-08-20
Strong coupling dynamics of Yang-Mills theories with chiral fermion content remained largely elusive despite much effort over the years. In this work, we propose a dynamical framework in which we can address non-perturbative properties of chiral, non-supersymmetric gauge theories, in particular, chiral quiver theories on S{sub 1} x R{sub 3}. Double-trace deformations are used to stabilize the center-symmetric vacuum. This allows one to smoothly connect smaller(S{sub 1}) to larger(S{sub 1}) physics (R{sub 4} is the limiting case) where the double-trace deformations are switched off. In particular, occurrence of the mass gap in the gauge sector and linear confinement due to bions are analytically demonstrated. We find the pattern of the chiral symmetry realization which depends on the structure of the ring operators, a novel class of topological excitations. The deformed chiral theory, unlike the undeformed one, satisfies volume independence down to arbitrarily small volumes (a working Eguchi-Kawai reduction) in the large N limit. This equivalence, may open new perspectives on strong coupling chiral gauge theories on R{sub 4}.
Running couplings in equivariantly gauge-fixed SU(N) Yang--Mills theories
Golterman, M F L; Golterman, Maarten; Shamir, Yigal
2006-01-01
In equivariantly gauge-fixed SU(N) Yang--Mills theories, the gauge symmetry is only partially fixed, leaving a subgroup $H\\subset SU(N)$ unfixed. Such theories avoid Neuberger's nogo theorem if the subgroup $H$ contains at least the Cartan subgroup $U(1)^{N-1}$, and they are thus non-perturbatively well defined if regulated on a finite lattice. We calculate the one-loop beta function for the coupling $\\tilde{g}^2=\\xi g^2$, where $g$ is the gauge coupling and $\\xi$ is the gauge parameter, for a class of subgroups including the cases that $H=U(1)^{N-1}$ or $H=SU(M)\\times SU(N-M)\\times U(1)$. The coupling $\\tilde{g}$ represents the strength of the interaction of the gauge degrees of freedom associated with the coset $SU(N)/H$. We find that $\\tilde{g}$, like $g$, is asymptotically free. We solve the renormalization-group equations for the running of the couplings $g$ and $\\tilde{g}$, and find that dimensional transmutation takes place also for the coupling $\\tilde{g}$, generating a scale $\\tilde{\\Lambda}$ which c...
Smooth Gauge Strings and D > 2 Lattice Yang-Mills Theories
Dubin, A Yu
2000-01-01
Employing the nonabelian duality transformation \\cite{Dub2}, I derive theGauge String representation of certain D>2 lattice Yang-Mills theories in theSC phase. With the judicious choice of the actions, in D>2 our constructiongeneralizes the Gross-Taylor stringy reformulation of the continuous YM_{2} ona 2d manifold. Using the Twisted Eguchi-Kawai model as an example, we developethe algorithm to determine the weights w[\\tilde{M}] for connected YM-fluxworldsheets $\\tilde{M}$ immersed, \\tilde{M}->T, into a given 2d cell-complex T.Owing to the invariance of w[\\tilde{M}] under a continuous group ofarea-preserving worldsheet homeomorphisms, the weights {w[\\tilde{M}]} can bereadily used to define the theory of the smooth YM-fluxes which unambiguouslyrefers to a particular continuous YM_{D} system. I argue that the latter YM_{D}models (with a finite ultraviolet cut-off \\Lambda) for sufficiently largevalues of the coupling constant(s) are reproduced, to all orders in 1/N, by thesmooth Gauge String thus associated. The...
Broken SU(3) x SU(3) x SU(3) x SU(3) Symmetry
Freund, P. G. O.; Nambu, Y.
1964-10-01
We argue that the "Eight-fold Way" version of the SU(3) symmetry should be extended to a product of up to four separate and badly broken SU(3) groups, including the gamma{sub 5} type SU(3) symmetry. A hierarchy of subgroups (or subalgebras) are considered within this framework, and two candidates are found to be interesting in view of experimental evidence. Main features of the theory are: 1) the baryons belong to a nonet; 2) there is an octet of axial vector gauge mesons in addition to one or two octets of vector mesons; 3) pseudoscalar and scalar mesons exist as "incomplete" multiplets arising from spontaneous breakdown of symmetry.
Directory of Open Access Journals (Sweden)
Trunev A. P.
2015-04-01
Full Text Available Metric describing the accelerated and rotating reference system in general relativity in the case of an arbitrary dependence of acceleration and angular velocity on time has been proposed. It is established that the curvature tensor in such metrics is zero, which corresponds to movement in the flat spaces. It is shown that the motion of test bodies in the metric accelerated and rotating reference system in general relativity is similarly to the classical motion in non-inertial reference frame. Maxwell's equations and Yang-Mills theory are converted to the moving axes in metric describes the acceleration and rotating reference frame in the general relativity in the case of an arbitrary dependence of acceleration and angular velocity of the system from time. The article discusses the known effects associated with acceleration and (or the rotation of the reference frame - the Sagnac effect, the effect of the Stewart-Tolman and other similar effects. The numerical model of wave propagation in non-inertial reference frames in the case when potential depending of one, two and three spatial dimensions has been developed. It has been shown in numerical experiment that the acceleration of the reference system leads to retardation effects, as well as to a violation of the symmetry of the wave front, indicating that there is local change of wave speed
Caporaso, Nicola; Cirafici, Michele; Griguolo, Luca; Pasquetti, Sara; Seminara, Domenico; Szabo, Richard J.
2006-01-01
We examine the problem of counting bound states of BPS black holes on local Calabi-Yau threefolds which are fibrations over a Riemann surface by computing the partition function of q-deformed Yang-Mills theory on the Riemann surface. We study in detail the genus zero case and obtain, at finite N, the instanton expansion of the gauge theory. It can be written exactly as the partition function for U(N) Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. The correspondence between two and three dimensional gauge theories is elucidated by an explicit mapping between two-dimensional Yang-Mills instantons and flat connections on the Lens space. In the large N limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces exactly to the trivial flat connection sector with instanton contributions exponentially suppressed, and the topological string partition function on the resolved conifold is reproduced in this regime. At a certain critical point all non-trivial vacua contribute, instantons are enhanced and the theory appears to undergo a phase transition into a strong coupling regime. We rederive these results by performing a saddle-point approximation to the exact partition function. We obtain a q-deformed version of the Douglas-Kazakov equation for two-dimensional Yang-Mills theory on the sphere, whose one-cut solution below the transition point reproduces the resolved conifold geometry. Above the critical point we propose a two-cut solution that should reproduce the chiral-antichiral dynamics found for black holes on the Calabi-Yau threefold and the Gross-Taylor string in the undeformed limit. The transition from the strong coupling phase to the weak coupling phase appears to be of third order.
Eggenschwiler, R; Straumann, N; Eggenschwiler, Reto; Scialom, David; Straumann, Norbert
1996-01-01
We study the coupled Einstein-Yang-Mills-Dilaton (EYMD) equations for a Fried\\-mann-Le\\-mai\\-tre universe with constant curvature k=1. Our detailed analysis is restricted to the case where the dilaton potential and the cosmological constant vanish. Also assuming a static gauge field, we present analytical and numerical results on the behavior of solutions of the EYMD equations. For different values of the dilaton coupling constant we analyze the phase portrait for the time evolution of the dilaton field and give the behavior of the scale factor. It turns out that there are no inflationary stages in this model.
Yang-Mills $\\beta$-function from a large-distance expansion of the Schrödinger functional
Mansfield, P; Mansfield, Paul; Sampaio, Marcos
1999-01-01
For slowly varying fields the Yang-Mills Schroedinger functional can be expanded in terms of local functionals. We show how analyticity in a complex scale parameter enables the Schroedinger functional for arbitrarily varying fields to be reconstructed from this expansion. We also construct the form of the Schroedinger equation that determines the coefficients. Solving this in powers of the coupling reproduces the results of the `standard' perturbative solution of the functional Schroedinger equation which we also describe. In particular the usual result for the beta-function is obtained illustrating how analyticity enables the effects of rapidly varying fields to be computed from the behaviour of slowly varying ones.
The topological susceptibility in the large-N limit of SU(N) Yang-Mills theory
Cè, Marco; García Vera, Miguel; Giusti, Leonardo; Schaefer, Stefan
2016-11-01
We compute the topological susceptibility of the SU (N) Yang-Mills theory in the large-N limit with a percent level accuracy. This is achieved by measuring the gradient-flow definition of the susceptibility at three values of the lattice spacing for N = 3 , 4 , 5 , 6. Thanks to this coverage of parameter space, we can extrapolate the results to the large-N and continuum limits with confidence. Open boundary conditions are instrumental to make simulations feasible on the finer lattices at the larger N.
A non-perturbative study of the correlation functions of three-dimensional Yang-Mills theory
Huber, Markus Q
2016-01-01
Yang-Mills theory is studied in three dimensions using the equations of motion of the $1$PI and $3$PI effective actions. The employed self-contained truncation includes the propagators, the three-point functions and the four-gluon vertex dynamically. In the gluon propagator also two-loop diagrams are taken into account. The higher gluonic correlation functions show sizable deviations from the tree-level only at low momenta. Also the couplings derived from the vertices agree well down to a few GeV. In addition, different methods to subtract spurious divergences are explored.
Predicting Planck scale and Newton constant from a Yang-Mills gauge theory: 1 and 2-loops estimates
Sobreiro, Rodrigo F
2016-01-01
Recently, a model for an emergent gravity based on $SO(5)$ Yang-Mills action in Euclidian four-dimensional spacetime was proposed. In this work we provide some 1 and 2-loop computations and show that the model can accomodate suitable predicting values for the Newton's gravitational constant. Moreover, it is shown that the typical scale of the expected phase transition between the quantum theory and the geometrodynamical phase is consistent with Planck scale. We also provide a discussion on the cosmological constant problem.
Tachyonic instabilities in 2+1 dimensional Yang-Mills theory and its connection to Number Theory
Chamizo, Fernando
2016-01-01
We consider the $2+1$ dimensional Yang-Mills theory with gauge group $\\text{SU}(N)$ 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.
Yang-Mills theory in 2+1 dimensions: Coupling of matter fields and string-breaking effects
Energy Technology Data Exchange (ETDEWEB)
Agarwal, Abhishek [Physics Department, City College of the CUNY, New York, NY 10031 (United States)], E-mail: abhishek@sci.ccny.cuny.edu; Karabali, Dimitra [Department of Physics and Astronomy, Lehman College of the CUNY, Bronx, NY 10468 (United States)], E-mail: dimitra.karabali@lehman.cuny.edu; Nair, V.P. [Physics Department, City College of the CUNY, New York, NY 10031 (United States)], E-mail: vpn@sci.ccny.cuny.edu
2008-02-11
We explore further the Hamiltonian formulation of Yang-Mills theory in 2+1 dimensions in terms of gauge-invariant matrix variables. Coupling to scalar matter fields is discussed in terms of gauge-invariant fields. We analyze how the screening of adjoint (and other screenable) representations can arise in this formalism. A Schroedinger equation is then derived for the gluelump states which are the daughter states when an adjoint string breaks. A variational solution of this Schroedinger equation leads to an analytic estimate of the string-breaking energy which is within 8.8% of the latest lattice estimates.
Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
Kamata, Norihiko; Sasaki, Shoichi
2017-03-01
We study several types of tree-level improvement in the Yang-Mills gradient flow method in order to reduce the lattice discretization errors in line with Fodor et al. [J. High Energy Phys. 09 (2014) 018., 10.1007/JHEP09(2014)018]. The tree-level O (a2) improvement can be achieved in a simple manner, where an appropriate weighted average is computed between the plaquette and clover-leaf definitions of the action density ⟨E (t )⟩ measured at every flow time t . We further develop the idea of achieving the tree-level O (a4) improvement within a usage of actions consisting of the 1 ×1 plaquette and 1 ×2 planar loop for both the flow and gauge actions. For testing our proposal, we present numerical results for ⟨E (t )⟩ obtained on gauge configurations generated with the Wilson and Iwasaki gauge actions at three lattice spacings (a ≈0.1 ,0.07 , and 0.05 fm). Our results show that tree-level improved flows significantly eliminate the discretization corrections on t2⟨E (t )⟩ in the relatively small-t regime for up to t ≳a2 . To demonstrate the feasibility of our tree-level improvement proposal, we also study the scaling behavior of the dimensionless combinations of the ΛMS ¯ parameter and the new reference scale tX, which is defined through tX2⟨E (tX)⟩=X for the smaller X , e.g., X =0.15 . It is found that √{t0.15 }ΛMS ¯ shows a nearly perfect scaling behavior as a function of a2 regardless of the types of gauge action and flow, after tree-level improvement is achieved up to O (a4) . Further detailed study of the scaling behavior exposes the presence of the remnant O (g2 na2) corrections, which are beyond the tree level. Although our proposal is not enough to eliminate all O (a2) effects, we show that the O (g2 na2) corrections can be well under control even by the simplest tree-level O (a2) improved flow.
Energy Technology Data Exchange (ETDEWEB)
Sandbrink, Dirk
2015-01-26
One of the most promising candidates to describe the physics beyond the standard model is the so-called supersymmetry. This work was created in the context of the DESY-Muenster-Collaboration, which studies in particular the N=1 supersymmetric Yang-Mills theory (SYM). SYM is a comparatively simple theory, which is therefore well-suited to study the expected properties of a supersymmetric theory with the help of Monte Carlo simulations on the lattice. This thesis is focused on the numerical determination of the quarkpotential, the glueball masses and the phase structur of the N=1 supersymmetric Yang-Mills theory. The quarkpotential is used to calculate the Sommer scale, which in turn is needed to convert the dimensionless lattice spacing into physical units. Glueballs are hypothetical particles built out of gluons, their masses are relatively hard to determine in lattice simulations due to their pure gluonic nature. For this reason, various methods are studied to reduce the uncertainties of the mass determination. The focus lies on smearing methods and their use in variational smearing as well as on the use of different glueball operators. Lastly, a first look is taken at the phase diagram of the model at finite temperature. Various simulations have been performed at finite temperature in parallel to those performed at temperature zero to analyse the behaviour of the Polyakov loop and the gluino condensate in greater detail.
Cho Abelian decomposition to the exact A-M-A solutions of the SU(2) Yang-Mills-Higgs theory
Wong, Khai-Ming; Teh, Rosy; Tie, Timothy
2015-04-01
We consider Cho Abelian decomposition to the exact A-M-A configurations in the SU(2) Yang-Mills-Higgs theory. The non-Abelian Yang-Mills gauge potential is decomposed into the restricted and the valence part. With the decomposition, the complete Abelian picture that draws to the various monopoles configurations can be seen clearly. The singularities for the two accompanying antimonopoles and the vortex ring are removed by the corresponding valence potential. However the singularity of the composite monopole at the origin is not removed, but strengthened. Hence the composite monopole is a different kind of monopole entity. Elsewhere, the plane singularity in the solution is not readily be removed by the valence potential. On the other hand, we also solve the decomposed equations to study the solutions that lead to the spatial infinity boundary conditions of the various numerical monopoles configurations. The decomposed equations are also solved in the near-origin region for exact solutions and their properties such as the magnetic field are plotted, which confirms the correspondence with their properties at the near infinity region.
Wilhelm, Matthias
2016-01-01
In the first part of this thesis, we study form factors of general gauge-invariant local composite operators in $\\mathcal{N}=4$ super Yang-Mills theory at various loop orders and for various numbers of external legs. We show how to use on-shell methods for their calculation and in particular extract the dilatation operator from the result. We also investigate the properties of the corresponding remainder functions. Moreover, we extend on-shell diagrams, a Gra{\\ss}mannian integral formulation and an integrability-based construction via R-operators to form factors, focussing on the chiral part of the stress-tensor supermultiplet as an example. In the second part, we study the $\\beta$- and the $\\gamma_i$-deformation, which were respectively shown to be the most general supersymmetric and non-supersymmetric field-theory deformations of $\\mathcal{N}=4$ super Yang-Mills theory that are integrable at the level of the asymptotic Bethe ansatz. For these theories, a new kind of finite-size effect occurs, which we call ...
Caporaso, N; Griguolo, L; Pasquetti, S; Seminara, D; Szabó, R J; Caporaso, Nicola; Cirafici, Michele; Griguolo, Luca; Pasquetti, Sara; Seminara, Domenico; Szabo, Richard J.
2006-01-01
We examine the problem of counting bound states of BPS black holes on local Calabi-Yau threefolds which are fibrations over a Riemann surface by computing the partition function of $q$-deformed Yang-Mills theory on the Riemann surface. We study in detail the genus zero case and obtain, at finite $N$, the instanton expansion of the gauge theory. It can be written exactly as the partition function for $U(N)$ Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. The correspondence between two and three dimensional gauge theories is elucidated by an explicit mapping between two-dimensional Yang-Mills instantons and flat connections on the Lens space. In the large $N$ limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces exactly to the trivial flat connection sector with instanton contributions exponentially suppressed, and the topological string partition function on the resolved conifold ...
Hsu, Jong-Ping
2013-01-01
Yang-Mills gravity is a new theory, consistent with experiments, that brings gravity back to the arena of gauge field theory and quantum mechanics in flat space-time. It provides solutions to long-standing difficulties in physics, such as the incompatibility between Einstein's principle of general coordinate invariance and modern schemes for a quantum mechanical description of nature, and Noether's 'Theorem II' which showed that the principle of general coordinate invariance in general relativity leads to the failure of the law of conservation of energy. Yang-Mills gravity in flat space-time a
Institute of Scientific and Technical Information of China (English)
寇谡鹏
2002-01-01
Used the dimensional reduction in the sense of Parisi and Sourlas, the gauge fixing term of the four-dimensionalYang-Mills field without the theta term is reduced to a two-dimensional principal chiral model. By adding the θ term(θ = π), the two-dimensional principal chiral model changes into the two-dimensional level 1 Wess-Zumino-Novikov-Witten model. The non-trivial fixed point indicates that Yang-Mills theory at θ = π is a critical theory without massgap and confinement.
Quantum fields in the non-perturbative regime. Yang-Mills theory and gravity
Energy Technology Data Exchange (ETDEWEB)
Eichhorn, Astrid
2011-09-06
In this thesis we study candidates for fundamental quantum field theories, namely non-Abelian gauge theories and asymptotically safe quantum gravity. Whereas the first ones have a stronglyinteracting low-energy limit, the second one enters a non-perturbative regime at high energies. Thus, we apply a tool suited to the study of quantum field theories beyond the perturbative regime, namely the Functional Renormalisation Group. In a first part, we concentrate on the physical properties of non-Abelian gauge theories at low energies. Focussing on the vacuum properties of the theory, we present an evaluation of the full effective potential for the field strength invariant F{sub {mu}}{sub {nu}}F{sup {mu}}{sup {nu}} from non-perturbative gauge correlation functions and find a non-trivial minimum corresponding to the existence of a dimension four gluon condensate in the vacuum. We also relate the infrared asymptotic form of the {beta} function of the running background-gauge coupling to the asymptotic behavior of Landau-gauge gluon and ghost propagators and derive an upper bound on their scaling exponents. We then consider the theory at finite temperature and study the nature of the confinement phase transition in d = 3+1 dimensions in various non-Abelian gauge theories. For SU(N) with N= 3,..,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. Our studies shed light on the question which property of a gauge group determines the order of the phase transition. In a second part we consider asymptotically safe quantum gravity. Here, we focus on the Faddeev-Popov ghost sector of the theory, to study its properties in the context of an interacting UV regime. We investigate several truncations, which all lend support to the conjecture that gravity may be asymptotically safe. In a first truncation, we study the ghost anomalous dimension
On some properties of SU(3) Fusion Coefficients
Coquereaux, Robert
2016-01-01
Three aspects of the SU(3) fusion coefficients are revisited: the generating polynomials of fusion coefficients are written explicitly; some curious identities generalizing the classical Freudenthal-de Vries formula are derived; and the properties of the fusion coefficients under conjugation of one of the factors, previously analysed in the classical case, are extended to the affine algebra of su(3) at finite level.
Institute of Scientific and Technical Information of China (English)
CAO Jun-Peng; HOU Bo-Yu; YUE Rui-Hong
2001-01-01
The Hamiltonians of the SU(3) Gaudin model are constructed based on the nonrelativistic limit of the SU(3) chain. After the quantum determinant being well defined, the eigenvectors and eigenvalues of the Hamiltonians of the SU(3) Gaudin model are given. These results can be generalized to any number of constituting spins (SU( N) ).
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The Hamiltonians of the SU(3) Gaudin model are constructed based on the nonrelativistic limit of the SU(3) chain.After the quantum determinant being well defined,the eigenvectors and eigenvalues of the Hamiltonians of the SU(3) Geudin model are given.These results can be generalized to any number of constituting spins (SU(N)).
Guimaraes, M S; Sorella, S P
2016-01-01
In this paper, we discuss non-perturbative infrared features of Yang-Mills theory in Euclidean space-time dimensions greater than four in the Landau gauge and within the Refined Gribov-Zwanziger framework, which enables us to take into account the existence of gauge copies by restricting the domain of integration in the path integral to the Gribov region. Evidences for a decoupling/massive solution for the gluon propagator in higher dimensions are provided. This behavior is strengthened the bigger the dimension is. Further, we show that, by a dimensional reduction of the Refined Gribov-Zwanziger action from five to four dimensions, a non-perturbative coupling between the inverse of the Faddeev-Popov operator and the scalar field corresponding to the fifth component of the gauge field naturally arises, being in agreement with the recently proposed mechanism \\cite{Capri:2014bsa} to generalize the Refined Gribov-Zwanziger construction to the matter sector.
The Hamiltonian approach to Yang-Mills (2+1): Expansion scheme and corrections to string tension
Energy Technology Data Exchange (ETDEWEB)
Karabali, Dimitra, E-mail: dimitra.karabali@lehman.cuny.ed [Department of Physics and Astronomy, Lehman College of the CUNY, Bronx, NY 10468 (United States); Nair, V.P., E-mail: vpn@sci.ccny.cuny.ed [Physics Department, City College of the CUNY, New York, NY 10031 (United States); Yelnikov, Alexandr, E-mail: yelnikov@yahoo.co [Physics Department, City College of the CUNY, New York, NY 10031 (United States)
2010-01-11
We carry out further analysis of the Hamiltonian approach to Yang-Mills theory in 2+1 dimensions which helps to place the calculation of the vacuum wave function and the string tension in the context of a systematic expansion scheme. The solution of the Schroedinger equation is carried out recursively. The computation of correlators is re-expressed in terms of a two-dimensional chiral boson theory. The effective action for this theory is calculated to first order in our expansion scheme and to the fourth order in a kinematic expansion parameter. The resulting corrections to the string tension are shown to be very small, in the range -0.3% to -2.8%, moving our prediction closer to the recent lattice estimates.
Bassetto, A; Torrielli, A
2002-01-01
Commutative Yang-Mills theories in 1+1 dimensions exhibit an interesting interplay between geometrical properties and U(N) gauge structures: in the exact expression of a Wilson loop with $n$ windings a non trivial scaling intertwines $n$ and $N$. In the non-commutative case the interplay becomes tighter owing to the merging of space-time and ``internal'' symmetries in a larger group $U(\\infty)$. We perform an explicit perturbative calculation of such a loop up to ${\\cal O}(g^6)$; rather surprisingly, we find that in the contribution from the crossed graphs (the genuine non-commutative terms) the scaling we mentioned occurs for large $n$ and $N$ in the limit of maximal non-commutativity $\\theta=\\infty$. We present arguments in favour of the persistence of such a scaling at any perturbative order and succeed in summing the related perturbative series.
Jusufi, Kimet
2016-01-01
In the present paper we extend the study of Hawking radiation as a quantum tunneling effect of spin-$1$ particles to the case of a five-dimensional, spherically symmetric, Einstein-Yang-Mills-Gauss-Bonnet (EYMGB) black hole. We solve the Proca equation (PE) by applying the WKB approximation and separation of variables via Hamilton-Jacobi (HJ) equation which results with a set of five differential equations, and reproduce in this way, the Hawking temperature. In the second part of this paper, we extend our results beyond the semiclassical approximation. In particular, we derive the logarithmic correction to the entropy of the EYMGB black hole and show that the quantum corrected specific heat indicates the possible existence of a remnant.
Black p-branes versus black holes in non-asymptotically flat Einstein-Yang-Mills theory
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.
From the holomorphic Wilson loop to `d log' loop-integrands for super-Yang-Mills amplitudes
Lipstein, Arthur E
2012-01-01
The S-matrix for planar N = 4 super Yang-Mills theory can be computed as the correlation function for a holomorphic polygonal Wilson loop in twistor space. In an axial gauge, this leads to the construction of the all-loop integrand via MHV diagrams in twistor space. We show that at MHV, this formulation leads directly to expressions for loop integrands in d log form; i.e., the integrand is a product of exterior derivatives of logarithms of rational functions. For higher MHV degree, it is in d log form multiplied by delta functions. The parameters appearing in the d log form arise geometrically as the coordinates of insertion points of propagators on the holomorphic Wilson loop or on MHV vertices. We discuss a number of examples at one and two loops and give a preliminary discussion of the evaluation of the 1-loop MHV amplitude.
On the correlation functions of three-dimensional Yang-Mills theory from Dyson-Schwinger equations
Huber, Markus Q
2016-01-01
The two- and three-point functions and the four-gluon vertex of three-dimensional Yang-Mills theory are calculated from their Dyson-Schwinger equations and the 3PI effective action. Within a self-contained truncation various effects of truncating Dyson-Schwinger equations are studied. Estimates for the errors induced by truncations are derived from comparisons between results from different equations, comparisons with lattice results and varying higher Green functions. The results indicate that the two-loop diagrams are important in the gluon propagator, where they are explicitly calculated, but not for the vertices. Furthermore, the influence of the four-gluon vertex on lower Green functions is found to be small.
Spacetime and flux tube S-matrices at finite coupling for N=4 supersymmetric Yang-Mills theory.
Basso, Benjamin; Sever, Amit; Vieira, Pedro
2013-08-30
We propose a nonperturbative formulation of planar scattering amplitudes in N=4 supersymmetric Yang-Mills theory, or, equivalently, polygonal Wilson loops. The construction is based on the operator product expansion approach and introduces a new decomposition of the Wilson loop in terms of fundamental building blocks named pentagon transitions. These transitions satisfy a simple relation to the worldsheet S matrix on top of the so-called Gubser-Klebanov-Polyakov vacuum which allows us to bootstrap them at any value of the coupling. In this Letter we present a subsector of the full solution which we call the gluonic part. We match our results with both weak and strong coupling data available in the literature.
Hebecker, A
2002-01-01
A manifestly gauge invariant formulation of 5-dimensional supersymmetric Yang-Mills theories in terms of 4d superfields is derived. It relies on a supersymmetry and gauge-covariant derivative operator in the $x^5$ direction. This formulation allows for a systematic study of higher-derivative operators by combining invariant 4d superfield expressions under the additional restriction of 5d Lorentz symmetry. In cases where the 5d theory is compactified on a gauge-symmetry-breaking orbifold, the formalism can be used for a simple discussion of possible brane operators invariant under the restricted symmetry of the fixed points. This is particularly relevant to recently constructed grand unified theories in higher dimensions (orbifold GUTs). Several applications, including proton decay operators and brane-localized mass terms, are discussed.
All-order bounds for correlation functions of gauge-invariant operators in Yang-Mills theory
Fröb, Markus B; Hollands, Stefan
2015-01-01
We give a complete, self-contained, and mathematically rigorous proof that Euclidean Yang-Mills theories are perturbatively renormalisable, in the sense that all correlation functions of arbitrary composite local operators fulfil suitable Ward identities. Our proof treats rigorously both all ultraviolet and infrared problems of the theory and provides, in the end, detailed analytical bounds on the correlation functions of an arbitrary number of composite local operators. These bounds are formulated in terms of certain weighted spanning trees extending between the insertion points of these operators. Our proofs are obtained within the framework of the Wilson-Wegner-Polchinski-Wetterich renormalisation group flow equations, combined with estimation techniques based on tree structures. Compared with previous mathematical treatments of massless theories without local gauge invariance [R. Guida and Ch. Kopper, arXiv:1103.5692; J. Holland, S. Hollands, and Ch. Kopper, arXiv:1411.1785] our constructions require seve...
Fröb, Markus B
2016-01-01
We prove the existence of the operator product expansion (OPE) in Euclidean Yang-Mills theories as a short-distance expansion, to all orders in perturbation theory. We furthermore show that the Ward identities of the underlying gauge theory are reflected in the OPE; especially, the OPE of an arbitrary number of gauge-invariant composite operators only involves gauge-invariant composite operators. Moreover, we derive recursion relations which allow to construct the OPE coefficients, the quantum BRST differential and the quantum antibracket order by order in perturbation theory, starting from the known free-theory objects. These relations are completely finite from the start, and do not need any further renormalisation as is usually the case in other approaches. Our results underline the importance of the OPE as a general structure underlying quantum field theories. The proofs are obtained within the framework of the Wilson-Wegner-Polchinski-Wetterich renormalisation group flow equations, and generalise similar...
Form factors and the dilatation operator in N= 4 super Yang-Mills theory and its deformations
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Wilhelm, Matthias Oliver
2016-02-12
In the first part of this thesis, we study form factors of general gauge-invariant local composite operators in N=4 super Yang-Mills theory at various loop orders and for various numbers of external legs. We show how to use on-shell methods for their calculation and in particular extract the dilatation operator from the result. We also investigate the properties of the corresponding remainder functions. Moreover, we extend on-shell diagrams, a Grassmannian integral formulation and an integrability-based construction via R-operators to form factors, focussing on the chiral part of the stress-tensor supermultiplet as an example. In the second part, we study the β- and the γ{sub i}-deformation, which were respectively shown to be the most general supersymmetric and non-supersymmetric field-theory deformations of N=4 super Yang-Mills theory that are integrable at the level of the asymptotic Bethe ansatz. For these theories, a new kind of finite-size effect occurs, which we call prewrapping and which emerges from double-trace structures that are required in the deformed Lagrangians. While the β-deformation is conformal when the double-trace couplings are at their non-trivial IR fixed points, the γ{sub i}-deformation has running double-trace couplings without fixed points, which break conformal invariance even in the planar theory. Nevertheless, the γ{sub i}-deformation allows for highly non-trivial field-theoretic tests of integrability at arbitrarily high loop orders.
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.
Status of the Lambda Lattice Scale for the SU(3) Wilson gauge action
Berg, Bernd A
2014-01-01
With the emergence of the Yang-Mills gradient flow technique there is renewed interest in the issue of scale setting in lattice gauge theory. Here I compare for the SU(3) Wilson gauge action the non-perturbative lambda scales of Edwards, Heller and Klassen (EHK), Necco and Sommer (NS), both relying on Sommer's method using the quark potential, with the lambda scale derived by Bazavov, Berg and Velytsky (BBV) from deconfining phase transition data of the Bielefeld group. It turns out that these scales are based on mutually inconsistent data. Nevertheless their over-all agreement is still at a better than +/- 2% in the coupling constant range for which one expects them to apply. Somewhat surprisingly the scale based on the deconfining transition is consistent with the relevant part of the EHK data (baring one data point, which is closest to the strong coupling region), while the NS scale is not.
Topological properties of the SU(3) random vortex world-surface model
Engelhardt, M
2008-01-01
The random vortex world-surface model is an infrared effective model of Yang-Mills dynamics based on center vortex degrees of freedom. These degrees of freedom carry topological charge through writhe and self-intersection of their world-surfaces. A practical implementation of the model realizes the vortex world-surfaces by composing them of elementary squares on a hypercubic lattice. The topological charge for specifically such configurations is constructed in the case of SU(3) color. This necessitates a proper treatment of vortex color structure at vortex branchings, a feature which is absent in the SU(2) color case investigated previously. On the basis of the construction, the topological susceptibility is evaluated in the random vortex world-surface ensemble, both in the confined low-temperature as well as in the deconfined high-temperature phase.
Physical observables from boundary artifacts: scalar glueball in Yang-Mills theory
Chowdhury, Abhishek; Maiti, Jyotirmoy
2015-01-01
By relating the functional averages of the time slice energy density in simulations with Open (O) and Periodic (P) boundary conditions (BCs) respectively for $SU(3)$ lattice gauge theory, we show that the scalar glueball mass and the glueball to vacuum matrix element can be extracted very efficiently from the former. The results are compared with those extracted from the two point function of the time slice energy density (both PBC and OBC). The scaling properties of the mass and the matrix element are studied with the help of Wilson (gradient) flow.
The Framed Standard Model (I) - A Physics Case for Framing the Yang-Mills Theory?
Chan, HM
2015-01-01
Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains: * the standard Higgs scalar as the framon in the electroweak sector; * a global $\\widetilde{su}(3)$ symmetry dual to colour to play the role of fermion generations. Renormalization via framon loops changes the orientation in generation space of the vacuum, hence also of the mass matrices of leptons and quarks, thus making them rotate with changing scale $\\mu$. From previous work, it is known already that a rotatiing mass matrix will lead automatically to: * CKM mixing and neutrino oscillations, * hierarachical masses for quarks and leptons, * a solution to the strong-CP problem transforming the theta-angle into a Kobayashi-Maskawa phase. Here in the FSM, the renormalization group equation has some special properties which explain the main qualitative feaures seen in experiment both for mixing matrices ...
Energy Technology Data Exchange (ETDEWEB)
Ferling, Alexander
2009-05-29
A main topic of this thesis was to transfer the hybrid Monte-Carlo algorithm on a N=1 supersymmetric model. As model served the two-step multi-boson algorithm (TSMB). Beside the essential algorithm in the TSMB program further optimizations were realized. A further step was to optimize the lattice action so that discretization artefacts at finite lattice parameters were more strongly suppressed.
The Framed Standard Model (I) -- A Physics Case for Framing the Yang-Mills Theory?
Chan, Hong-Mo; Tsou, Sheung Tsun
Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains: * the standard Higgs scalar as the framon in the electroweak sector; * a global widetilde{su}(3) symmetry dual to colour to play the role of fermion generations. Renormalization via framon loops changes the orientation in generation space of the vacuum, hence also of the mass matrices of leptons and quarks, thus making them rotate with changing scale μ. From previous work, it is known already that a rotating mass matrix will lead automatically to: * CKM mixing and neutrino oscillations, * hierarchical masses for quarks and leptons, * a solution to the strong-CP problem transforming the theta-angle into a Kobayashi-Maskawa phase. Here in the framed standard model (FSM), the renormalization group equation has some special properties which explain the main qualitative features seen in experiment both for mixing matrices of quarks and leptons, and for their mass spectrum. Quantitative results will be given in Paper II. The present paper ends with some tentative predictions on Higgs decay, and with some speculations on the origin of dark matter...
Energy Technology Data Exchange (ETDEWEB)
Byrd, M.
1997-10-01
The group SU(3) is parameterized in terms of generalized {open_quotes}Euler angles{close_quotes}. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is found, and some relevant comments about the geometry of the group manifold are made.
1999-01-01
Some aspects of the relation between differential geometry of curves and surfaces and multidimensional soliton equations is discussed. The connection between multidimensional soliton equations and Self-dual Yang-Mills equation is studied.
Vacaru, Sergiu I.; Yazici, Enis
2014-01-01
We show that a geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in $f(R,T)$--modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. There are provided and analyzed some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations.
Lattice gradient flow with tree-level $\\mathcal{O}(a^4)$ improvement in pure Yang-Mills theory
Kamata, Norihiko
2015-01-01
Following a recent paper by Fodor et al. (arXiv:1406.0827), we reexamine several types of tree-level improvements on the flow action with various gauge actions in order to reduce the lattice discretization errors in the Yang-Mills gradient flow method. We propose two types of tree-level, $\\mathcal{O}(a^4)$ improved lattice gradient flow including the rectangle term in both the flow and gauge action within the minimal way. We then perform numerical simulations with the simple plaquette gauge action for testing our proposal. Our numerical results of the expectation value of the action density, $\\langle E(t)\\rangle$, show that two $\\mathcal{O}(a^4)$ improved flows significantly eliminate the discretization corrections in the small flow time $t$ regime. On the other hand, the values of $t^2\\langle E(t)\\rangle$ in the large $t$ regime, where the lattice spacing dependence of the tree-level term dies out as inverse powers of $t/a^2$, are different between the results given by two optimal flows leading to the same $...
Nishino, Hitoshi
2012-01-01
We present a system of a self-dual Yang-Mills field and a self-dual vector-spinor field with nilpotent fermionic symmetry (but not supersymmetry) in 2+2 dimensions, that generates supersymmetric integrable systems in lower dimensions. Our field content is (A_\\mu{}^I, \\psi_\\mu{}^I, \\chi^{I J}), where I and J are the adjoint indices of arbitrary gauge group. The \\chi^{I J} is a Stueckelberg field for consistency. The system has local nilpotent fermionic symmetry with the algebra \\{N_\\alpha{}^I, N_\\beta{}^J \\} = 0. This system generates supersymmetric Kadomtsev-Petviashvili equations in D=2+1, and supersymmetric Korteweg-de Vries equations in D=1+1 after appropriate dimensional reductions. We also show that a similar self-dual system in seven dimensions generates self-dual system in four dimensions. Based on our results we conjecture that lower-dimensional supersymmetric integral models can be generated by non-supersymmetric self-dual systems in higher dimensions only with nilpotent fermionic symmetries.
Bondarenko, S
2015-01-01
We revisit the next-to-leading order~(NLO) correction to the eigenvalue of the BFKL equation in the adjoint representation and investigate its properties in analogy with the singlet BFKL in planar $\\mathcal{N}=4$ super Yang-Mills Theory~(SYM). We show that the adjoint NLO BFKL eigenvalue is needed to be slightly modified in order to have a property of hermitian separability present for the singlet BFKL. After this modification the adjoint NLO BFKL eigenvalue is expressed through holomorphic and antiholomophic parts of the leading order eigenvalue and their derivatives. The proposed choice of the modified NLO expression is supported by the fact that it is possible to obtain the same result in a relatively straightforward way directly from the singlet NLO BFKL eigenvalue replacing alternating series by series of constant sign. This transformation corresponds to changing cylindrical topology of the singlet BFKL to the planar topology of the adjoint BFKL. We believe that the original NLO calculation of Fadin and ...
Energy Technology Data Exchange (ETDEWEB)
Krishnaswami, Govind S [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Postbus 80.195, 3508 TD, Utrecht (Netherlands)], E-mail: govind.krishnaswami@durham.ac.uk
2008-04-11
We consider large-N multi-matrix models whose action closely mimics that of Yang-Mills theory, including gauge-fixing and ghost terms. We show that the factorized Schwinger-Dyson loop equations, expressed in terms of the generating series of gluon and ghost correlations G({xi}), are quadratic equations S{sup i}G=G{xi}{sup i}G in concatenation of correlations. The Schwinger-Dyson operator S{sup i} is built from the left annihilation operator, which does not satisfy the Leibnitz rule with respect to concatenation. So the loop equations are not differential equations. We show that left annihilation is a derivation of the graded shuffle product of gluon and ghost correlations. The shuffle product is the point-wise product of Wilson loops, expressed in terms of correlations. So in the limit where concatenation is approximated by shuffle products, the loop equations become differential equations. Remarkably, the Schwinger-Dyson operator as a whole is also a derivation of the graded shuffle product. This allows us to turn the loop equations into linear equations for the shuffle reciprocal, which might serve as a starting point for an approximation scheme.
The one and a half monopoles solution of the SU(2) Yang-Mills-Higgs field theory
Teh, Rosy; Ng, Ban-Loong; Wong, Khai-Ming
2014-04-01
Recently we have reported on the existence of finite energy SU(2) Yang-Mills-Higgs particle of one-half topological charge. In this paper, we show that this one-half monopole can co-exist with a ’t Hooft-Polyakov monopole. The magnetic charge of the one-half monopole is of opposite sign to the magnetic charge of the ’t Hooft-Polyakov monopole. However the net magnetic charge of the configuration is zero due to the presence of a semi-infinite Dirac string along the positive z-axis that carries the other half of the magnetic monopole charge. The solution possesses gauge potentials that are singular along the z-axis, elsewhere they are regular. The total energy is found to increase with the strength of the Higgs field self-coupling constant λ. However the dipole separation and the magnetic dipole moment decrease with λ. This solution is non-BPS even in the BPS limit when the Higgs self-coupling constant vanishes.
García-Jiménez, I; Toscano, J J
2016-01-01
One-loop Standard Model observables produced by virtual heavy Kaluza-Klein fields play a prominent role in the minimal model of universal extra dimensions. Motivated by this aspect, we integrate out all the Kaluza-Klein heavy modes coming from the Yang-Mills theory set on a spacetime with an arbitrary number, $n$, of compact extra dimensions. After fixing the gauge with respect to the Kaluza-Klein heavy gauge modes in a covariant manner, we calculate a gauge independent effective Lagrangian expansion containing multiple Kaluza-Klein sums that entail a bad divergent behavior. We use the Epstein-zeta function to regularize and characterize discrete divergences within such multiple sums, and then we discuss the interplay between the number of extra dimensions and the degree of accuracy of effective Lagrangians to generate or not divergent terms of discrete origin. We find that nonrenormalizable terms with mass dimension $k$ are finite as long as $k>4+n$. Multiple Kaluza-Klein sums of nondecoupling logarithmic te...
On the Global Structure of Deformed Yang-Mills Theory and QCD(adj) on R^3XS^1
Anber, Mohamed M
2015-01-01
Spatial compactification on R^{3}XS^1_L at small S^1-size L often leads to a calculable vacuum structure, where various "topological molecules" are responsible for confinement and the realization of the center and discrete chiral symmetries. Within this semiclassically calculable framework, we study how distinct theories with the same SU(N_c)/Z_k gauge group (labeled by "discrete theta-angles") arise upon gauging of appropriate Z_k subgroups of the one-form global center symmetry of an SU(N_c) gauge theory. We determine the possible Z_k actions on the local electric and magnetic effective degrees of freedom, find the ground states, and use domain walls and confining strings to give a physical picture of the vacuum structure of the different SU(N_c)/Z_k theories. Some of our results reproduce ones from earlier supersymmetric studies, but most are new and do not invoke supersymmetry. We also study a further finite-temperature compactification to R^{2}XS^1_betaXS^1_L. We argue that, in deformed Yang-Mills theory...
García-Jiménez, I.; Novales-Sánchez, H.; Toscano, J. J.
2016-05-01
One-loop Standard Model observables produced by virtual heavy Kaluza-Klein fields play a prominent role in the minimal model of universal extra dimensions. Motivated by this aspect, we integrate out all the Kaluza-Klein heavy modes coming from the Yang-Mills theory set on a spacetime with an arbitrary number, n , of compact extra dimensions. After fixing the gauge with respect to the Kaluza-Klein heavy gauge modes in a covariant manner, we calculate a gauge-independent effective Lagrangian expansion containing multiple Kaluza-Klein sums that entail a bad divergent behavior. We use the Epstein-zeta function to regularize and characterize discrete divergences within such multiple sums, and then we discuss the interplay between the number of extra dimensions and the degree of accuracy of effective Lagrangians to generate or not divergent terms of discrete origin. We find that nonrenormalizable terms with mass dimension k are finite as long as k >4 +n . Multiple Kaluza-Klein sums of nondecoupling logarithmic terms, not treatable by Epstein-zeta regularization, are produced by four-dimensional momentum integration. On the grounds of standard renormalization, we argue that such effects are unobservable.
Gürdoǧan, Ömer; Kazakov, Vladimir
2016-11-01
We introduce a family of new integrable quantum field theories in four dimensions by considering the γ -deformed N =4 supersymmetric Yang-Mills (SYM) theory in the double scaling limit of large imaginary twists and small coupling. This limit discards the gauge fields and retains only certain Yukawa and scalar interactions with three arbitrary effective couplings. In the `t Hooft limit, these 4D theories are integrable, and contain a wealth of conformal correlators such that the whole arsenal of AdS /CFT integrability remains applicable. As a special case of these models, we obtain a quantum field theory of two complex scalars with a chiral, quartic interaction. The Berenstein-Maldacena-Nastase vacuum anomalous dimension is dominated in each loop order by a single "wheel" graph, whose bulk represents an integrable "fishnet" graph. This explicitly demonstrates the all-loop integrability of gamma-deformed planar N =4 SYM theory, at least in our limit. Using this feature and integrability results we provide an explicit conjecture for the periods of double-wheel graphs with an arbitrary number of spokes in terms of multiple zeta values of limited depth.
The Gauge Hierarchy Problem and High Dimensional Yang-Mills Theories
Hatanaka, H; Lim, C S
1998-01-01
We report on an attempt to solve the gauge hierarchy problem in the framework of higher dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to vanish. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the choice of boundary condition for matter fields, and a way to fix it dynamically is presented. We also point out that on the simply-connected space $S^2$ even the finite mass correction vanishes.
Energy Technology Data Exchange (ETDEWEB)
Epple, Mark Dominik
2008-12-03
In this work we examine the Yang-Mills-Schroedinger equation, which is a result from minimizing the vacuum energy density in Coulomb gauge. We use an ansatz for the vacuum wave functional which is motivated by the exact wave functional of quantum electrodynamics. The wave functional is by construction singular on the Gribov horizon and has a variational kernel in the exponent which represents the gluon energy. We derive the so-called Dyson-Schwinger-equations from the variational principle, that the vacuum energy density is stationary under variation with respect to the variational kernel. These Dyson-Schwinger-equations build a set of coupled integral equations for the gluon and ghost propagator, and for the curvature in gauge orbit space. These equations have been derived in the last few years, have been examined analytically in certain approximations, and first numerical results have been obtained. The case of the so-called horizon condition, which means that the ghost form factor is divergent in the infrared, has always been of special interest. But is has been found in certain approximations analytically as well als numerically that the fully coupled system has no self-consistent solution within the employed truncation on two-loop level in the energy. But one can obtain a solvable system by inserting the bare ghost-propagator into the Coulomb equation. This system possesses two different kind of infrared-divergent solutions which differ in the exponents of the power laws of the form factors in the infrared. The weaker divergent solution has previously been found, but not the stronger divergent solution. The subject of this work is to develop a deeper understanding of the presented system. We present a new renormalization scheme which enables us to reduce the number of renormalization parameters by one. This new system of integral equations is solved numerically with greatly increased precision. Doing so we found the stronger divergent solution for the first
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Bern, Zvi; Czakon, Michael; Dixon, Lance J.; Kosower, David A.; Smirnov, Vladimir A.
2006-11-15
We present an expression for the leading-color (planar) four-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4-2{epsilon} dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around {epsilon} = 0, and obtain analytic expressions for the poles from 1/{epsilon}{sup 8} through 1/{epsilon}{sup 4}. We give numerical results for the coefficients of the 1/{epsilon}{sup 3} and 1/e{sup 2} poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/{epsilon}{sup 2} coefficient allows us to test a conjecture of Eden and Staudacher for the four-loop cusp (soft) anomalous dimension. We find that the conjecture is incorrect, although our numerical results suggest that a simple modification of the expression, flipping the sign of the term containing {zeta}{sub 3}{sup 2}, may yield the correct answer. Our numerical value can be used, in a scheme proposed by Kotikov, Lipatov and Velizhanin, to estimate the two constants in the strong-coupling expansion of the cusp anomalous dimension that are known from string theory. The estimate works to 2.6% and 5% accuracy, providing non-trivial evidence in support of the AdS/CFT correspondence. We also use the known constants in the strong-coupling expansion as additional input to provide approximations to the cusp anomalous dimension which should be accurate to under one percent for all values of the coupling. When the evaluations of the integrals are completed through the finite terms, it will be possible to test the iterative, exponentiated structure of the finite terms in the four-loop four-point amplitude, which was uncovered earlier at two and three loops.
Level Statistics of SU(3)-SU(3)* Transitional Region
Jafarizadeh, M A; Sabri, H; gavifekr, P Hossein nezhade; Ranjbar, Z
2012-01-01
The level statistics of SU(3)-SU(3)* transitional region of IBM is described by the nearest neighbor spacing distribution statistics. The energy levels are determined by using the SO(6)representation of eigenstates. By employing the MLE technique, the parameter of Abul-Magd distribution is estimated where suggest less regular dynamics for transitional region in compare to dynamical symmetry limits. Also, the O(6)dynamical symmetry which is known as the critical point of this transitional region, describes a deviation to more regular dynamics.
Holographic Three-Jet Events in Strongly Coupled N=4 Yang-Mills Plasma
Casalderrey-Solana, Jorge
2015-01-01
We analyse classical string configurations with non-trivial transverse dynamics in $AdS_5$-Schwarzschild. These strings develop kink-like structures which, via the gauge/gravity duality, can be interpreted as the propagation of hard gluons produced in association with a quark-antiquark pair in a strongly coupled $\\mathcal{N}=4$ SYM plasma. We observe the appearance of two physically distinct regimes of the in-plasma dynamics, depending on whether the medium is able to resolve the transverse structure of the string prior to its total quench. From these studies we extract the medium resolution scale of the strongly coupled SYM plasma, defined as the smallest angular separation between two jets that the medium can resolve, $\\theta_{\\rm res} = \\mathcal{C}_{\\rm res} ( E /\\sqrt{\\lambda} T)^{-2/3}$, where $\\mathcal{C}_{\\rm res}= \\frac{2^{4/3}}{\\pi}\\frac{\\Gamma(3/4)^2}{\\Gamma(5/4)^2}$. Our analysis constitutes the first study of proxies for three-jet events in a holographic context.
The Gribov problem in presence of background field for $SU(2)$ Yang-Mills theory
Canfora, Fabrizio; Pais, Pablo
2016-01-01
The Gribov problem in the presence of a background field is analyzed: in particular, we study the Gribov copies equation in the Landau-De Witt gauge as well as the semi-classical Gribov gap equation. As background field, we choose the simplest non-trivial one which corresponds to a constant gauge potential with non-vanishing component along the Euclidean time direction. This kind of constant non-Abelian background fields is very relevant in relation with (the computation of) the Polyakov loop but it also appears when one considers the non-Abelian Schwinger effect. We show that the Gribov copies equation is affected directly by the presence of the background field, constructing an explicit example. The analysis of the Gribov gap equation shows that the larger the background field, the smaller the Gribov mass parameter. These results strongly suggest that the relevance of the Gribov copies (from the path integral point of view) decreases as the size of the background field increases.
The Gribov problem in presence of background field for SU(2) Yang-Mills theory
Canfora, Fabrizio; Hidalgo, Diego; Pais, Pablo
2016-12-01
The Gribov problem in the presence of a background field is analyzed: in particular, we study the Gribov copies equation in the Landau-De Witt gauge as well as the semi-classical Gribov gap equation. As background field, we choose the simplest non-trivial one which corresponds to a constant gauge potential with non-vanishing component along the Euclidean time direction. This kind of constant non-Abelian background fields is very relevant in relation with (the computation of) the Polyakov loop but it also appears when one considers the non-Abelian Schwinger effect. We show that the Gribov copies equation is affected directly by the presence of the background field, constructing an explicit example. The analysis of the Gribov gap equation shows that the larger the background field, the smaller the Gribov mass parameter. These results strongly suggest that the relevance of the Gribov copies (from the path integral point of view) decreases as the size of the background field increases.