Confining properties of the classical SU(3) Yang - Mills theory
Dzhunushaliev, V D
1996-01-01
The spherically and cylindrically symmetric solutions of the $SU(3)$ Yang - Mills theory are obtained. The corresponding gauge potential has the confining properties. It is supposed that: a) the spherically symmetric solution is a field distribution of the classical ``quark'' and in this sense it is similar to the Coulomb potential; b) the cylindrically symmetric solution describes a classical field ``string'' (flux tube) between two ``quarks''. It is noticed that these solutions are typically for the classical $SU(3)$ Yang - Mills theory in contradiction to monopole that is an exceptional solution. This allows to conclude that the confining properties of the classical $SU(3)$ Yang - Mills theory are general properties of this theory.
Unconstrained SU(2) and SU(3) Yang-Mills classical mechanics
A systematic study of contraints in SU(2) and SU(3) Yang-Mills classical mechanics is performed. Expect for the SU(2) case with spatial angular momenta they turn out to be nonholonomic. The complete elimination of the unphysical gauge and rotatinal degrees of freedom is achieved using Dirac's constraint formalism. We present an effective unconstrained formulation of the general SU(2) Yang-Mills classical mechanics as well as for SU(3) in the subspace of vanishing spatial angular momenta that is well suited for further explicit dynamical investigations. (orig.)
This work uses FORM software aspects for obtaining a series of formal results in the non-Abelian gauge theory, with SU(3) group. The work also studies field transformation, Lagrangian density invariance, field equations, energy distribution and the theory reparametrization in terms of fields associated to particles which are possible to be detected in accelerators
Mean field analysis of SU(3) lattice Yang-Mills theory at finite temperature
The phase diagram of the SU(3) four-dimensional space-time lattice Yang-Mills field theory at finite temperature is analysed by the extended mean-field technique. With this technique, finite temperature effects are present already at the saddle point approximation. A reasonable quantitative agreement with Monte Carlo numerical simulations is obtained. (author)
Discriminating between two reformulations of SU(3) Yang-Mills theory on a lattice
Shibata, Akihiro [Computing Research Center, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801 (Japan); 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)
2016-01-22
In order to investigate quark confinement, we give a new reformulation of the SU (N) Yang-Mills theory on a lattice and present the results of the numerical simulations of the SU (3) Yang-Mills theory on a lattice. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the “Abelian” dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc.
Magnetic monopole and confinement/deconfinement phase transition in SU(3) Yang-Mills theory
Shibata, Akihiro; Kato, Seikou; Shinohara, Toru
2015-01-01
We have proposed the non-Abelian dual superconductivity in SU(3) Yang-Mills theory for the mechanism of quark confinement,and we presented the numerical evidences in preceding lattice conferences by using the proposed gauge link decomposition to extract magnetic monopole in the gauge invariant way. In this talk, we focus on the dual Meissner effects in view of the magnetic monopole in SU(3) Yang-Mills theory. We measure the chromoelectric and chromomagnetic flux due to a pair of quark and antiquark source at finite temperature. Then, we measure the correlation function of Polyakov loops and Polyakov loop average at various temperatures, and investigate chromomagnetic monopole current induced by chromo-magnetic flux in both confinement and deconfinement phase. We will discuss the role of the chromoelectric monopole in confinement/deconfinement phase transition.
Functional Approach to Classical Yang-Mills Theories
Carta, P
2002-01-01
Sometime ago it was shown that the operatorial approach to classical mechanics, pioneered in the 30's by Koopman and von Neumann, can have a functional version. In this talk we will extend this functional approach to the case of classical field theories and in particular to the Yang-Mills ones. We shall show that the issues of gauge-fixing and Faddeev-Popov determinant arise also in this classical formalism.
Exact solutions to D=2 Supersymmetric Yang-Mills Quantum Mechanics with SU(3) gauge group
Korcyl, Piotr
2009-01-01
In this article we present the cut Fock space approach to the D=d+1=2, Supersymmetric Yang-Mills Quantum Mechanics (SYMQM). We start by briefly introducing the main features of the framework. We concentrate on those properties of the method which make it a convenient set up not only for numerical calculations but also for analytic computations. In the main part of the article a sample of results are discussed, namely, analytic and numerical analysis of the D=2, SYMQM systems with SU(2) and SU(3) gauge symmetry.
A precise determination of the running coupling in the SU(3) Yang-Mills theory
A non-perturbative finite-size scaling technique is used to study the evolution of the running coupling (in a certain adapted scheme) in the SU(3) Yang-Mills theory. At low energies contact is made with the fundamental dynamical scales, such as the string tension K, while at larger energies the coupling is shown to evolve according to perturbation theory. In that regime the coupling in the anti M anti S scheme of dimensional regularization is obtained with an estimated total error of a few percent. (orig.)
The reinterpretation of the BRS equations of Quantum Field Theory as the Maurer Cartan equation of a classical principal fiber bundle leads to a simple gauge invariant classification of the anomalies in Yang Mills theory and gravity
Stiefel-Skyrem-Higgs models, their classical static solutions and Yang-Mills-Higgs monopoles
A new series of models is introduced by adding Higgs fields to the earlier proposed euclidean four-dimensional Skyrme-like models with Yang-Mills composite fields constructed from Stiefel manifold-valued fields. The classical static versions of these models are discussed. The connection with the monopole solutions of the Yang-Mills-Higgs models in the Prasad-Sommerfield limit is pointed out and the BPS monopole is reobtained as an example. (author)
This paper concludes our efforts in describing SU(3)-Yang-Mills theories at different couplings/temperatures in terms of effective Polyakov-loop models. The associated effective couplings are determined through an inverse Monte Carlo procedure based on novel Schwinger-Dyson equations that employ the symmetries of the Haar measure. Because of the first-order nature of the phase transition we encounter a fine-tuning problem in reproducing the correct behavior of the Polyakov-loop from the effective models. The problem remains under control as long as the number of effective couplings is sufficiently small
Shibata, Akihiro; Kato, Seikou; Shinohara, Toru
2014-01-01
The dual superconductivity is a promising mechanism for quark confinement. We proposed the non-Abelian dual superconductivity picture for SU(3) Yang-Mills theory, and demonstrated the restricted field dominance (called conventionally "Abelian" dominance), and non-Abelian magnetic monopole dominance in the string tension. In the last conference, we have demonstrated by measuring the chromoelectric flux that the non-Abelian dual Meissner effect exists and determined that the dual superconductivity for SU(3) case is of type I, which is in sharp contrast to the SU(2) case: the border of type I and type II. In this talk, we focus on the confinement/deconfinemen phase transition and the non-Abelian dual superconductivity at finite temperature: We measure the chromoelectric flux between a pair of static quark and antiquark at finite temperature, and investigate its relevance to the phase transition and the non-Abelian dual Meissner effect.
Silva, P J
2016-01-01
The correlations between the modulus of the Polyakov loop, its phase $\\theta$ and the Landau gauge gluon propagator at finite temperature are investigated in connection with the center symmetry for pure Yang-Mills SU(3) theory. In the deconfined phase, where the center symmetry is spontaneously broken, the phase of the Polyakov loop per configuration is close to $\\theta = 0$, $\\pm \\, 2 \\pi /3$. We find that the gluon propagator form factors associated with $\\theta \\approx 0$ differs quantitatively and qualitatively from those associated to $\\theta \\approx \\pm \\, 2 \\pi /3$. This difference between the form factors is a property of the deconfined phase and a sign of the spontaneous breaking of the center symmetry. Furthermore, given that this difference vanishes in the confined phase, it can be used as an order parameter associated to the deconfinement transition. For simulations near the critical temperature $T_c$, the difference between the propagators associated to $\\theta \\approx 0$ and $\\theta \\approx \\pm ...
Classical Yang-Mills Mechanics: Instant vs. Light-cone Form
Two different forms of relativistic dynamics, the instant and the light-cone form, for the pure SU(2) Yang-Mills field theory in 4-dimensional Minkowski space are examined under the supposition that the gauge fields depend on the time evolution parameter only. The obtained under that restriction of gauge potential space homogeneity mechanical matrix model, sometimes called Yang-Mills classical mechanics, is systematically studied in its instant and light-cone form of dynamics using the Dirac's generalized Hamiltonian approach. In the both cases the constraint content of the obtained mechanical systems is found. In contrast to its well-known instant-time counterpart the light-cone version of SU(2) Yang-Mills classical mechanics has in addition to the constraints generating the SU(2) gauge transformations the new first and second class constraints also. On account of all of these constraints a complete reduction in number of the degrees of freedom is performed. In the instant form of dynamics it is shown that after elimination of the gauge degrees of freedom from the classical SU(2) Yang-Mills mechanics the resulting unconstrained system represents the ID3 Euler-Calogero-Moser model with a certain external fourth-order potential, whereas in the light-cone form it is argued that the classical evolution of the unconstrained degrees of freedom is equivalent to a free one-dimensional particle dynamics.
Effective lattice Polyakov loop theory vs. full SU(3) Yang-Mills at finite temperature
Bergner, G. [Institut für Theoretische Physik, Goethe-Universität Frankfurt,Max-von-Laue-Str. 1, 60438 Frankfurt am Main (Germany); Langelage, J. [Institute for Theoretical Physics, ETH Zürich,CH-8093 Zürich (Switzerland); Philipsen, O. [Institut für Theoretische Physik, Goethe-Universität Frankfurt,Max-von-Laue-Str. 1, 60438 Frankfurt am Main (Germany)
2014-03-06
A three-dimensional effective theory of Polyakov loops has recently been derived from Wilson’s Yang-Mills lattice action by means of a strong coupling expansion. It is valid in the confined phase up to the deconfinement phase transition, for which it predicts the correct order and gives quantitative estimates for the critical coupling. In this work we study its predictive power for further observables like correlation functions and the equation of state. We find that the effective theory correctly reproduces qualitative features and symmetries of the full theory as the continuum is approached. Regarding quantitative predictions, we identify two classes of observables by numerical comparison as well as analytic calculations: correlation functions and their associated mass scales cannot be described accurately from a truncated effective theory, due to its inherently non-local nature involving long-range couplings. On the other hand, phase transitions and bulk thermodynamic quantities are accurately reproduced by the leading local part of the effective theory. In particular, the effective theory description is numerically superior when computing the equation of state at low temperatures or the properties of the phase transition.
Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond
Reinosa, U.; Serreau, J.; Tissier, M.; Wschebor, N.
2016-05-01
We study the confinement-deconfinement phase transition of pure Yang-Mills theories at finite temperature using a simple massive extension of standard background field methods. We generalize our recent next-to-leading-order perturbative calculation of the Polyakov loop and of 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 also 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. Finally, we 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 of the background field itself as an order parameter for confinement. In both cases, we obtain first-order transitions, in agreement with lattice simulations and other continuum approaches.
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...
Silva, P. J.; Oliveira, O.
2016-06-01
The correlations between the modulus of the Polyakov loop, its phase θ , and the Landau gauge gluon propagator at finite temperature are investigated in connection with the center symmetry for pure Yang-Mills SU(3) theory. In the deconfined phase, where the center symmetry is spontaneously broken, the phase of the Polyakov loop per configuration is close to θ =0 , ±2 π /3 . We find that the gluon propagator form factors associated with θ ≈0 differ quantitatively and qualitatively from those associated to θ ≈±2 π /3 . This difference between the form factors is a property of the deconfined phase and a sign of the spontaneous breaking of the center symmetry. Furthermore, given that this difference vanishes in the confined phase, it can be used as an order parameter associated to the deconfinement transition. For simulations near the critical temperature Tc, the difference between the propagators associated to θ ≈0 and θ ≈±2 π /3 allows one to classify the configurations as belonging to the confined or deconfined phase. This establishes a selection procedure which has a measurable impact on the gluon form factors. Our results also show that the absence of the selection procedure can be erroneously interpreted as lattice artifacts.
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
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.)
Perturbative quantization of Yang-Mills theory with classical double as gauge algebra
Ruiz Ruiz, F.
2016-02-01
Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary.
Perturbative quantization of Yang-Mills theory with classical double as gauge algebra
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.)
What can we learn from the classical theory of Yang-Mills and Dirac fields
Minimally coupled classical Yang-Mills and Dirac fields in the Minkowski space-time and in spatially bounded domains are investigated. The extended phase space, defined as the space of the Cauchy data admitting solutions of the evolution equations, is identified. The structure of the gauge symmetry group, defined as the group of all gauge transformations acting in the extended phase space is analysed. In the Minkowski space-time the Lie algebra of infinitesimal gauge symmetries has an ideal giving rise to the constraints. The quotient algebra, isomorphic to the structure algebra, labels the conserved colour charges. In the case of spatially bounded domains, each set of the boundary data gives rise to an extended phase space in which the evolution is Hamiltonian. The problem of a physical interpretation of the boundary data is discussed. (author)
Fukushima, Kimichika
2014-01-01
This article reports an explicit function of confining classical Yang-Mills vector potentials as well as quantum fluctuations around the classical field. The classical vector potential, which is composed of a confining localized function and an unlocalized function, satisfies the classical Yang-Mills equation. The confining localized function contributes to the Wilson loop, while the unlocalized function has no contribution to this loop. The confining linear potential between a pair of a heavy fermion particle and an antiparticle is due to the Lie algebra and the form of the confining localized function, which have opposite signs at positions of the particle and antiparticles along the Wilson loop in the time direction. Some classical confining parts of vector potentials also have the opposite sign for the inversion of coordinate of the axis perpendicular to the axis between two particles. The localized functions of vector potentials are squeezed around the axis connecting two particles, and the string tensio...
Parametric Instability of Classical Yang-Mills Fields under Color Magnetic Background
Tsutsui, Shoichiro; Kunihiro, Teiji; Ohnishi, Akira
2014-01-01
We investigate instabilities of classical Yang-Mills fields in a time-dependent spatially homogeneous color magnetic background field in a non-expanding geometry for elucidating the earliest stage dynamics of ultra-relativistic heavy-ion collisions. The background gauge field configuration considered in this article is spatially homogeneous and temporally periodic, and is alluded by Berges-Scheffler-Schlichting-Sexty (BSSS). We discuss the whole structure of instability bands of fluctuations around the BSSS background gauge field on the basis of Floquet theory, which enables us to discuss the stability in a systematic way. We find various instability bands on the $(p_z, p_T)$-plane. These instability bands are caused by parametric resonance despite the fact that the momentum dependence of the growth rate for $|\\mathbf{p}| \\leq \\sqrt{B}$ is similar to a Nielsen-Olesen instability. Moreover, some of instability bands are found to emerge not only in the low momentum but also in the high momentum region; typicall...
Shibata, Akihiro; Kato, Seikou; Shinohara, Toru
2014-01-01
The dual superconductivity is a promising mechanism for quark confinement. We have proposed the non-Abelian dual superconductivity picture for SU(3) Yang-Mills theory, and showed the restricted field dominance (called conventionally Abelian dominance), and non-Abelian magnetic monopole dominance in the string tension. We have further demonstrated by measuring the chromoelectric flux that the non-Abelian dual Meissner effect exists and determined that the dual superconductivity for SU(3) case is of type I, which is in sharp contrast to the SU(2) case: the border of type I and type II. In this talk, we focus on the confinement/deconfinement phase transition and the non-Abelian dual superconductivity at a finite temperature: We measure the Polyakov loop average and correlator and investigate the restricted field dominance in the Polyakov loop. Then, we measure the chromoelectric flux between a pair of static quark and antiquark created by a pair of Polyakov loops, and investigate the non-Abelian dual Meissner ef...
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.
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
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.
Entropy production in quantum Yang-Mills mechanics in semi-classical approximation
Tsukiji, Hidekazu; Kunihiro, Teiji; Ohnishi, Akira; Takahashi, Toru T
2015-01-01
We discuss thermalization of isolated quantum systems by using the Husimi-Wehrl entropy evaluated in the semiclassical treatment. The Husimi-Wehrl entropy is the Wehrl entropy obtained by using the Husimi function for the phase space distribution. The time evolution of the Husimi function is given by smearing the Wigner function, whose time evolution is obtained in the semiclassical approximation. We show the efficiency and usefullness of this semiclassical treatment in describing entropy production of a couple of quantum mechanical systems, whose classical counter systems are known to be chaotic. We propose two methods to evaluate the time evolution of the Husimi-Wehrl entropy, the test-particle method and the two-step Monte-Carlo method. We demonstrate the characteristics of the two methods by numerical calculations, and show that the simultaneous application of the two methods ensures the reliability of the results of the Husimi-Wehrl entropy at a given time.
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...
SIMULATION OF NONLINEAR COLOR OSCILLATIONS IN YANG-MILLS THEORY
Trunev A. P.
2015-01-01
The article presents the simulation of non-linear spatial-temporal color oscillations in Yang-Mills theory in the case of SU (2) and SU (3) symmetry. We examined three systems of equations derived from the Yang-Mills theory, which describes the transition to chaotic behaviour. These transitions are caused by nonlinear vibrations of colour, depending on the model parameters - the coupling constants and the initial wave amplitude. Such transitions to chaotic behaviour by increasing the paramete...
Lin, C.-J. David; Ogawa, Kenji; Ramos, Alberto
2015-12-01
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 GF 2 ˜ 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, although we cannot draw definite conclusion regarding possible infrared conformality of this theory. Furthermore, we comment on the issue regarding the continuum extrapolation near an infrared fixed point. In addition to adopting the fit ansätz a' la Symanzik for performing this task, we discuss a possible alternative procedure inspired by properties derived from low-energy scale invariance at strong coupling. Based on this procedure, we propose a finite-size scaling method for the renormalised coupling as a means to search for infrared fixed point. Using this method, it can be shown that the behaviour of the theory around g GF 2 ˜ 6 is still not governed by possible infrared conformality.
A model of unified quantum chromodynamics and Yang-Mills gravity
Hsu, Jong-Ping
2011-01-01
Based on a generalized Yang-Mills framework, gravitational and strong interactions can be unified in analogy with the unification in the electroweak theory. By gauging $T(4) \\times [SU(3)]_{color} $ in flat 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.
A model of unified quantum chromodynamics and Yang-Mills gravity
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.
Bagchi, Arjun; Basu, Rudranil; Kakkar, Ashish; Mehra, Aditya
2015-01-01
We investigate the symmetry structure of the non-relativistic limit of Yang-Mills theories. Generalising previous results in the Galilean limit of electrodynamics, we discover that for Yang-Mills theories there are a variety of limits inside the Galilean regime. We first explicitly work with the $SU(2)$ theory and then generalise to $SU(N)$ for all $N$, systematising our notation and analysis. We discover that the whole family of limits lead to different sectors of Galilean Yang-Mills theorie...
Marateck, Samuel
2011-01-01
In their 1954 paper, Yang and Mills invented the non-Abelian field strength to satisfy certain criteria but didn't explain how it could be derived. In the penultimate section we show how the Yang-Mills field strength derives from Yang's gauge transformation. The preceding sections place Yang-Mills theory in historical perspective and cover material relating to the field strength. The final section shows how Yang-Mills theory was combined with spontaneous symmetry breaking, the Goldstone theorem and subsequent work to contribute to the Standard Model of particle physics.
Gauss' law and nonlinear plane waves for Yang-Mills theory
Tsapalis, A.; Politis, E. P.; Maintas, X. N.; Diakonos, F. K.
2016-04-01
We investigate nonlinear plane-wave solutions of the classical Minkowskian Yang-Mills (YM) equations of motion. By imposing a suitable ansatz which solves Gauss' law for the SU(3) theory, we derive solutions which consist of Jacobi elliptic functions depending on an enumerable set of elliptic modulus values. The solutions represent periodic anharmonic plane waves which possess arbitrary nonzero mass and are exact extrema of the nonlinear YM action. Among them, a unique harmonic plane wave with a nontrivial pattern in phase, spin, and color is identified. Similar solutions are present in the SU(4) case, while they are absent from the SU(2) theory.
Einstein-Yang-Mills from pure Yang-Mills amplitudes
Nandan, Dhritiman; Schlotterer, Oliver; Wen, Congkao
2016-01-01
We present new relations for scattering amplitudes of color ordered gluons and gravitons in Einstein-Yang-Mills theory. Tree-level amplitudes of arbitrary multiplicities and polarizations involving up to three gravitons and up to two color traces are reduced to partial amplitudes of pure Yang-Mills theory. In fact, the double-trace identities apply to Einstein-Yang-Mills extended by a dilaton and a B-field. Our results generalize recent work of Stieberger and Taylor for the single graviton case with a single color trace. As the derivation is made in the dimension-agnostic Cachazo-He-Yuan formalism, our results are valid for external bosons in any number of spacetime dimensions. Moreover, they generalize to the superamplitudes in theories with 16 supercharges.
Bagchi, Arjun; Kakkar, Ashish; Mehra, Aditya
2015-01-01
We investigate the symmetry structure of the non-relativistic limit of Yang-Mills theories. Generalising previous results in the Galilean limit of electrodynamics, we discover that for Yang-Mills theories there are a variety of limits inside the Galilean regime. We first explicitly work with the $SU(2)$ theory and then generalise to $SU(N)$ for all $N$, systematising our notation and analysis. We discover that the whole family of limits lead to different sectors of Galilean Yang-Mills theories and the equations of motion in each sector exhibit hitherto undiscovered infinite dimensional symmetries, viz. infinite Galilean Conformal symmetries in $D=4$. These provide the first examples of interacting Galilean Conformal Field Theories (GCFTs) in $D>2$.
Bagchi, Arjun; Basu, Rudranil; Kakkar, Ashish; Mehra, Aditya
2016-04-01
We investigate the symmetry structure of the non-relativistic limit of Yang-Mills theories. Generalising previous results in the Galilean limit of electrodynamics, we discover that for Yang-Mills theories there are a variety of limits inside the Galilean regime. We first explicitly work with the SU(2) theory and then generalise to SU( N) for all N, systematising our notation and analysis. We discover that the whole family of limits lead to different sectors of Galilean Yang-Mills theories and the equations of motion in each sector exhibit hitherto undiscovered infinite dimensional symmetries, viz. infinite Galilean Conformal symmetries in D = 4. These provide the first examples of interacting Galilean Conformal Field Theories (GCFTs) in D > 2.
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
SIMULATION OF NONLINEAR COLOR OSCILLATIONS IN YANG-MILLS THEORY
Trunev A. P.
2015-06-01
Full Text Available The article presents the simulation of non-linear spatial-temporal color oscillations in Yang-Mills theory in the case of SU (2 and SU (3 symmetry. We examined three systems of equations derived from the Yang-Mills theory, which describes the transition to chaotic behaviour. These transitions are caused by nonlinear vibrations of colour, depending on the model parameters - the coupling constants and the initial wave amplitude. Such transitions to chaotic behaviour by increasing the parameters are characteristic of hydrodynamic turbulence. A model of spatial-temporal oscillations of the Yang-Mills 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 of five colors or vice versa - the first three five other colors. The kinetic energy fluctuations or shared equally between the color components, or dominated by the kinetic energy of repressed groups of colors. Note that the general property of physical systems described by nonlinear equations in the Yang-Mills theory and hydrodynamics is particularly strong in the formation of quark-gluon plasma and hadrons jets, when the Yang-Mills is involved in the formation of hydrodynamic flow. Note that there is a relationship between the Einstein and Yang-Mills theory, on the one hand, Einstein's equations and hydrodynamics - on the other. All of this points to the existence in the nature of a general mechanism of formation of a special type of turbulence - geometric turbulence
On deformations of Yang-Mills algebras
Movshev, M.
2005-01-01
This is a next paper from a sequel devoted to algebraic aspects of Yang-Mills theory. We undertake a study of deformation theory of Yang-Mills algebra YM - a ``universal solution'' of Yang-Mills equation. We compute (cyclic) (co)homology of YM.
Effective gluon potential and Yang-Mills thermodynamics
Sasaki, Chihiro [Frankfurt Institute for Advanced Studies (FIAS), Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main (Germany); Redlich, Krzysztof [Institute of Theoretical Physics, University of Wroclaw, PL-50204 Wroclaw (Poland)
2013-07-01
We show that the Polyakov-loop potential can be derived, using a field theoretical methods, directly from the SU(3) Yang-Mills theory. A class of the Polyakov-loop effective potentials used so far in literature appears as limiting cases of our potential. We deduce the correspondence of U(L) to the strong-coupling expansion, of which the relevant coefficients of the gluon energy distribution are specified solely by characters of the SU(3) group. At high temperatures the derived gluon potential exhibits the correct asymptotic behavior, whereas at low temperatures, it disfavors gluons as appropriate dynamical degrees of freedom. To quantify the Yang-Mills thermodynamics in a confined phase, we propose a hybrid approach which matches the effective gluon potential to the one of glueballs constrained by the QCD trace anomaly in the context of dilaton fields.
Polyakov Loop and Gluon Quasiparticles in Yang-Mills Thermodynamics
Ruggieri, M.; Alba, P.; P. Castorina(INFN Sezione di Catania and Dipartimento di Fisica e Astronomia, Universita' di Catania, Italy); Plumari, S.; Ratti, C.; Greco, V.
2012-01-01
We study the interpretation of Lattice data about the thermodynamics of the deconfinement phase of SU(3) Yang-Mills theory, in terms of gluon quasiparticles propagating in a background of a Polyakov loop. A potential for the Polyakov loop, inspired by the strong coupling expansion of the QCD action, is introduced; the Polyakov loop is coupled to tranverse gluon quasiparticles by means of a gas-like effective potential. This study is useful to identify the effective degrees of freedom propagat...
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.
Lai, Sheng-Hong; Tsai, I-Hsun
2016-01-01
The SL(2,C) Yang-Mills instanton solutions constructed recently by the biquaternion method were shown to satisfy the complex version of the ADHM equations and the Monad construction. Moreover, we discover that, in addition to the holomorphic vector bundles on CP^3 similar to the case of SU(2) ADHM construction, the SL(2,C) instanton solutions can be used to explicitly construct instanton sheaves on CP^3. Presumably, the existence of these instanton sheaves is related to the jumping lines of the SL(2,C) instantons on S^4 which do not exist for SU(2) instantons.
Gauss' Law and Non-Linear Plane Waves for Yang-Mills Theory
Tsapalis, A; Maintas, X N; Diakonos, F K
2016-01-01
We investigate Non-Linear Plane-Wave solutions of the classical Minkowskian Yang-Mills (YM) equations of motion. By imposing a suitable ansatz which solves Gauss' law for the $SU(3)$ theory, we derive solutions which consist of Jacobi elliptic functions depending on an enumerable set of elliptic modulus values. The solutions represent periodic anharmonic plane waves which possess arbitrary non-zero mass and are exact extrema of the non-linear YM action. Among them, a unique harmonic plane wave with a non-trivial pattern in phase, spin and color is identified. Similar solutions are present in the $SU(4)$ case while are absent from the $SU(2)$ theory.
Interface Yang-Mills, supersymmetry, and Janus
We consider theories consisting of a planar interface with N=4 super-Yang-Mills on either side and varying gauge coupling across the interface. The interface does not carry any independent degrees of freedom, but is allowed to support local gauge invariant operators, included with independent interface couplings. In general, both conformal symmetry and supersymmetry will be broken, but for special arrangements of the interface couplings, these symmetries may be restored. We provide a systematic classification of all allowed interface supersymmetries. We find new theories preserving eight and four Poincare supersymmetries, which get extended to sixteen and eight supersymmetries in the conformal limit, respectively with SU(2)xSU(2), SO(2)xSU(2) internal symmetry. The Lagrangians for these theories are explicitly constructed. We also recover the theory with two Poincare supersymmetries and SU(3) internal symmetry proposed earlier as a candidate CFT dual to super-Janus. Since our new interface theories have only operators from the supergravity multiplet turned on, dual supergravity solutions are expected to exist. We speculate on the possible relation between the interface theory with maximal supersymmetry and the near-horizon limit of the D3-D5 system
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.
Towards the fundamental spectrum of the Quantum Yang-Mills Theory
Liegener, Klaus
2016-01-01
In this work we focus on the quantum Einstein-Yang-Mills sector quantised by the methods of Loop Quantum Gravity (LQG). We point out the improved UV behaviour of the coupled system as compared to pure quantum Yang-Mills theory on a fixed, classical background spacetime as was considered in a seminal work by Kogut and Susskind. Furthermore, we develop a calculational scheme by which the fundamental spectrum of the quantum Yang-Mills Hamiltonian can be computed in principle and by which one can make contact to the Wilsonian renormalization group, possibly purely within the Hamiltonian framework. Finally, we comment on the relation of the fundamental spectrum to that of pure Yang-Mills theory on a (flat) classical spacetime.
Implementation of chromomagnetic gluons in Yang-Mills thermodynamics
Sasaki, Chihiro; Redlich, Krzysztof
2013-01-01
Motivated by the recent high-precision lattice data on Yang-Mills equations of state, we propose an effective theory of SU(3) gluonic matter. The theory is constructed based on the center and scale symmetries and their dynamical breaking, so that the interplay between color-electric and color-magnetic gluons is included coherently. We suggest, that the magnetic gluon condensate changes its thermal behavior qualitatively above the critical temperature, as a consequence of the matching to dimensionally-reduced magnetic theories. We consider thermodynamics in the mean field approximation and discuss the properties and interpretation of the trace anomaly.
Glueball Spectra from a Matrix Model of Pure Yang-Mills Theory
Acharyya, Nirmalendu; Sanyal, Sambuddha; Vaidya, Sachindeo
2016-01-01
We present the numerical results of a simple matrix model that approximates $SU(N)$ pure Yang-Mills theory. The low-lying physical spectrum of the Hamiltonian is estimated by variational techniques of $SU(2)$ and $SU(3)$. In both these cases, we find an excellent agreement with lattice simulations. However, in the matrix model, the computation is much simpler and faster.
On the classification of Yang Mills fields
A scheme of Classification for Yang Mills fields analogous to the Petrov Classification in general relativity is discussed. It is also shown how such a classification is used to obtain explicit solutions of the equations of motion. (author)
Fiber spaces, connections and Yang-Mills fields
From the point of view of a differential geometer, Yang-Mills Fields are connections on principal fiber bundles whose curvature satisfies certain first-order differential equations. These lectures notes assume a knowledge of the formalism of calculus on manifolds, i.e., the theory of differential forms and vector fields, and are based on the theory of connections in fiber spaces, developed primarily by E. Cartan and C. Ehresmann in the period 1920-1955. To make the material more readily accessible to someone familiar with classical physics, the emphasis will be on Maxwell electromagnetic theory, considered as a Yang-Mills with an abelian structure group. Some of the material is from Interdisciplinary Mathematics, some is new. (orig.)
Introduction to instantons in Yang-Mills theory
The Yang-Mills theory is outlined; the classical formalism is discussed first, and then the difficulties related to gauge invariance in the canonical quantization of the theory are taken up. Next, the task of finding and studying Euclidean gauge field configurations of finite action as solutions to the equation of motion is addressed. It is found that configurations which contribute the most in the semi-classical approximation are those which minimize the action. The question of a lower bound for the Euclidean action is considered. Properties of topological charge and the behavior of topological charge under gauge transformation are discussed. Then instanton solutions to the field equations are produced. Finally, the physical interpretation of the instanton is considered. It is found that the instanton, the Euclidean gauge field configuration which minimizes the action, induces tunneling among the infinitely degenerate vacua of the Yang-Mills theory by lifting the degeneracy and creating new distinct inequivalent (invariant under topologically nontrivial gauge transformations) vacua labelled by a superselection index theta. The angle theta is shown not to be a gauge artifact. In conclusion, the tunneling Hamiltonian and effective Lagrangian for the Yang-Mills theory are discussed
Higgs potential and confinement in Yang-Mills theory on exotic R^4
Asselmeyer-Maluga, Torsten
2013-01-01
We show that pure SU(2) Yang-Mills theory formulated on certain exotic R^4 from the radial family shows confinement. The condensation of magnetic monopoles and the qualitative form of the Higgs potential are derived from the exotic R^4, e. A relation between the Higgs potential and inflation is discussed. Then we obtain a formula for the Higgs mass and discuss a particular smoothness structure so that the Higgs mass agrees with the experimental value. The singularity in the effective dual U(1) potential has its cause by the exotic 4-geometry and agrees with the singularity in the maximal abelian gauge scenario. We will describe the Yang-Mills theory on e in some limit as the abelian-projected effective gauge theory on the standard R^4. Similar results can be derived for SU(3) Yang-Mills theory on an exotic R^4 provided dual diagonal effective gauge bosons propagate in the exotic 4-geometry.
Linear growth of the trace anomaly in Yang-Mills thermodynamics
In the lattice work by Miller and in the work by Zwanziger a linear growth of the trace anomaly for high temperatures was found in pure SU(2) and SU(3) Yang-Mills theories. While future numerical work is needed to confirm or to rule out the linear growth, the aforementioned results point to the remarkable property that the corresponding systems are strongly interacting even at high temperatures. We show that within an analytical approach to Yang-Mills thermodynamics this linear rise is obtained and is directly connected to the presence of a temperature-dependent ground state, which describes (part of) the nonperturbative nature of the Yang-Mills system. Our predictions are in approximate agreement with Miller and Zwanziger
Deconfinement in Yang-Mills Theory through Toroidal Compactification
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.
Representations of Super Yang-Mills Algebras
Herscovich, Estanislao
2013-06-01
We study in this article the representation theory of a family of super algebras, called the super Yang-Mills algebras, by exploiting the Kirillov orbit method à la Dixmier for nilpotent super Lie algebras. These super algebras are an extension of the so-called Yang-Mills algebras, introduced by A. Connes and M. Dubois-Violette in (Lett Math Phys 61(2):149-158, 2002), and in fact they appear as a "background independent" formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras {{Cliff}q(k) ⊗ Ap(k)}, for p ≥ 3, or p = 2 and q ≥ 2, appear as a quotient of all super Yang-Mills algebras, for n ≥ 3 and s ≥ 1. This provides thus a family of representations of the super Yang-Mills algebras.
A gluon cluster solution of effective Yang-Mills theory
Pavlovsky, O V
2001-01-01
A classical solution of the effective Yang-Mills (YM) theory with a finite energy and nonstandard Lagrangian was obtained. Influence of vacuum polarization on gluon cluster formation was discussed. Appearance of cluster solutions in the theory of non-Abelian fields can take place only if the result goes beyond the framework of pure YM theory. It is shown that account of quantum effects of polarized vacuum in the presence of a classical gluon field can also result in formation of the solutions. Solutions with the finite intrinsic energy are provided. Besides, fields of colour groups SU(2) were studied
Entropy Production and Equilibration in Yang-Mills Quantum Mechanics
Tsai, Hung-Ming
Entropy production in relativistic heavy-ion collisions is an important physical quantity for studying the equilibration and thermalization of hot matters of quantum chromodynamics (QCD). To formulate a nontrivial definition of entropy for an isolated quantum system, a certain kind of coarse graining may be applied so that the entropy for this isolated quantum system depends on time explicitly. The Husimi distribution, which is a coarse grained distribution in the phase space, is a suitable candidate for this approach. We proposed a general and systematic method of solving the equation of motion of the Husimi distribution for an isolated quantum system. The Husimi distribution is positive (semi-)definite all over the phase space. In this method, we assume the Husimi distribution is composed of a large number of Gaussian test functions. The equation of motion of the Husimi distribution, formulated as a partial differential equation, can be transformed into a system of ordinary differential equations for the centers and the widths of these Gaussian test functions. We numerically solve the system of ordinary differential equations for the centers and the widths of these test functions to obtain the Husimi distribution as a function of time. To ensure the numerical solutions of the trajectories of the test particles preserve physical conservation laws, we obtain a constant of motion for the quantum system. We constructed a coarse grained Hamiltonian whose expectation value is exactly conserved. The conservation of the coarse grained energy confirms the validity of this method. Moreover, we calculated the time evolution of the coarse grained entropy for a model system (Yang-Mills quantum mechanics). Yang-Mills quantum mechanics is a quantum system whose classical correspondence possesses chaotic behaviors. The numerical results revealed that the coarse grained entropy for Yang-Mills quantum mechanics saturates to a value that coincides with the microcanonical entropy
Confinement--deconfinement phase transition and gauge-invariant gluonic mass in Yang-Mills theory
Kondo, Kei-Ichi
2015-01-01
We give an analytical derivation of the confinement/deconfinement phase transition at finite temperature in the $SU(N)$ Yang-Mills theory in the $D$-dimensional space time for $D>2$. We elucidate what is the mechanism for quark confinement and deconfinement at finite temperature and why the phase transition occurs at a certain temperature. For this purpose, we use a novel reformulation of the Yang-Mills theory which allows the gauge-invariant gluonic mass term and calculate analytically the effective potential of the Polyakov loop average concretely for the $SU(2)$ and $SU(3)$ Yang-Mills theories by including the gauge-invariant dynamical gluonic mass. For $D=4$, we give an estimate on the transition temperature $T_d$ as the ratio to the gauge-invariant gluonic mass $M$ which has been measured on the lattice at zero temperature and is measurable also at finite temperature. We show that the order of the phase transition at $T_d$ is the second order for $SU(2)$ and (weakly) first order for $SU(3)$ Yang-Mills th...
Note about Yang Mills, QCD and their supersymmetric counterparts
Jora, Renata
2011-01-01
We analyze in an effective Lagrangian framework the connection between Super QCD (Super Yang Mills) and QCD (Yang Mills) by highlighting the crucial role that the zero modes play in the process of decoupling gluinos and squarks.
QUANTUM GRAVITY AND YANG-MILLS THEORY
Trunev A. P.
2014-01-01
Full Text Available In this paper, we consider Einstein's theory of gravitation in connection with Yang-Mills theory. The model of the metric satisfying the basic requirements of quantum theory is proposed. The mechanism of generation of baryonic matter of dark energy is discussed
Yang-Mills theory in Coulomb gauge
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.)
Baecklund Transformations (BT) and the derivation of local conservation laws are first reviewed in the classic case of the Sine-Gordon equation. The BT, conservation laws (local and nonlocal), and the inverse-scattering formulation are discussed for the chiral and the self-dual Yang-Mills fields. Their possible applications to the loop formulation for the Yang-Mills fields are mentioned. 55 references, 1 figure
Topological susceptibility in lattice Yang-Mills theory with open boundary condition
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; 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.
Real-time dynamics of a hot Yang-Mills theory: a numerical analysis
Ambjørn, J.; Anagnostopoulos, K. N.; Krasnitz, A.
2002-03-01
We discuss recent results obtained from simulations of high temperature, classical, real time dynamics of SU(2) Yang-Mills theory at temperatures of the order of the electroweak scale. Measurements of gauge covariant and gauge invariant autocorrelations of the fields indicate that the ASY-Bödecker scenario is irrelevant at these temperatures.
Superstring limit of Yang-Mills theories
Lechtenfeld, Olaf
2016-01-01
It was pointed out by Shifman and Yung that the critical superstring on $X^{10}={\\mathbb R}^4\\times Y^6$, where $Y^6$ is the resolved conifold, appears as an effective theory for a U(2) Yang-Mills-Higgs system with four fundamental Higgs scalars defined on $\\Sigma_2\\times{\\mathbb R}^2$, where $\\Sigma_2$ is a two-dimensional Lorentzian manifold. Their Yang-Mills model supports semilocal vortices on ${\\mathbb R}^2\\subset\\Sigma_2\\times{\\mathbb R}^2$ with a moduli space $X^{10}$. When the moduli of slowly moving thin vortices depend on the coordinates of $\\Sigma_2$, 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 $\\Sigma_2\\times T^2_p$, where $T^2_p$ 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 $T^2_p$, d...
Dynamical Breaking of Generalized Yang-Mills Theory
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
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.
Dark Matter from a Classically Scale-Invariant $SU(3)_X$
Karam, Alexandros; Tamvakis, Kyriakos
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 ...
Yang-Mills theory in Coulomb gauge; Yang-Mills-theorie in Coulombeichung
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.)
Yang-Mills instantons over Riemann surfaces
Exact solutions to the self-dual Yang-Mills equations over Riemann surfaces of arbitrary genus are constructed. They are characterized by the conformal class of the Riemann surface. They correspond to U(1) instantonic solutions for an Abelian-Higgs system. A functional action of a genus g Riemann surface is constructed, with minimal points being the two-dimensional self-dual connections. The exact solutions may be interpreted as connecting initial and final nontrivial vacuum states of a conformal theory, in the sense of Segal, with a Feynman functor constructed from the functional integral of the action. (orig.)
YANG-MILLS FIELDS AND THE LATTICE.
CREUTZ,M.
2004-05-18
The Yang-Mills theory lies at the heart of our understanding of elementary particle interactions. For the strong nuclear forces, we must understand this theory in the strong coupling regime. The primary technique for this is the lattice. While basically an ultraviolet regulator, the lattice avoids the use of a perturbative expansion. I discuss some of the historical circumstances that drove us to this approach, which has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles.
Observables in Topological Yang-Mills Theories
Boldo, J L; Gieres, François; Lefrançois, M; Piguet, O; Boldo, Jose Luis; Constantinidis, Clisthenis P.; Gieres, Francois; Lefrancois, Matthieu; Piguet, Olivier
2003-01-01
Using topological Yang-Mills theory as example, we discuss the definition and determination of observables in topological field theories (of Witten-type) within the superspace formulation proposed by Horne. This approach to the equivariant cohomology leads to a set of bi-descent equations involving the BRST and supersymmetry operators as well as the exterior derivative. This allows us to determine superspace expressions for all observables, and thereby to recover the Donaldson-Witten polynomials when choosing a Wess-Zumino-type gauge.
Duality in supersymmetric Yang-Mills theory
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.
Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory
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
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.
Function group approach to unconstrained Hamiltonian Yang-Mills theory
Starting from the temporal gauge Hamiltonian for classical pure Yang-Mills theory with the gauge group SU(2) a canonical transformation is initiated by parametrizing 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
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...
Yang-Mills connections valued on the octonionic algebra
Restuccia, A.; Veiro, J. P.
2016-05-01
We consider a formulation of Yang-Mills theory where the gauge field is valued on an octonionic algebra and the gauge transformation is the group of automorphisms of it. We show, under mild assumptions, that the only possible gauge formulations are the usual su(2) or u(1) Yang-Mills theories.
On the bag models based on the singular solution of Yang-Mills equations
The report is devoted to the problem of constructing the model of quark bag on the basis of singular solutions of the classical Yang-Mills (YM) equations. The basic assumption is that quarks in the zero approximation move in a certain effective YM potential that is a solution to classical YM equations with singularity on the sphere. The obtained result is in agreement with experimental data with accuracy 3-7% for all hadron masses except those of light pseudoscalar mesons
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...
Bogolyubov, N N; Taneri, U; Prykarpatsky, Y A
2009-01-01
Symplectic structures associated to connection forms on certain types of principal fiber bundles are constructed via analysis of reduced geometric structures on fibered manifolds invariant under naturally related symmetry groups. This approach is then applied to nonstandard Hamiltonian analysis of of dynamical systems of Maxwell and Yang-Mills type. A symplectic reduction theory of the classical Maxwell equations is formulated so as to naturally include the Lorentz condition (ensuring the existence of electromagnetic waves), thereby solving the well known Dirac -Fock - Podolsky problem. Symplectically reduced Poissonian structures and the related classical minimal interaction principle for the Yang-Mills equations are also considered. 1.
Nonperturbative aspects of Yang-Mills theory
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
Nonperturbative aspects of Yang-Mills theory
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
The classically perfect fixed point action for SU(3) gauge theory
DeGrand, T; Hasenfratz, A.; Hasenfratz, P.; Niedermayer, F.
1995-01-01
In this paper (the first of a series) we describe the construction of fixed point actions for lattice $SU(3)$ pure gauge theory. Fixed point actions have scale invariant instanton solutions and the spectrum of their quadratic part is exact (they are classical perfect actions). We argue that the fixed point action is even 1--loop quantum perfect, i.e. in its physical predictions there are no $g^2 a^n$ cut--off effects for any $n$. We discuss the construction of fixed point operators and presen...
Convergent Yang-Mills matrix theories
We consider the partition function and correlation functions in the bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. In the supersymmetric case, we show that the partition function converges when D=4, 6 and 10, and that correlation functions of degree kc=2(D-3) are convergent independently of the group. In the bosonic case we show that the partition function is convergent when D≥Dc, and that correlation functions of degree kc are convergent, and calculate Dc and kc for each group, thus extending our previous results for SU(N). As a special case these results establish that the partition function and a set of correlation functions in the IKKT IIB string matrix model are convergent. (author)
Yang-Mills for historians and philosophers
Crease, R. P.
2016-01-01
The phrase “Yang-Mills” can be used (1) to refer to the specific theory proposed by Yang and Mills in 1954; or (2) as shorthand for any non-Abelian gauge theory. The 1954 version, physically speaking, had a famous show-stopping defect in the form of what might be called the “Pauli snag,” or the requirement that, in the Lagrangian for non-Abelian gauge theory the mass term for the gauge field has to be zero. How, then, was it possible for (1) to turn into (2)? What unfolding sequence of events made this transition possible, and what does this evolution say about the nature of theories in physics? The transition between (1) and (2) illustrates what historians and philosophers a century from now might still find instructive and stimulating about the development of Yang-Mills theory.
A model of unified quantum chromodynamics and Yang-Mills gravity
Hsu, Jong-Ping
2011-01-01
Based on a generalized Yang-Mills framework, gravitational and strong interactions can be unified in analogy with the unification in the electroweak theory. By gauging $T(4) \\times [SU(3)]_{color} $ in flat 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 t...
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...
Four dimensional supersymmetric Yang-Mills quantum mechanics with three colors
Ambrozinski, Zbigniew
2014-01-01
The $D=4$ supersymmetric Yang-Mills quantum mechanics with $SU(2)$ and $SU(3)$ gauge symmetry groups is studied. A numerical method to find finite matrix representation of the Hamiltonian is presented in detail. It is used to find spectrum of the theory. In the $SU(2)$ case there are bound states in all channels with definite total number of fermions and angular momentum. For 2,3,4 fermions continuous and discrete spectra coexist in the same range of energies. These results are confirmation of earlier studies. With $SU(3)$ gauge group, the continuous spectrum is moved to sectors with more fermions. Supersymmetry generators are used to identify supermultiplets and determine the level of restoration of supersymmetry for a finite cutoff. For both theories, with $SU(2)$ and $SU(3)$ symmetry, wavefunctions are studied and different behavior of bound and scattering states is observed.
Yang-Mills theory on noncommutative space: does it exist?
Hanada, Masanori
2016-01-01
I revisit a basic question about the noncommutative Yang-Mills theory: if it exists or not, or more precisely, whether a nonperturbative formulation exists. As the most promising approach, I consider a formulation based on matrix models. It is explained that the existence of the noncommutative Yang-Mills theory is closely related to the Eguchi-Kawai equivalence. I argue that supersymmetric noncommutative Yang-Mills theory can be defined straightforwardly. Non-supersymmetric theories, such as QCD and pure bosonic theories, can presumably be defined, by modifying the ultraviolet and infrared behaviors appropriately.
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.
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.
Cosmological coevolution of Yang-Mills fields and perfect fluids
We study the coevolution of Yang-Mills fields and perfect fluids in Bianchi type I universes. We investigate numerically the evolution of the universe and the Yang-Mills fields during the radiation and dust eras of a universe that is almost isotropic. The Yang-Mills field undergoes small amplitude chaotic oscillations, as do the three expansion scale factors which are also displayed by the expansion scale factors of the universe. The results of the numerical simulations are interpreted analytically and compared with past studies of the cosmological evolution of magnetic fields in radiation and dust universes. We find that, whereas magnetic universes are strongly constrained by the microwave background anisotropy, Yang-Mills universes are principally constrained by primordial nucleosynthesis but the bound is comparatively weak with ΩYMrad
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.
Gravity as the square of Yang-Mills?
Borsten, L.; Duff, M. J.
2015-10-01
In these lectures we review how 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. Lecture delivered by M. J. Duff.
Yangian symmetry of smooth Wilson loops in super Yang-Mills theory
Müller, Dennis; Münkler, Hagen; Plefka, Jan; Pollok, Jonas; Zarembo, Konstantin
2013-11-01
We show that appropriately supersymmetrized smooth Maldacena-Wilson loop operators in super Yang-Mills theory are invariant under a Yangian symmetry Y [(2, 2|4)] built upon the manifest superconformal symmetry algebra of the theory. The existence of this hidden symmetry is demonstrated at the one-loop order in the weak coupling limit as well as at leading order in the strong coupling limit employing the classical integrability of the dual AdS5 × S 5 string description. The hidden symmetry generators consist of a canonical non-local second order variational derivative piece acting on the superpath, along with a novel local path dependent contribution. We match the functional form of these Yangian symmetry generators at weak and strong coupling and find evidence for an interpolating function. Our findings represent the smooth counterpart to the Yangian invariance of scattering superamplitudes dual to light-like polygonal super Wilson loops in the super Yang-Mills theory.
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.
Interacting fields of arbitrary spin and N > 4 supersymmetric self-dual Yang-Mills equations
We show that the self-dual Yang-Mills equations afford supersymmetrization to systems of equations invariant under global N-extended super-Poincare transformations for arbitrary values of N, without the limitation (N ≤ 4) applicable to standard non-self-dual Yang-Mills theories. These systems of equations provide novel classically consistent interactions for vector supermultiplets containing fields of spin up to N-2/2. The equations of motion of the component fields of spin greater than 1/2 are interacting variants of the first-order Dirac-Fierz equations for zero rest-mass fields of arbitrary spin. The interactions are governed by conserved currents which are constructed by an iterative procedure. In (arbitrarily extended) chiral superspace, the equations of motion for the (arbitrarily large) self-dual supermultiplet are shown to be completely equivalent to the set of algebraic supercurvature defining the self-dual superconnection. (author). 25 refs
Massive Yang-Mills Fields in Interaction with Gravity
Grigore, D. R.; Scharf, G.
2008-01-01
We determine the most general form of the interaction between the gravitational field and an arbitrary Yang-Mills system of fields (massless and massive). We work in the perturbative quantum framework of the causal approach (of Epstein and Glaser) and use a cohomological definition of gauge invariance for both gauge fields. We also consider the case of massive gravity. We discuss the question whether gravity couples to the unphysical degrees of freedom in the Yang-Mills fields.
Quantum metamorphosis of conformal symmetry in N=4 super Yang-Mills theory
In gauge theories, not all rigid symmetries of the classical action can be maintained manifestly in the quantization procedure, even in the absence of anomalies. If this occurs for an anomaly-free symmetry, the effective action is invariant under a transformation that differs from its classical counterpart by quantum corrections. As shown by Fradkin and Palchik years ago, such a phenomenon occurs for conformal symmetry in quantum Yang-Mills theories with vanishing beta function, such as the N=4 super Yang-Mills theory. More recently, Jevicki et al. demonstrated that the quantum metamorphosis of conformal symmetry sheds light on the nature of the AdS/CFT correspondence. In this paper, we derive the conformal Ward identity for the bosonic sector of the N=4 super Yang-Mills theory using the background field method. We then compute the leading quantum modification of the conformal transformation for a specific Abelian background which is of interest in the context of the AdS/CFT correspondence. In the case of scalar fields, our final result agrees with that of Jevicki et al. The resulting vector and scalar transformations coincide with those which are characteristic of a D3-brane embedded in AdS5xS5. (author)
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.
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...
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...
Vacuum of the quantum Yang-Mills theory and magnetostatics
It is argued that since in asymptotically free Yang-Mills theories the quantum ground state is not controlled by perturbation theory, there is no a priori reason to believe that individual orbits corresponding to minima of the classical action dominate the Euclidean functional integral. To examine and classify the vacua of the quantum gauge theory, the authors propose an effective action in which the gauge field coupling constant g is replaced by the effective coupling g(mean)(t), t = ln (Fsup(a)sub(μγ)2/μ4). The vacua of this model correspond to paramagnetism and perfect paramagnetism, for which the gauge field is Fsup(a)sub(μγ) = 0, and ferromagnetism, for which Fsup(a)sub(μγ)2 = lambda2, i.e. spontaneous magnetization of the vacuum occurs. It is shown that there are no instanton solutions to the quantum effective action. The equations for a point classical source of color spin are solved, and it is shown that the field infrared energy becomes linearly divergent in the limit of spontaneous magnetization. This implies bag formation, and an electric Meissner effect confining the bag contents. (Auth.)
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.
Dzhunushaliev, V D
1997-01-01
The spherically symmetric solution in classical SU(3) Yang - Mills theory is found. It is supposed that such solution describes a classical quark. It is regular in origin and hence the interaction between two quarks is small on the small distance. The obtained solution has the singularity on infinity. It is possible that is the reason why the free quark cannot exist. Evidently, nonlocality of this object leads to the fact that in quantum chromodynamic the difficulties arise connected with investigation of quarks interaction on large distance.
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.
On the Formulation of Yang-Mills Theory with the Gauge Field Valued on the Octonionic Algebra
Restuccia, A
2014-01-01
We consider a formulation of Yang-Mills theory where the gauge field is valued on a non-associative algebra and the gauge transformation is the group of automorphisms of it. We show, under mild assumptions, that the only possible gauge formulation for the octonionic non-associative algebra are the usual $\\mathfrak{su}(2)$ or $\\mathfrak{u}(1)$ Yang-Mills theories. We also discuss the particular cases where the gauge transformations are the subalgebras $\\mathfrak{su}(3)$, $\\mathfrak{su}(2)$, or $\\mathfrak{u}(1)$ of the algebra $\\mathfrak{g}_2$, related to the corresponding subgroups of $G_2$, the group of automorphisms of the octonions.
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. ...
Yang-Mills theory and fermionic path integrals
Fujikawa, Kazuo
2016-01-01
The Yang-Mills gauge field theory, which was proposed 60 years ago, is extremely successful in describing the basic interactions of fundamental particles. The Yang-Mills theory in the course of its developments also stimulated many important field theoretical machinery. In this brief review I discuss the path integral techniques, in particular, the fermionic path integrals which were developed together with the successful applications of quantized Yang-Mills field theory. I start with the Faddeev-Popov path integral formula with emphasis on the treatment of fermionic ghosts as an application of Grassmann numbers. I then discuss the ordinary fermionic path integrals and the general treatment of quantum anomalies. The contents of this review are mostly pedagogical except for a recent analysis of path integral bosonization.
New perspectives on Yang-Mills theories with sixteen supersymmetries
We describe various approaches that give matrix descriptions of compactified NS five-branes. As a result, we obtain matrix models for Yang-Mills theories with sixteen supersymmetries in dimensions 2,3,4 and 5. The equivalence of the various approaches relates the Coulomb branch of certain gauge theories to the moduli space of instantons on T4. We also obtain an equivalence between certain six-dimensional string theories. Further, we discuss how various perturbative and non-perturbative features of these Yang-Mills theories appear in their matrix formulations. The matrix model for four-dimensional Yang-Mills is manifestly S-dual. In this case, we describe how electric fluxes, magnetic fluxes and the interaction between vector particles are realized in the matrix model. (author)
New Perspectives on Yang-Mills Theories With Sixteen Supersymmetries
Ganor, O J; Ganor, Ori J.; Sethi, Savdeep
1998-01-01
We describe various approaches that give matrix descriptions of compactified NS five-branes. As a result, we obtain matrix models for Yang-Mills theories with sixteen supersymmetries in dimensions $2,3,4$ and $5$. The equivalence of the various approaches relates the Coulomb branch of certain gauge theories to the moduli space of instantons on $T^4$. We also obtain an equivalence between certain six-dimensional string theories. Further, we discuss how various perturbative and non-perturbative features of these Yang-Mills theories appear in their matrix formulations. The matrix model for four-dimensional Yang-Mills is manifestly S-dual. In this case, we describe how electric fluxes, magnetic fluxes and the interaction between vector particles are realized in the matrix model.
Supertwistor space for 6D maximal super Yang-Mills
Dennen, Tristan; Siegel, Warren
2009-01-01
6D maximal super Yang-Mills on-shell amplitudes are formulated in superspace using 6 dimensional twistors. The 3,4,5-point tree amplitudes are obtained by supersymmetrizing their bosonic counterparts and confirmed through the BCFW construction. In contrast to 4D this superspace is non-chiral, reflecting the fact that one cannot differentiate MHV from $\\bar{{\\rm MHV}}$ in 6D. Combined with unitarity methods, this superspace should be useful for the study of multi-loop D dimensional maximal super Yang-Mills and gravity amplitudes. Furthermore, the non-chiral nature gives a natural framework for an off-shell construction. We show this by matching our result with off-shell D=4 N=4 super Yang-Mills amplitudes, expressed in projective superspace.
Gauging quantum groups: Yang-Baxter joining Yang-Mills
Wu, Yong-Shi
2016-02-01
This review is an expansion of my talk at the conference on Sixty Years of Yang-Mills Theory. I review and explain the line of thoughts that lead to a recent joint work with Hu and Geer [Hu et al., arXiv:1502.03433] on the construction, exact solutions and ubiquitous properties of a class of quantum group gauge models on a honey-comb lattice. Conceptually the construction achieves a synthesis of the ideas of Yang-Baxter equations with those of Yang-Mills theory. Physically the models describe topological anyonic states in 2D systems.
Super Yang-Mills theories coupled to supergravity
Supersymmetric Yang-Mills theories coupled to supergravity are analyzed by using the tangent bundle to a supergroup manifold as geometrical framework. The factorization condition imposed on these theories is considered from this point of view. The so-called H-gauge transformation for both, the super Yang-Mills and supergravity one-forms gauge fields are obtained as a consequence of a change of trivialization in the corresponding coset manifold. The authors point out the existence of factorized solutions not diffeomorphically equivalent for the set of pseudo-connections one-forms or gauge fields
Gauge covariance approach to massive Yang-Mills fields
By observation of the gauge structure introduced in the SU(2) Higgs-Kibble model on the basis of a massless Yang-Mills field theory with gauge covariance, another possible formalism of a massive Yang-Mills field theory with gauge covariance is presented. The formalism exhibits a close analogy to the case of massive abelian-gauge fields. In contrast with the case of the Higgs-Kibble model, no dipole-ghost field is introduced in the formalism. Supplementary conditions for physical states are given in a consistent way. (author)
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.
Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with $G_2$-structure
Haupt, Alexander S
2015-01-01
We study $\\mathfrak{g}$-valued Yang-Mills fields on cylinders $Z(G/H)=\\mathbb{R} \\times G/H$, where G/H is a compact seven-dimensional coset space with $G_2$-structure, $\\mathfrak{g}$ is the Lie algebra of G, and Z(G/H) inherits a Spin(7)-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on Z(G/H) reduces to Newtonian mechanics of a point particle moving in $\\mathbb{R}^n$ under the influence of some quartic potential and possibly additional constraints. The kinematics and dynamics depends on the chosen coset space. We consider in detail three coset spaces with nearly parallel $G_2$-structure and four coset spaces with SU(3)-structure. For each case, we analyze the critical points of the potential and present a range of finite-energy solutions. We also study a higher-dimensional analog of the instanton equation. Its solutions yield G-invariant Spin(7)-instanton configurations on Z(G/H), which are special cases of Yang-Mills configurations with torsion.
A new quantum representation for canonical gravity and SU(2) Yang-Mills theory
Starting from Rovelli-Smolin's infinite-dimensional graded Poisson-bracket algebra of loop variables, we propose a new way of constructing a corresponding quantum representation. After eliminating certain quadratic constraints, we 'integrate' an infinite-dimensional subalgebra of loop variables, using a formal group law expansion. With the help of techniques from the representation theory of semidirect-product groups, we find an exact quantum representation of the full classical Poisson-bracket algebra of loop variables, without any higher-order correction terms. This opens new ways of tackling the quantum dynamics for both canonical gravity and Yang-Mills theory. (orig.)
Yang-Mills theory as bimetrical gravity: Polarization effects and finite-energy gluon clusters
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.
Yang-Mills theory as bimetrical gravity: Polarization effects and finite-energy gluon clusters
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
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.
Wilson loop in N=4 super Yang-Mills theory
Förste, S.; Ghoshal, D.; Theisen, S.
2000-01-01
The Wilson loop in N = 4 super Yang-Mills theory admits a dual description as a macroscopic string configuration in the adS/CFT correspondence. We discuss the correction to the quark anti-quark potential arising from the fluctuations of the superstring.
Path integral quantization of Yang-Mills theory
Muslih, Sami I.
2000-01-01
Path integral formulation based on the canonical method is discussed. Path integral for Yang-Mills theory is obtained by this procedure. It is shown that gauge fixing which is essential procedure to quantize singular systems by Faddeev's and Popov's method is not necessary if the canonical path integral formulation is used.
On the infrared behaviour of Yang-Mills Greens functions
Making certain assumptions (valid to any finite order of perturbation theory), it is shown that non-perturbatively pure Yang-Mills Greens functions are power behaved in the momenta in a limit related to the infrared limit. It is also shown that the fundamental vertices have a more singular behaviour than indicated by perturbation theory. (Auth.)
Quantum theory of massive Yang-Mills fields, 2
By generalization of a basic formulation presented in a preceding part of the same series, a massive Yang-Mills field theory with gauge covariance is formulated within one-parameter invariant gauge families. It is consequently concluded that all cases of different gauges belonging to the same gauge family are equivalent to one another in a rigorous field-theoretical sense. (author)
Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
Chiodaroli, Marco; Johansson, Henrik; Roiban, Radu
2015-01-01
Color/kinematics duality and the double-copy construction have proved to be systematic tools for gaining new insight into gravitational theories. Extending our earlier work, in this paper we introduce new double-copy constructions for large classes of spontaneously-broken Yang-Mills-Einstein theories with adjoint Higgs fields. One gauge-theory copy entering the construction is a spontaneously-broken (super-)Yang-Mills theory, while the other copy is a bosonic Yang-Mills-scalar theory with trilinear scalar interactions that display an explicitly-broken global symmetry. We show that the kinematic numerators of these gauge theories can be made to obey color/kinematics duality by exhibiting particular additional Lie-algebraic relations. We discuss in detail explicit examples with N=2 supersymmetry, focusing on Yang-Mills-Einstein supergravity theories belonging to the generic Jordan family in four and five dimensions, and identify the map between the supergravity and double-copy fields and parameters. We also bri...
Einstein-Yang-Mills theory : I. Asymptotic symmetries
Barnich, Glenn
2013-01-01
Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in three dimensions but also in the four dimensional asymptotically flat case.
Numerical investigations of supersymmetric Yang-Mills quantum mechanics with 4 supercharges
Ambrozinski, Zbigniew [Krakow Univ. (Poland). Inst. of Physics; Korcyl, Piotr [Krakow Univ. (Poland). Inst. of Physics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2014-12-15
We report on our non-perturbative investigations of supersymmetric Yang-Mills quantum mechanics with 4 supercharges. We employ two independent numerical methods. First of them is the cut Fock space method whose numerical implementation was recently generalized to include the SU(N) gauge group. It allowed us to calculate for the first time the spectrum of the model with SU(3) symmetry in all fermionic sectors. Independently, we implemented the Rational Hybrid Monte Carlo algorithm and reproduced the accessible part of the low-energy spectrum of the model with SU(2) gauge symmetry. We argue that by simulating at imaginary chemical potential one can get access to observables defined in sectors of Hilbert space with a given quark number.
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.
A perturbative description of the deconfinement transition in Yang-Mills theories
Serreau, Julien
2015-01-01
We investigate the deconfinement transition of static quarks in SU(N) Yang-Mills theories using a perturbative approach based on a massive extension of the Landau-DeWitt gauge-fixed action, where the gluon mass term is related to the issue of Gribov ambiguities. A leading-order, one-loop calculation of the effective potential for the Polyakov loop produces a deconfinement transition of second order for the SU(2) theory and of first order for SU(3) with transition temperatures in qualitative agreement with known values. We also report on the results of a two-loop calculation of the critical temperature and of thermodynamical quantities in the SU(2) case.
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.
Monopole dynamics and BPS dyons in N=2 super-Yang-Mills theories
We determine the low-energy dynamics of monopoles in pure N=2 Yang-Mills theories for points in the vacuum moduli space where the two Higgs fields are not aligned. The dynamics is governed by a supersymmetric quantum mechanics with potential terms and four real supercharges. The corresponding superalgebra contains a central charge but nevertheless supersymmetric states preserve all four supercharges. The central charge depends on the sign of the electric charges and consequently so does the BPS spectrum. We focus on the SU(3) case where certain BPS states are realized as zero modes of a Dirac operator on Taub-NUT space twisted by the triholomorphic Killing vector field. We show that the BPS spectrum includes hypermultiplets that are consistent with the strong- and weak-coupling behavior of Seiberg-Witten theory. (c) 2000 The American Physical Society
Based on analysis of reduced geometric structures on fibered manifolds, invariant under action of a certain symmetry group, we construct the symplectic structures associated with connection forms on suitable principal fiber bundles. The application to the non-standard Hamiltonian analysis of the Maxwell and Yang-Mills type dynamical systems is presented. A symplectic reduction theory of the classical Maxwell electromagnetic field equations is formulated, the important Lorentz condition, ensuring the existence of electromagnetic waves, is naturally included into the Hamiltonian picture, thereby solving the well known Dirac, Fock and Podolsky problem. The symplectically reduced Poissonian structures and the related classical minimal interaction principle, concerning the Yang-Mills type equations, are considered. (author)
Gale, Charles; Jeon, Sangyong; Schenke, Bjoern; Tribedy, Prithwish; Venugopalan, Raju
2012-01-01
Anisotropic flow coefficients v_1-v_5 in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The glasma dynamics, as realized in the IP-Glasma model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic sub-nucleon scale color charge fluctuations; the pre-equilibrium fl...
The self-dual Yang-Mills equations play a central role in the study of integrable systems. In this paper we develop a formalism for deriving a four dimensional integrable hierarchy of commuting nonlinear flows containing the self-dual Yang-Mills flow as the first member. We show that upon appropriate reduction and suitable choice of gauge group it produces virtually all well known hierarchies of soliton equations in 1 + 1 and 2 + 1 dimensions and can be considered as a ''universal'' integrable hierarchy. Prototypical examples of reductions to classical soliton equations are presented and related issues such as recursion operators, symmetries, and conservation laws are discussed. (orig.)
Properties of non-BPS SU(3) monopoles
This paper is concerned with magnetic monopole solutions of SU(3) Yang-Mills-Higgs system beyond the Bogomol'nyi-Prasad-Sommerfield limit. The different SU(2) embeddings, which correspond to the fundamental monopoles, as well the embedding along composite root are studied. The interaction of two different fundamental monopoles is considered. Dissolution of a single fundamental non-BPS SU(3) monopole in the limit of the minimal symmetry breaking is analyzed. (author)
(Super)Yang-Mills at Finite Heavy-Quark Density
Faedo, Anton F; Mateos, David; Tarrio, Javier
2014-01-01
We study the gravitational duals of $d$-dimensional Yang-Mills theories with $d\\leq 6$ in the presence of an ${\\cal O} (N^2)$ density of heavy quarks, with $N$ the number of colors. For concreteness we focus on maximally supersymmetric Yang-Mills, but our results apply to a larger class of theories with or without supersymmetry. The gravitational solutions describe renormalization group flows towards infrared scaling geometries characterized by fixed dynamical and hyperscaling-violating exponents. The special case $d=5$ yields an $AdS_3 \\times \\mathbb{R}^4 \\times S^4$ geometry upon uplifting to M-theory. We discuss the multitude of physical scales that separate different dynamical regimes along the flows, as well as the validity of the supergravity description. We also present exact black brane solutions that encode the low-temperature thermodynamics.
Yang-Mills fields which are not self-dual
The purpose of this paper is to prove the existence of a new family of non-self-dual finite-energy solutions to the Yang-Mills equations on Euclidean four-space, with SU(2) as a gauge group. The approach is that of 'equivariant geometry': Attention is restricted to a special class of fields, those that satisfy a certain kind of rotational symmetry, for which it is proved that (1) a solution to the Yang-Mills equations exists among them; and (2) no solution to the self-duality equations exists among them. The first assertion is proved by an application of the direct method of the calculus of variations (existence and regularity of minimizers), and the second assertion by studying the symmetry properties of the linearized-self-duality equations. The same technique yields a new family of non-self-dual solutions on the complex projective plane. (orig.)
Non self-dual Yang-Mills fields
The purpose of the thesis is to prove the existence of a new family of non self-dual finite-energy solutions to the Yang-Mills equations on Euclidean four-space, with SU(2) as a gauge group. The approach is that of equivalent geometry: attention is restricted to a special class of fields, those that satisfy a certain kind of rotational symmetry which it is proved that (1) a solution to the Yang-Mills equations exists for among them, and (2) no solution to the self-duality equations exists among them. The first assertion is proved by an application of the direct method of the calculus of variations (existence and regularity of minimizers), and the second assertion by showing that the self-duality equations, linearized at a symmetric self-dual solution, cannot possess the required symmetry
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...
Saddle point solutions in Yang-Mills-dilaton theory
Bizón, P
1993-01-01
The coupling of a dilaton to the $SU(2)$-Yang-Mills field leads to interesting non-perturbative static spherically symmetric solutions which are studied by mixed analitical and numerical methods. In the abelian sector of the theory there are finite-energy magnetic and electric monopole solutions which saturate the Bogomol'nyi bound. In the nonabelian sector there exist a countable family of globally regular solutions which are purely magnetic but have zero Yang-Mills magnetic charge. Their discrete spectrum of energies is bounded from above by the energy of the abelian magnetic monopole with unit magnetic charge. The stability analysis demonstrates that the solutions are saddle points of the energy functional with increasing number of unstable modes. The existence and instability of these solutions are "explained" by the Morse-theory argument recently proposed by Sudarsky and Wald.
Intrinsic moment of inertia of membranes as bounds for the mass gap of Yang-Mills theories
We obtain the precise condition on the potentials of Yang-Mills theories in 0+1 dimensions and D0-brane quantum mechanics ensuring the discreteness of the spectrum. It is given in terms of a moment of inertia of the membrane. From it we obtain a bound for the mass gap of any D+1 Yang-Mills theory in the slow-mode regime. In particular we analyze the physical case D=3. The quantum mechanical behavior of the theories, concerning its spectrum, is determined by harmonic oscillators with frequencies given by the inertial tensor of the membrane. We find a class of quantum mechanic potential polynomials of any degree, with classical instabilities that at quantum level have purely discrete spectrum
Background field dependence from the Slavnov-Taylor identity in (non-perturbative) Yang-Mills theory
Quadri, Andrea
2011-01-01
We show that in Yang-Mills theory the Slavnov-Taylor (ST) identity, extended in the presence of a background gauge connection, allows to fix in a unique way the dependence of the vertex functional on the background, once the 1-PI amplitudes at zero background are known. The reconstruction of the background dependence is carried out by purely algebraic techniques and therefore can be applied in a non-perturbative scheme (e.g. on the lattice or in the Schwinger-Dyson approach), provided that the latter preserves the ST identity. The field-antifield redefinition, which replaces the classical background-quantum splitting when quantum corrections are taken into account, is considered on the example of an instanton background in SU(2) Yang-Mills theory.
Formation and decay of Einstein-Yang-Mills black holes
Rinne, O.
2014-01-01
We study various aspects of black holes and gravitational collapse in Einstein-Yang-Mills theory under the assumption of spherical symmetry. Numerical evolution on hyperboloidal surfaces extending to future null infinity is used. We begin by constructing colored and Reissner-Nordstrom black holes on surfaces of constant mean curvature and analyze their perturbations. These linearly perturbed black holes are then evolved into the nonlinear regime and the masses of the final Schwarzschild black...
Towards a unification of gravity and Yang-Mills theory
Chakraborty, Subenoy; Peldan, Peter
1994-01-01
We introduce a gauge and diffeomorphism invariant theory on Yang-Mills phase space. The theory is well defined for an arbitrary gauge group with an invariant bilinear form, it contains only first class constraints, and the spacetime metric has a simple form in terms of the phase space variables. With gauge group $SO(3,C)$, the theory equals the Ashtekar formulation of gravity with a cosmological constant. For Lorentzian signature, the theory is complex, and we have not found any good reality ...
Local BRST cohomology in Einstein-Yang-Mills theory
We analyse in detail the local BRST cohomology in Einstein-Yang-Mills theory using the antifield formalism. We do not restrict the Lagrangian to be the sum of the standard Hilbert and Yang-Mills Lagrangians, but allow for more general diffeomorphism and gauge invariant (normal) actions. The analysis is carried out in spacetimes with IRn topology, for all spacetime dimensions strictly larger than 2 and for all ghost numbers. This covers the classification of all candidate anomalies, of all consistent deformations of the action, as well as the computation of the (equivariant) characteristic cohomology, i.e. the cohomology of the spacetime exterior derivative in the space of (gauge invariant) local differential forms modulo forms that vanish on-shell. We show in particular that for a semi-simple Yang-Mills gauge group the antifield dependence can be entirely removed both from the consistent deformations of the Lagrangian and from the candidate anomalies. Thus, the allowed deformations of the action necessarily preserve the gauge structure, while the only candidate anomalies are those provided by previous works not dealing with antifields, and by ''topological'' candidate anomalies related to the non-triviality of the manifold of the gravitational variables. This result no longer holds in presence of abelian factors where new candidate anomalies and deformations of the action can be constructed out of the conserved Noether currents (if any). The Noether currents themselves are shown to be covariantizable, i.e. they can be chosen to be invariant under local Lorentz and Yang-Mills transformations and covariant under diffeomorphisms, with a few exceptions discussed as well. (orig.)
Equivalence of twistor prescriptions for super Yang-Mills
Gukov, S; Neitzke, A; Gukov, Sergei; Motl, Lubos; Neitzke, Andrew
2004-01-01
There is evidence that one can compute tree level super Yang-Mills amplitudes using either connected or completely disconnected curves in twistor space. We argue that the two computations are equivalent, by showing that they can both be reduced to the same integral over a moduli space of singular curves, if the integration contours are chosen in a specific way. We also formulate a class of new "intermediate" prescriptions to calculate the same amplitudes.
Equivalence of twistor prescriptions for super Yang-Mills
Gukov , Sergei; Motl, Lubos; Neitzke, Andrew
2007-01-01
There is evidence that one can compute tree-level super Yang-Mills amplitudes using either connected or completely disconnected curves in twistor space. We give a partial explanation of the equivalence between the two computations, by showing that they could both be reduced to the same integral over a moduli space of singular curves, subject to some assumptions about the choices of integration contours. We also formulate a class of new “intermediate” prescriptions to calculate the same amplit...
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.
Three dimensional lattice gravity as supersymmetric Yang-Mills theory
Catterall, Simon
2010-01-01
We argue that a certain twisted supersymmetric Yang-Mills theory in three dimensions with gauge group SU(2) possesses a set of topological observables whose expectation values can be computed in a related Chern Simons theory. This Chern Simons theory has been proposed as a definition of three dimensional Euclidean quantum gravity. Since the YM theory admits a discretization which preserves the values of topological observables we conjecture that it can be used as a non-perturbative definition...
String theory as a generalised Yang-Mills theory
We summarise the result of a recent investigation which shows that the standard theory of interacting open bosonic strings can be reformulated as a generalised Yang-Mills theory in which (i) the string co-ordinates themselves function as the internal gauge degrees of freedom, and (ii) parallel transport is based on the nonabelian conformal group in place of the usual space-time translation groups. (author)
Supersymmetry algebra in super Yang-Mills theories
Yokoyama, Shuichi
2015-01-01
We compute supersymmetry algebra (superalgebra) in supersymmetric Yang-Mills theories (SYM) consisting of a vector multiplet including fermionic contribution in six dimensions. We show that the contribution of fermion is given by boundary terms. From six dimensional results we determine superalgebras of five and four dimensional SYM by dimensional reduction. In five dimensional superalgebra the Kaluza-Klein momentum and the instanton particle charge are not the same but algebraically indistin...
Dirac equations for generalised Yang-Mills systems
We present Dirac equations in 4p dimensions for the generalised Yang-Mills (GYM) theories introduced earlier. These Dirac equations are related to the self-duality equations of the GYM and are checked to be elliptic in a ''BPST'' background. In this background these Dirac equations are integrated exactly. The possibility of imposing supersymmetry in the GYM-Dirac system is investigated, with negative results. (orig.)
Dirac equations for generalised Yang-Mills systems
We present Dirac equations in 4p dimensions for the generalised Yang-Mills (GYM) theories introduced earlier. These Dirac equations are related to the self-duality equations of the GYM and are checked to be elliptic in a 'BPST' background. In this background these Dirac equations are integrated exactly. The possibility of imposing supersymmetry in the GYM-Dirac system is investigated, with negative results. (orig.)
Matrix Strings in Two-dimensional Yang-Mills Theory
Kogan, Ian I; Szabo, Richard J.
1997-01-01
We describe the structure of string vacuum states in the supersymmetric matrix model for M theory compactified on a circle in the large-N limit. We show that the theory admits topological instanton field configurations which at short-distance scales reduce to ordinary Yang-Mills instantons that interpolate between degenerate vacua of the theory. We show that there exists further classes of hadronic strings associated with the D-string super-fields. We discuss the relationships between these n...
Monopoles and Strings in Yang-Mills Theories
Langfeld, K.; Reinhardt, H.; Quandt, M.
1996-01-01
Yang-Mills theory is studied in a variant of 't Hooft's maximal Abelian gauge. In this gauge magnetic monopoles arise in the Abelian magnetic field. We show, however, that the full (non-Abelian) magnetic field does not possess any monopoles, but rather strings of magnetic fluxes. We argue that these strings are the relevant infrared degrees of freedom. The properties of the magnetic strings which arise from a dilute instanton gas are investigated for the gauge group SU(2).
Slavnov determinants, Yang-Mills structure constants, and discrete KP
Foda, O.; Wheeler, M.
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.
Quantum theory of massive Yang-Mills fields, 3
The renormalizable structure of a massive Yang-Mills field theory proposed previously is revealed in view of nonpolynomial Lagrangian theories. Analytic properties of several relevant superpropagators are elucidated in the sense of distributions. It is shown that these superpropagators exhibit a strong infinity-suppression mechanism making the theory renormalizable. There appears a divergence-free model as a subcase of the present theory. (authors)
Biquaternion Construction of SL(2,C) Yang-Mills Instantons
Lee, Jen-Chi
2015-01-01
We use biquaternion to construct SL(2,C) ADHM Yang-Mills instantons. The solutions contain 16k-6 moduli parameters for the kth homotopy class, and include as a subset the SL(2,C) (M,N) instanton solutions constructed previously. In constrast to the SU(2) instantons, the SL(2,C) instantons inhereit jumping lines or singulariries which are not gauge artifacts and can not be gauged away.
Local BRST cohomology in Einstein-Yang-Mills theory
Barnich, G. [Universite Libre de Bruxelles (Belgium). Faculte des Sciences; Brandt, F. [Leuven Univ. (Belgium). Inst. voor Theoretische Fysica; Henneaux, M. [Universite Libre de Bruxelles (Belgium). Faculte des Sciences
1995-11-20
We analyse in detail the local BRST cohomology in Einstein-Yang-Mills theory using the antifield formalism. We do not restrict the Lagrangian to be the sum of the standard Hilbert and Yang-Mills Lagrangians, but allow for more general diffeomorphism and gauge invariant (normal) actions. The analysis is carried out in spacetimes with IR{sup n} topology, for all spacetime dimensions strictly larger than 2 and for all ghost numbers. This covers the classification of all candidate anomalies, of all consistent deformations of the action, as well as the computation of the (equivariant) characteristic cohomology, i.e. the cohomology of the spacetime exterior derivative in the space of (gauge invariant) local differential forms modulo forms that vanish on-shell. We show in particular that for a semi-simple Yang-Mills gauge group the antifield dependence can be entirely removed both from the consistent deformations of the Lagrangian and from the candidate anomalies. Thus, the allowed deformations of the action necessarily preserve the gauge structure, while the only candidate anomalies are those provided by previous works not dealing with antifields, and by ``topological`` candidate anomalies related to the non-triviality of the manifold of the gravitational variables. This result no longer holds in presence of abelian factors where new candidate anomalies and deformations of the action can be constructed out of the conserved Noether currents (if any). The Noether currents themselves are shown to be covariantizable, i.e. they can be chosen to be invariant under local Lorentz and Yang-Mills transformations and covariant under diffeomorphisms, with a few exceptions discussed as well. (orig.).
Yang-Mills Theories as Deformations of Massive Integrable Models
Cubero, Axel Cortés
2014-01-01
Yang Mills theory in 2+1 dimensions can be expressed as an array of coupled (1+1)-dimensional principal chiral sigma models. The $SU(N)\\times SU(N)$ principal chiral sigma model in 1+1 dimensions is integrable, asymptotically free and has massive excitations. We calculate all the form factors and two-point correlation functions of the Noether current and energy-momentum tensor, in 't~Hooft's large-$N$ limit (some form factors can be found even at finite $N$). We use these new form factors to calculate physical quantities in (2+1)-dimensional Yang-Mills theory, generalizing previous $SU(2)$ results from Orland to $SU(N)$. The anisotropic gauge theory is related to standard isotropic one by a Wilsonian renormalization group with ellipsoidal cutoffs in momentum. We calculate quantum corrections to the effective action of QED and QCD, as the theory flows from isotropic to anisotropic. The exact principal chiral sigma model S-matrix is also used to examine the spectrum of (1+1)-dimensional massive Yang Mills theor...
New Relations for Einstein-Yang-Mills Amplitudes
Stieberger, Stephan
2016-01-01
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.
Quantum Chromodynamics -- The Perfect Yang-Mills Gauge Field Theory
Gross, David
David Gross: My talk today is about the most beautiful of all Yang-Mills Theories (non-Abelian gauge theories), the theory of the strong nuclear interactions, Quantum Chromodynamics, QCD. We are celebrating 60 years of the publication of a remarkable paper which introduced the concept of non-Abelian local gauge symmetries, now called the Yang-Mills theory, to physics. In the introduction to this paper it is noted that the usual principle of isotopic spin symmetry is not consistent with the concept of localized fields. This sentence has drawn attention over the years because the usual principle of isotopic spin symmetry is consistent, it is just not satisfactory. The authors, Yang and Mills, introduced a more satisfactory notion of local symmetry which did not require one to rotate (in isotopic spin space) the whole universe at once to achieve the symmetry transformation. Global symmetries are thus are similar to `action at a distance', whereas Yang-Mills theory is manifestly local...
Conrady, F
2006-01-01
In this series of three papers, we generalize the derivation of photons and monopoles by Polyakov and Banks, Myerson and Kogut, to obtain gluon-monpole representations of SU(2) lattice gauge theory. The papers take three different representations as their starting points: the representation as a BF Yang-Mills theory, the spin foam representation and the plaquette representation. The subsequent derivations are based on semiclassical expansions. In this first article, we cast d-dimensional SU(2) lattice gauge theory in the form of a lattice BF Yang-Mills theory. In several steps, the expectation value of a Wilson loop is transformed into a path integral over a gluon field and monopole-like degrees of freedom. The action contains the tree-level Coulomb interaction and a nonlinear coupling between gluons, monopoles and current. At the end, we compare the results from all three papers.
Griguolo, L; Szabó, R J; Tanzini, A; Griguolo, Luca; Seminara, Domenico; Szabo, Richard J.; Tanzini, Alessandro
2006-01-01
We study the relationship between instanton counting in N=4 Yang-Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang-Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-dimensional Yang-Mills theory and Chern-Simons theory on generic Lens spaces, and use it to show that the correct instanton counting is only reproduced when the Chern-Simons contributions are treated as non-dynamical boundary conditions in the D4-brane gauge theory. We also use this correspondence to discuss the counting of instantons on higher genus ruled Riemann surfaces.
Path integral measure factorization in path integrals for diffusion of Yang--Mills fields
Storchak, S. N.
2007-01-01
Factorization of the (formal) path integral measure in a Wiener path integrals for Yang--Mills diffusion is studied. Using the nonlinear filtering stochastic differential equation, we perform the transformation of the path integral defined on a total space of the Yang--Mills principal fiber bundle and come to the reduced path integral on a Coulomb gauge surface. Integral relation between the path integral representing the "quantum" evolution given on the original manifold of Yang--Mills field...
Quantum cosmological Friedman models with a massive Yang-Mills field
We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the matter field is provided by a massive Yang-Mills field. The resolution is achieved by first solving the free eigenvalue problem for the gravitational field and then the constrained eigenvalue problem for the Yang-Mills field. In the latter case, the mass of the Yang-Mills field assumes the role of the eigenvalue.
Relations for Einstein-Yang-Mills amplitudes from the CHY representation
de la Cruz, Leonardo; Weinzierl, Stefan
2016-01-01
We show that a recently discovered relation, which expresses tree-level single trace Einstein-Yang-Mills amplitudes with one graviton and $(n-1)$ gauge bosons as a linear combination of pure Yang-Mills tree amplitudes with $n$ gauge bosons, can be derived from the CHY representation. In addition we show that there is a generalisation, which expresses tree-level single trace Einstein-Yang-Mills amplitudes with $r$ gravitons and $(n-r)$ gauge bosons as a linear combination of pure Yang-Mills tree amplitudes with $n$ gauge bosons. We present a general formula for this case.
Yang-Mills Theory In, Beyond, and Behind Observed Reality
Wilczek, Frank
2004-01-01
The character of jets is dominated by the influence of intrinsically nonabelian gauge dynamics. These proven insights into fundamental physics ramify in many directions, and are far from being exhausted. I will discuss three rewarding explorations from my own experience, whose point of departure is the hard Yang-Mills interaction, and whose end is not yet in sight. Given an insight so profound and fruitful as Yang and Mills brought us, it is in order to try to consider its broadest implications, which I attempt at the end.
Yang-Mills theories at high energy accelerators
Sterman, George
2016-03-01
I will 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.
Yang-Mills Spectrum with an Arbitrary Simple Gauge Algebra
The mass spectrum of pure Yang-Mills theory in 3 + 1 dimensions is discussed for an arbitrary simple gauge algebra within a quasi gluon picture. The general structure of the low-lying gluelump and glueball spectrum is shown to be common to all algebras, excepted the lightest C = - glueballs that only exist when the gauge algebra is Ar≥2. The shape of the static energy between adjoint sources is also discussed assuming the Casimir scaling hypothesis and finally, the obtained results are shown to be consistent with existing lattice data in the large-N limit of an su(N) gauge algebra. (author)
N=1 supersymmetric Yang-Mills theory on the lattice
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.
The thermal β-function in Yang-Mills theory
Previous calculations of the thermal β function in a hot Yang-Mills gas at the one-loop level have exposed problems with the gauge dependence and with the sign, which is opposite to what one would expect for asymptotic freedom. It is shown that inclusion of higher-loop effects through a static Braaten-Pisarski resummation is necessary to consistently obtain the leading term, but alters the results only quantitatively. The sign, in particular, remains the same. It is also explored, by a crude parametrization, the effects a (non-perturbative) magnetic mass may have on these results. (author). 30 refs., 2 figs
On the Holography of Free Yang-Mills
Bae, Jin-Beom; Lal, Shailesh
2016-01-01
We study the AdS$_5$/CFT$_4$ duality where the boundary CFT is free Yang-Mills theory with gauge group SU(N). At the planar level we use the spectrum and correlation functions of the boundary theory to explicate features of the bulk theory. Further, by computing the one-loop partition function of the bulk theory using the methods of arXiv:1603.05387, we argue that the bulk coupling constant should be shifted to $N^2$ from $N^2-1$. Similar conclusions are reached by studying the dualities in thermal AdS$_5$ with $S^1\\times S^3$ boundary.
Supersymmetry Algebra in Super Yang-Mills Theories
Yokoyama, Shuichi
2015-01-01
We compute supersymmetry algebra (superalgebra) in supersymmetric Yang-Mills theories (SYM) consisting of a vector multiplet including fermionic contribution in six dimensions. We show that the contribution of fermion is given by boundary terms. From six dimensional results we determine superalgebras of five and four dimensional SYM by dimensional reduction. In five dimensional superalgebra the Kaluza-Klein momentum and the instanton particle charge are not the same but algebraically indistinguishable. We also extend this calculation including a hyper multiplet and for maximally SYM. We derive extended supersymmetry algebras in those four dimensional SYM with the holomorphic coupling constant given in hep-th/9408099.
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.
Permeability of the interacting Yang-Mills instanton gas
The permeability μ of the interacting Yang-Mills instanton gas from the partition function, treating the dipole-like interaction by a functional method is calculated. The approach is based on the semiclassical approximation. Following Callan, Dashen, Gross the expression for μ to the discussion of the bag-vacuum phase transition and to the interpolation of the β-function from weak to strong coupling is applied. The results presented in different renormalization schemes confirm the existence of the first order transition
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 ac...
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.
N=1 Supersymmetric Yang-Mills theory on the lattice
The N=1 Super Yang-Mills theory is the supersymmetric extension of the pure gauge sector of QCD. The theory describes the strong interactions between gluons and gluinos, the gauge bosons and their fermion superpartners respectively. Effective models have been proposed to describe the bound spectrum of the theory. The expectation value of many observables can be computed exactly, providing important predictions that can be eventually extended to QCD. Lattice investigations can provide a closer insight to these results, but unfortunately a finite lattice spacing breaks SUSY explicitly. Recent results demonstrate the restoration of SUSY in the continuum limit and will be presented during the talk.
Extremal curves in 2+1-dimensional Yang-Mills theory
Orland, P; Orland, Peter; Semenoff, Gordon W.
2000-01-01
We examine the structure of the potential energy of 2+1-dimensional Yang-Mills theory on a torus with gauge group SU(2). We use a standard definition of distance on the space of gauge orbits. The curves of extremal potential energy in orbit space satisfy a certain partial differential equation. We argue that the energy spectrum is gapped because the extremal curves are of finite length. Though classical gluon waves satisfy our differential equation, they are not extremal curves. We construct examples of extremal curves and find how the length of these curves depends on the dimensions of the torus. The intersections with the Gribov horizon are determined explicitly. The results are discussed in the context of Feynman's ideas about the origin of the mass gap.
Higher spin gravitational couplings: Ghosts in the Yang-Mills detour complex
Gravitational interactions of higher spin fields are generically plagued by inconsistencies. There exists however, a simple framework that couples higher spins to a broad class of gravitational backgrounds (including Ricci flat and Einstein) consistently at the classical level. The model is the simplest example of a Yang-Mills detour complex and has broad mathematical applications, especially to conformal geometry. Even the simplest version of the theory, which couples gravitons, vectors and scalar fields in a flat background is rather rich, providing an explicit setting for detailed analysis of ghost excitations. Its asymptotic scattering states consist of a physical massless graviton, scalar, and massive vector along with a degenerate pair of zero norm photon excitations. Coherent states of the unstable sector do have positive norms, but their evolution is no longer unitary and amplitudes grow with time. The class of models proposed is extremely general and of considerable interest for ghost condensation and invariant theory
Impressions on the algebraic renormalization of the N=2 supersymmetric Yang-Mills field theories
We investigate the ultraviolet behavior of a class of N=2 supersymmetric Yang-Mills field theories which are built up in terms of N=1 superfields. Our results are obtained within the framework of the so-called algebraic renormalization technique of Becchi, Rouet, and Stora. Thanks to the algebraic renormalization setup, we have been able to write down the most general local counterterm functional which is compatible with all the classical symmetries of the model in the N=1 superspace. As a consequence of having parametrized both physical and unphysical renormalizations of the theory, we have also been able to present its corresponding Callan-Symanzik equation. In particular, due to the existence of a pair of linearly broken Ward identities, the nonrenormalization property of the gauge ghosts' wave functions is also proven to occur in this broad class of N=2 supersymmetric gauge field models
Wilson loop, Regge trajectory and hadron masses in a Yang-Mills theory from semiclassical strings
We compute the one-loop string corrections to the Wilson loop, glueball Regge trajectory and stringy hadron masses in the Witten model of non supersymmetric, large-N Yang-Mills theory. The classical string configurations corresponding to the above field theory objects are respectively: open straight strings, folded closed spinning strings, and strings orbiting in the internal part of the supergravity background. For the rectangular Wilson loop we show that besides the standard Luscher term, string corrections provide a rescaling of the field theory string tension. The one-loop corrections to the linear glueball Regge trajectories render them nonlinear with a positive intercept, as in the experimental soft Pomeron trajectory. Strings orbiting in the internal space predict a spectrum of hadronic-like states charged under global flavor symmetries which falls in the same universality class of other confining models. (author)
Notes on Theta Dependence in Holographic Yang-Mills
Bigazzi, Francesco; Sisca, Roberto
2015-01-01
Effects of the $\\theta$ parameter are studied in Witten's model of holographic 4d Yang-Mills, where $\\theta$ is the coefficient of the CP-breaking topological term. First, the gravity background, including the full backreaction of the RR form dual to the $\\theta$ parameter, is revisited. Then, a number of observables are computed holographically: the ground-state energy density, the string tension, the 't Hooft loop, the light scalar glueball mass, the baryon mass scale, the critical temperature for deconfinement - and thus the whole $(T,\\theta)$ phase diagram - and the entanglement entropy. A simple rule is provided to derive the $\\theta$ corrections to (at least) all the CP-neutral observables of the model. Some of the observables we consider can and have been in fact studied in pure 4d Yang-Mills on the lattice. In that framework the results, obtained in the small $\\theta$ regime, are given up to very few powers of $\\theta^2$. The corresponding holographic results agree qualitatively with available lattice...
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...
Fermion actions extracted from lattice super Yang-Mills theories
Misumi, Tatsuhiro
2013-12-01
We revisit 2D = (2, 2) super Yang-Mills lattice formulation (Sugino model) to investigate its fermion action with two (Majorana) fermion flavors and exact chiral-U(1) R symmetry. We show that the reconcilement of chiral symmetry and absence of further species-doubling originates in the 4D clifford algebra structure of the action, where 2D two flavors are spuriously treated as a single 4D four-spinor with four 4D gamma matrices introduced into kinetic and Wilson terms. This fermion construction based on the higher-dimensional clifford algebra is extended to four dimensions in two manners: (1) pseudo-8D sixteen-spinor treatment of 4D four flavors with eight 8D gamma matrices, (2) pseudo-6D eight-spinor treatment of 4D two flavors with five out of six 6D gamma matrices. We obtain 4D four-species and two-species lattice fermions with unbroken subgroup of chiral symmetry and other essential properties. We discuss their relations to staggered and Wilson twisted-mass fermions. We also discuss their potential feedback to 4D super Yang-Mills lattice formulations.
Should $E_8$ SUSY Yang-Mills be Reconsidered as a Family Unification Model?
Adler, Stephen L.
2002-01-01
We review earlier proposals for $E_8$ family unification, and discuss why recent work of Kovner and Shifman on condensates in supersymmetric Yang-Mills theories suggests the reconsideration of $E_8$ supersymmetric Yang-Mills as a family unification theory.
A Static Solution of Yang-Mills Equation on Anti-de Sitter Space
CHEN Li; REN Xin-An
2009-01-01
Since product metric on AdS space has played a very important role in Lorentz version of AdS/CFT correspondence, the Yang-Mills equation on AdS space with this metric is considered and a static solution is obtained in this paper, which helps to understand the AdS/CFT correspondence of Yang-Mills fields.
Local BRST cohomology and Seiberg-Witten maps in noncommutative Yang-Mills theory
Barnich, Glenn E-mail: gbarnich@ulb.ac.be; Brandt, Friedemann; Grigoriev, Maxim
2004-01-26
We analyze in detail the recursive construction of the Seiberg-Witten map and give an exhaustive description of its ambiguities. The local BRST cohomology for noncommutative Yang-Mills theory is investigated in the framework of the effective commutative Yang-Mills type theory. In particular, we show how some of the conformal symmetries get obstructed by the noncommutative deformation.
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 ...
Phase transition in D=3 Yang-Mills Chern-Simons gauge theory
SU(N) Yang-Mills theory in three dimensions, with a Chern-Simons term of level k (an integer) added, has two-dimensionful coupling constants g2k and g2N; its possible phases depend on the size of k relative to N. For k>N, this theory approaches topological Chern-Simons theory with no Yang-Mills term, and expectation values of multiple Wilson loops yield Jones polynomials, as Witten has shown; it can be treated semiclassically. For k=0, the theory is badly infrared singular in perturbation theory, a nonperturbative mass and subsequent quantum solitons are generated, and Wilson loops show an area law. We argue that there is a phase transition between these two behaviors at a critical value of k, called kc, with kc/N≅2±0.7. Three lines of evidence are given. First, a gauge-invariant one-loop calculation shows that the perturbative theory has tachyonic problems if k≤29N/12. The theory becomes sensible only if there is an additional dynamic source of gauge-boson mass, just as in the k=0 case. Second, we study in a rough approximation the free energy and show that for k≤kc there is a nontrivial vacuum condensate driven by soliton entropy and driving a gauge-boson dynamical mass M, while both the condensate and M vanish for k≥kc. Third, we study possible quantum solitons stemming from an effective action having both a Chern-Simons mass m and a (gauge-invariant) dynamical mass M. We show that if M approx-gt 0.5m, there are finite-action quantum sphalerons, while none survive in the classical limit M=0, as shown earlier by D'Hoker and Vinet. There are also quantum topological vortices smoothly vanishing as M→0. copyright 1996 The American Physical Society
The framework is weak interactions, interpreted as residual (hypercolor) interactions among composite q,l,Wsup(+-) and Z. An effective Lagrangian Lsub(eff) for ''low energies'' (E 0), 2. local U(1)sub(em)xSU(3)sub(c) gauge invariance and 3. vector boson dominance in the operator form of current-field identities. The result is a massive Yang-Mills Lagrangian with respect to the global group G. Lsub(eff) for q,l,W,Z interactions, basing on G = SU(2)sub(WI) of global weak isospin, turns out to be identical (in its dimension 0 (e.g. G = SU(2)sub(WI)xSU(4)sub(Pati-Salam)) is proposed. This implies the existence of new colored (and uncolored) composite vector bosons and vector dominance in the gluon sector. Lsub(eff) then determines the interactions of these new bosons with quarks and leptons in terms of a few free parameters. Interesting consequences for panti p collider and HERA experiments as well as for precision experiments at low energies emerge. (orig.)
In this paper we express the velocity-dependent, spin-dependent heavy quark potential Vqbarq in QCD in terms of a Wilson loop W(Γ) determined by pure Yang-Mills theory. We use an effective dual theory of long-distance Yang-Mills theory to calculate W(Γ) for large loops, i.e., for loops of size R approx-gt RFT. [RFT 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-close-quote t Hooft dual superconductor mechanism of confinement.] We replace W(Γ) by Weff(Γ), given by a functional integral over the dual variables, which for R approx-gt RFT 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 Weff(Γ) and yields a velocity-dependent heavy quark potential that for large R becomes linear in R, and that for small R approaches lowest-order perturbative QCD. This latter fact means that these results should remain applicable down to distances where radiative corrections giving rise to a running coupling constant become important. The spin dependence of the potential at long range as well as at short range reflects the vector coupling of quarks in QCD combined with the dual treatment of long-distance Yang-Mills theory. The methods developed here should be applicable to any realization of the dual superconductor mechanism. They give an expression determining Weff(Γ) independent of the classical approximation, but semiclassical corrections due to fluctuations of the flux tube are not worked out in this paper. Taking these into account should lead to an effective string theory free from the conformal anomaly. copyright 1996 The American Physical Society
Dual superconductivity and vacuum properties in Yang--Mills theories
D'Alessandro, A; Tagliacozzo, L
2006-01-01
We address, within the dual superconductivity model for color confinement, the question whether the Yang-Mills vacuum behaves as a superconductor of type I or type II. In order to do that we compare, for the theory with gauge group SU(2), the determination of the field penetration depth $\\lambda$ with that of the superconductor correlation length $\\xi$. The latter is obtained by measuring the temporal correlator of a disorder parameter developed by the Pisa group to detect dual superconductivity. The comparison places the vacuum close to the border between type I and type II and marginally on the type II side. We also check our results against the study of directly measurable effects such as the interaction between two parallel flux tubes, obtaining consistent indications for a weak repulsive behaviour. Future strategies to improve our investigation are discussed.
Dual superconductivity and vacuum properties in Yang Mills theories
D'Alessandro, A.; D'Elia, M.; Tagliacozzo, L.
2007-07-01
We address, within the dual superconductivity model for color confinement, the question whether the Yang-Mills vacuum behaves as a superconductor of type I or type II. In order to do that we compare, for the theory with gauge group SU(2), the determination of the field penetration depth λ with that of the superconductor correlation length ξ. The latter is obtained by measuring the temporal correlator of a disorder parameter developed by the Pisa group to detect dual superconductivity. The comparison places the vacuum close to the border between type I and type II and marginally on the type II side. We also check our results against the study of directly measurable effects such as the interaction between two parallel flux tubes, obtaining consistent indications for a weak repulsive behaviour. Future strategies to improve our investigation are discussed.
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.
Lifting the Gribov ambiguity in Yang-Mills theories
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.
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.
Hamiltonian reduction of SU(2) Dirac---Yang-Mills mechanics
The SU(2) gauge invariant Dirac---Yang-Mills mechanics of a spatially homogeneous isospinor and gauge fields is considered in the framework of the generalized Hamiltonian approach. The unconstrained Hamiltonian system equivalent to the model is obtained using the gaugeless method of Hamiltonian reduction. The latter includes the Abelianization of the first class constraints, putting the second class constraints into the canonical form and performing a canonical transformation to a set of adapted coordinates such that a subset of the new canonical pairs coincides with the second class constraints and part of the new momenta is equal to the Abelian constraints. In the adapter basis the pure gauge degrees of freedom automatically drop out from the consideration after projection of the model into the constraint shell. Apart from the elimination of these ignorable degrees of freedom a further Hamiltonian reduction is achieved due to the three-dimensional group of rigid symmetry possessed by the system
Closed strings from SO(8) Yang-Mills instantons
When eight-dimensional instantons, satisfying F and F=±*8(F and F), shrink to zero size, we find stringy objects in higher order ten-dimensional Yang-Mills (viewed as a low-energy limit of open string theory). The associated F4 action is a combination of two independent parts having a single-trace and a double-trace structure. As a result we get a D-string from the single-trace term and a fundamental string from the double-trace. The latter has (8,0) supersymmetry on the world-sheet and couplings to the background gauge fields of a heterotic string. A correlation between the conformal factor of the instanton and the tachyon field is conjectured
N=1 supersymmetric Yang-Mills theory on the lattice
We perform Monte Carlo investigations of the N=1 supersymmetric Yang-Mills (SYM) theory on the lattice with dynamical gluinos. The motivation is the determination of the mass spectrum of the low-lying bound states of the theory. These states are expected to form two supermultiplets consisting of gluionballs, glueballs and gluino-glueballs. We adopt the Wilson discretization of the action, which explicitly breaks SUSY and chirality at finite lattice spacing. At gauge coupling β=2.3, we analyzed 163.32 lattices at three values of the gluino mass (κ=0.1955,0.196,0.1965). The critical gluino mass, where the restoration of chiral symmetry and the supersymmetry is expected in the continuum limit, is estimated to be κcr≅0.1969. The two-step multi-bosonic (TSMB) Monte Carlo algorithm is used for the dynamical gluino. Some features of a novel Polynomial-Hybrid-Monte-Carlo (PHMC) implementation are also discussed
Three-dimensional super Yang-Mills with unquenched flavor
Faedo, Anton F; Tarrio, Javier
2015-01-01
We construct analytically the gravity duals of three-dimensional, super Yang-Mills-type theories with $\\mathcal N=1$ supersymmetry coupled to $N_f$ quark flavors. The backreaction of the quarks on the color degrees of freedom is included, and corresponds on the gravity side to the backreaction of $N_f$ D6-branes on the background of $N$ D2-branes. The D6-branes are smeared over the compact part of the geometry, which must be a six-dimensional nearly K\\"ahler manifold in order to preserve supersymmetry. For massless quarks, the solutions flow in the IR to an $AdS_4$ fixed point dual to a Chern-Simons-matter theory. For light quarks the theories exhibit quasi-conformal dynamics (walking) at energy scales $m_q \\ll E \\ll \\lambda N_f / N$, with $\\lambda = g_{\\text{YM}}^2 N$ the 't Hooft coupling.
Yang-Mills theory at non-vanishing temperature
Fister, Leonard
2011-01-01
We compute ghost and gluon propagators of Yang-Mills theory in the Landau gauge at non-vanishing temperature within a functional renormalisation group setting. We construct purely thermal flows, that project onto thermal fluctuations only. For temperatures and momenta above the confinement-deconfinement temperature Tc the electric propagator shows a thermal suppression due to Debye screening. The magnetic gluon propagator shows a thermal scaling and tends towards the three-dimensional one. In this region both propagators match the lattice propagators. The thermal scaling is also reflected in the infrared suppression of the ghost-gluon vertex. For temperatures below Tc the electric propagator shows an enhancement which is in qualitative agreement with the lattice behaviour.
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 ...
Minding the Gap in N=4 Super-Yang-Mills
DeWolfe, Oliver; Rosen, Christopher
2013-01-01
We analyze fermionic response in the geometry holographically dual to zero-temperature N=4 Super-Yang-Mills theory with two equal nonvanishing chemical potentials, which is characterized by a singular horizon and zero ground state entropy. We show that fermionic fluctuations are completely stable within a gap in energy around a Fermi surface singularity, beyond which non-Fermi liquid behavior returns. This gap disappears abruptly once the final charge is turned on, and is associated to a discontinuity in the corresponding chemical potential. We also show that the singular near-horizon geometry lifts to a smooth AdS_3 x R^3, and interpret the gap as a region where the quasiparticle momentum is spacelike in six dimensions due to the momentum component in the Kaluza-Klein direction, corresponding to the final charge.
Superconformal Yang-Mills quantum mechanics and Calogero model with OSp(N|2,R) symmetry
Copland, Neil B; Park, Jeong-Hyuck
2012-01-01
In spacetime dimension two, pure Yang-Mills possesses no physical degrees of freedom, and consequently it admits a supersymmetric extension to couple to an arbitrary number, N say, of Majorana-Weyl gauginos. This results in (N,0) super Yang-Mills. Further, its dimensional reduction to mechanics doubles the number of supersymmetries, from N to N+N, to include conformal supercharges, and leads to a superconformal Yang-Mills quantum mechanics with symmetry group OSp(N|2,R). We comment on its connection to AdS_2 \\times S^{N-1} and reduction to a supersymmetric Calogero model.
PP-wave string interactions from perturbative Yang-Mills theory
Constable, Neil R.; Freedman, Daniel Z.; Headrick, Matthew; Minwalla, Shiraz; Motl, Lubos; Postnikov, Alexander; Skiba, Witold
2002-01-01
Recently, Berenstein et al. have proposed a duality between a sector of N=4 super-Yang-Mills theory with large R-charge J, and string theory in a pp-wave background. In the limit considered, the effective 't Hooft coupling has been argued to be lambda'=g_{YM}^2 N/J^2=1/(mu p^+ alpha')^2. We study Yang-Mills theory at small lambda' (large mu) with a view to reproducing string interactions. We demonstrate that the effective genus counting parameter of the Yang-Mills theory is g_2^2=J^4/N^2=(4 p...
Supercurrent interactions in noncommutative Yang-Mills and IIB matrix model
It is known that noncommutative Yang-Mills is equivalent to IIB matrix model with a noncommutative background, which is interpreted as a twisted reduced model. In noncommutative Yang-Mills, long range interactions can be seen in nonplanar diagrams after integrating high momentum modes. These interactions can be understood as block-block interactions in the matrix model. Using this relation, we consider long range interactions in noncommutative Yang-Mills associated with fermionic backgrounds. Exchanges of gravitinos, which couple to a supersymmetry current, are examined
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...
Study of entropy production in Yang-Mills theory with use of Husimi function
Tsukiji, Hidekazu; Kunihiro, Teiji; Ohnishi, Akira; Takahashi, Toru T
2015-01-01
Understanding the thermalization process in a pure quantum system is a challenge in theoretical physics. In this work, we explore possible thermalization mechanism in Yang-Mills(YM) theory by using a positive semi-definite quantum distribution function called a Husimi function which is given by a coarse graining of the Wigner function within the minimum uncertainty. Then entropy is defined in terms of the Husimi function, which is called the Husimi-Wehrl(HW) entropy. We propose two numerical methods to calculate the HW entropy. We find that it is feasible to apply the semi-classical approximation with the use of classical YM equation. It should be noted that the semi-classical approximation is valid in the systems of physical interest including the early stage of heavy-ion collisions. Using a product ansatz for the Husimi function, which is confirmed to reproduce the HW entropy within 20% error (overestimate) for a few-body quantum system, we succeed in a numerical evaluation of HW entropy of YM fields and sh...
Cosmological Co-evolution of Yang-Mills Fields and Perfect Fluids
Barrow, J D; Maeda, K; Barrow, John D.; Jin, Yoshida; Maeda, Kei-ichi
2005-01-01
We study the co-evolution of Yang-Mills fields and perfect fluids in Bianchi type I universes. We investigate numerically the evolution of the universe and the Yang-Mills fields during the radiation and dust eras of a universe that is almost isotropic. The Yang-Mills field undergoes small amplitude chaotic oscillations, as do the three expansion scale factors which are also displayed by the expansion scale factors of the universe. The results of the numerical simulations are interpreted analytically and compared with past studies of the cosmological evolution of magnetic fields in radiation and dust universes. We find that, whereas magnetic universes are strongly constrained by the microwave background anisotropy, Yang-Mills universes are principally constrained by primordial nucleosynthesis and the bound is comparatively weak, and Omega_YM < 0.105 Omega_rad.
A Unified Field Theory of Gravity, Electromagnetism, and the Yang-Mills Gauge Field
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.
Effective potential for the order parameter of the SU(2) Yang-Mills deconfinement transition
Engelhardt, Michael; Reinhardt, Hugo
1997-01-01
The Polyakov loop variable serves as an order parameter to characterize the confined and deconfined phases of Yang-Mills theory. By integrating out the vector fields in the SU(2) Yang-Mills partition function in one-loop approximation, an effective action is obtained for the Polyakov loop to second order in a derivative expansion. The resulting effective potential for the Polyakov loop is capable of describing a second-order deconfinement transition as a function of temperature.
Kinetic energy for the nuclear Yang-Mills collective model
Rosensteel, George; Sparks, Nick
2015-10-01
The Bohr-Mottelson-Frankfurt model of nuclear rotations and quadrupole vibrations is a foundational model in nuclear structure physics. The model, also called the geometrical collective model or simply GCM, has two hidden mathematical structures, one Lie group theoretic and the other differential geometric. Although the group structure has been understood for some time, the geometric structure is a new unexplored feature that shares the same mathematical origin as Yang-Mills, viz., a vector bundle with a non-abelian structure group and a connection. Using the de Rham Laplacian ▵ = * d * d from differential geometry for the kinetic energy extends significantly the physical scope of the GCM model. This Laplacian contains a ``magnetic'' term due to the coupling between base manifold rotational and fiber vorticity degrees of freedom. When the connection specializes to irrotational flow, the Laplacian reduces to the Bohr-Mottelson kinetic energy operator. More generally, the connection yields a moment of inertia that is intermediate between the extremes of irrotational flow and rigid body motion.
N=1 supersymmetric yang-mills theory in Ito Calculus
The stochastic quantization method is applied to N = 1 supersymmetric Yang-Mills theory, in particular in 4 and 10 dimensions. In the 4 dimensional case, based on Ito calculus, the Langevin equation is formulated in terms of the superfield formalism. The stochastic process manifestly preserves both the global N = 1 supersymmetry and the local gauge symmetry. The expectation values of the local gauge invariant observables in SYM4 are reproduced in the equilibrium limit. In the superfield formalism, it is impossible in SQM to choose the so-called Wess-Zumino gauge in such a way to gauge away the auxiliary component fields in the vector multiplet, while it is shown that the time development of the auxiliary component fields is determined by the Langevin equations for the physical component fields of the vector multiplet in an ''almost Wess-Zumino gauge''. The physical component expressions of the superfield Langevin equation are naturally extended to the 10 dimensional case, where the spinor field is Majorana-Weyl. By taking a naive zero volume limit of the SYM10, the IIB matrix model is studied in this context. (author)
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...
Wilson loops in N=4 supersymmetric Yang-Mills theory
Perturbative computations of the expectation value of the Wilson loop in N=4 supersymmetric Yang-Mills theory are reported. For the two special cases of a circular loop and a pair of antiparallel lines, it is shown that the sum of an infinite class of ladder-like planar diagrams, when extrapolated to strong coupling, produces an expectation value characteristic of the results of the AdS/CFT correspondence, ∼exp((constant)√g2N). For the case of the circular loop, the sum is obtained analytically for all values of the coupling. In this case, the constant factor in front of √g2N also agrees with the supergravity results. We speculate that the sum of diagrams without internal vertices is exact for the circular loop and support this conjecture by showing that the leading corrections to the ladder diagrams cancel identically in four dimensions. We also show that, for arbitrary smooth loops, the ultraviolet divergences cancel to order g4N2
Color flux and Yang-Mills structure - a dynamical model
In view of the basic difficulties of QCD to bring the confinement hypothesis to a calculational level, a field-theoretic flux tube model with local color gauge invariance is set up which exhibits triality confinement ab initio. This is achieved by an appropriate formulation of Gauss' law using the tube operator as canonical degree of freedom. Along the tube there are vectorlike gauge-invariant color excitations related to splitting and to the short-distance behavior. They receive their degrees of freedom from the tube oscillations and thus are a realization of Polyakov's program. The quarkless system averaged over the directions of the flux tubes passing through a given world point reproduces the pure Yang-Mills equations. The guide to the model is the loop-space formulation of the confining Gauss law of the abelian confinement theory. Basically we generalize to a nonabelian gauge structure not a local abelian field theory but directly the loop-space formulation of the abelian confinement theory. (orig.)
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.
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...
Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory
Pérez, Margarita García; González-Arroyo, Antonio; Okawa, Masanori
2013-09-01
We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N , the length of the torus L and the Z N magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x = λ N L and an angle defined in terms of the magnetic flux (λ is `t Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence ( N L dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable scaling of the magnetic flux.
Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory
Pérez, Margarita García; Okawa, Masanori
2013-01-01
We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N, the length of the torus L and the Z_N magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x=\\lambda NL and an angle defined in terms of the magnetic flux (\\lambda\\ is 't Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence (NL dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable sc...
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 ...
Gauge-covariant decomposition and magnetic monopole for G (2 ) Yang-Mills field
Matsudo, Ryutaro; Kondo, Kei-Ichi
2016-08-01
We provide a gauge-covariant decomposition of the Yang-Mills field with the exceptional gauge group G (2 ), which extends the field decomposition proposed by Cho, Duan-Ge, and Faddeev-Niemi for the S U (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 semisimple Lie group other than S U (N ) and G (2 ).
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 $G(2)$.
Radiating black holes in Einstein-Yang-Mills theory and cosmic censorship
Exact nonstatic spherically symmetric black-hole solutions of the higher dimensional Einstein-Yang-Mills equations for a null dust with Yang-Mills gauge charge are obtained by employing Wu-Yang ansatz, namely, HD-EYM Vaidya solution. It is interesting to note that gravitational contribution of Yang-Mills (YM) gauge charge for this ansatz is indeed opposite (attractive rather than repulsive) that of Maxwell charge. It turns out that the gravitational collapse of null dust with YM gauge charge admits strong curvature shell focusing naked singularities violating cosmic censorship. However, there is significant shrinkage of the initial data space for a naked singularity of the HD-Vaidya collapse due to presence of YM gauge charge. The effect of YM gauge charge on structure and location of the apparent and event horizons is also discussed.
A BRST gauge-fixing procedure for Yang-Mills theory on sphere
A gauge-fixing procedure for the Yang-Mills theory on an n-dimensional sphere (or a hypersphere) is discussed in a systematic manner. We claim that Adler's gauge-fixing condition used in massless Euclidean QED on a hypersphere is not conventional because of the presence of an extra free index, and hence is unfavorable for the gauge-fixing procedure based on the BRST invariance principle (or simply BRST gauge-fixing procedure). Choosing a suitable gauge condition, which is proved to be equivalent to a generalization of Adler's condition, we apply the BRST gauge-fixing procedure to the Yang-Mills theory on a hypersphere to obtain consistent results. Field equations for the Yang-Mills field and associated fields are derived in manifestly O(n+1) covariant or invariant forms. In the large radius limit, these equations reproduce the corresponding field equations defined on the n-dimensional flat space
Superspace Gauge Fixing in Yang-Mills Matter Coupled Conformal Supergravity
Kugo, Taichiro; Yoshioka, Koichi
2016-01-01
In $D=4$, $\\cal{N}=1$ 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 K\\"ahler isometry group of chiral matter fields. There are two gauge-fixing procedures to get to the component Poincar\\'e supergravity: one via the superconformal component formalism and the other via the Poincar\\'e superspace formalism. These two types of superconformal gauge-fixing conditions are analyzed in detail and their correspondence is clarified.
Dark Energy and Dark Matter from Yang-Mills Condensate and the Peccei-Quinn mechanism
Addazi, Andrea; Donà, Pietro; Marcianò, Antonino
2016-01-01
The idea that Dark Energy originates from a Yang-Mills condensate has been so far instantiated relying on the asymptotically-free perturbative expansion of SU(N) gauge-theories. This procedure is more appropriate in the ultra-violet regime than in the infrared limit, since SU(N) Yang-Mills theories generically show confinement. We approach the problem from the point of view of the functional renormalization group, and ground our study on the properties of the effective Lagrangian, to be deter...
Quantum Metamorphosis of a Conformal Transformation in D3-Brane Yang-Mills Theory
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 AdS5x S5 supergravity and super-Yang-Mills theory (SYM). Furthermore, our work sheds elucidating light on the nature of the AdS/SYM correspondence. copyright 1998 The American Physical Society
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.
Electric-Magnetic Duality in Infrared SU(2) Yang-Mills Theory
Faddeev, L D; Faddeev, Ludvig; Niemi, Antti J.
2002-01-01
We explicitly realize the dual structure between the electric and magnetic variables in the long-distance SU(2) Yang-Mills theory. The electric variables correspond to an abelian scalar multiplet with two complex scalar fields, while the dual magnetic variables yield a relativistic version of the Heisenberg model. This leads to a selfdual picture, where the same effective action describes both the electric and the magnetic phase of the theory. Our results are consistent with the proposal that the physical spectrum of the long-distance Yang-Mills theory involves confining strings which are tied into stable knotted solitons.
On the invariant measure for the Yang-Mills configuration space in (3+1) dimensions
We consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parametrized 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
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.
BPS Domain Walls in super Yang-Mills and Landau-Ginzburg models
We study domain walls in two different extensions of super Yang-Mills characterized by the absence of a logarithmic term in their effective superpotential. The models, defined by the usual gaugino condensate and an extra field Y, give different patterns of domain walls despite both leading to the same effective limit for heavy Y, i.e. the Veneziano-Yankielowicz effective Lagrangian of super Yang-Mills. We explain the origin of those differences and also give a physical motivation for introducing the field Y. (author)
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.
Super Yang-Mills theories coupled to supergravity; Tangent bundle to a supergroup manifold approach
Foussats, A.; Zandron, O. (Instituto de Fisica Rosario, Facultad de Ciencias Exactas e Ingenieria, U.N.R., Av. Pellegrini 250, 2000 Rosario (AR))
1988-01-01
Supersymmetric Yang-Mills theories coupled to supergravity are analyzed by using the tangent bundle to a supergroup manifold as geometrical framework. The factorization condition imposed on these theories is considered from this point of view. The so-called H-gauge transformation for both, the super Yang-Mills and supergravity one-forms gauge fields are obtained as a consequence of a change of trivialization in the corresponding coset manifold. The authors point out the existence of factorized solutions not diffeomorphically equivalent for the set of pseudo-connections one-forms or gauge fields.
Generalized 2D Yang-Mills theories: Large-N limit and Phase Structure
Alimohammadi, Masoud
2000-01-01
After review the 2D Yang--Mills theories (YM2) and its large--N behaviour, the Generalized 2D Yang--Mills theories (gYM2) and their partition functions on a general two--dimensional Riemann surface are discussed.The large--N behaviour of these models is studied in weak regime, and in strong regime, we restrict ourselves to f4 gYM2. We show that this model has a third order phase transition, similar to ordinary YM2 theory.