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...
Violation of the Weak Energy Condition by the Inflationary Yang-Mills Condensate
张杨
2002-01-01
Recent cosmic microwave background data favours a blueshifted primeval perturbation spectrum with an indexn＞1, which implies that the equation of state of dominant matter should be such that p + p＜0 during theinflationary expansion of the early universe. We study the quantum Yang-Mills condensate inflationary modeland find that this requirement can be satisfied by the effective quantum Yang-Mills condensate naturally in thestates with the negative dielectric constant.
Propagation properties and condensate formation of the confined Yang-Mills field
Stingl, M.
1986-12-01
The dynamical generation of a pole in the self-energy of a Yang-Mills field-an extension of the Schwinger mechanism-establishes a link between the tendency of the field to form nonperturbative vacuum condensates and its ``noninterpolating'' property in the confining phase-the fact that it has no particles associated with it. The nonvanishing residue of such a pole-a parameter b4 of dimension (mass)4-on the one hand provides for a nonvanishing value of , a contribution to the ``gluon condensate.'' On the other hand, it implies a dominant nonperturbative form of the propagator that has no particle singularity on the real k2 axis; instead, it describes a quantized field whose elementary excitations are short lived. The dispersion law for these excitations is given and shows that they grow more particlelike (are asymptotically free) at large momenta, thus providing a qualitative description of the short-lived excitation at the origin of a gluon jet. At large k2, the nonperturbative propagator reproduces nonperturbative corrections derived from the operator-product expansion. Moreover, it is a solution to the Euclidean Dyson-Schwinger equation for the Yang-Mills field in the following sense: there exist nonperturbative three-vector vertices Γ3 and auxiliary ghost-ghost-vector vertices G3, satisfying all symmetry and invariance requirements, and in conjunction with which this propagator solves both the Euclidean Dyson-Schwinger equation through one-dressed-loop terms and the Γ3 Slavnov-Taylor identity up to perturbative corrections of order g2. The consistency conditions for this solution give b2=μ0 2exp[-(4π)2 /11g2] to this order, confirming the nonperturbative nature of the residue parameter, and providing a paradigm for the dynamical determination of condensates.
Dark energy as a fixed point of the Einstein Yang-Mills Higgs Equations
Rinaldi, Massimiliano
2015-01-01
We study the Einstein Yang-Mills Higgs equations in the $SO(3)$ representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into a closed dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to matter domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.
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
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
Neutrino Oscillation, Finite Self-Mass and General Yang-Mills Symmetry
Hsu, Jong-Ping
2016-01-01
The conservation of lepton number is assumed to be associated with a general Yang-Mills symmetry. New transformations involve (Lorentz) vector gauge functions and characteristic phase functions, and they form a group. General Yang-Mills fields are associated with new fourth-order equations and linear potentials. Lepton self-masses turn out to be finite and proportional to the inverse of lepton masses, which implies that neutrinos should have non-zero masses. Thus, general Yang-Mills symmetry could provide an understanding of neutrino oscillations and suggests that neutrinos with masses and very weak leptonic force may play a role in dark matter.
Galtsov, D V; Volkov, M S; Davydov, Evgeny A.; Gal'tsov, Dmitri V.; Volkov, Mikhail S.
2006-01-01
We present globally regular vortex-type solutions for a pure SU(2) Yang-Mills field coupled to gravity in 3+1 dimensions. These gravitating vortices are static, cylindrically symmetric and purely magnetic, and they support a non-zero chromo-magnetic flux through their cross section. In addition, they carry a constant non-Abelian current, and so in some sense they are analogs of the superconducting cosmic strings. They have a compact central core dominated by a longitudinal magnetic field and endowed with an approximately Melvin geometry. This magnetic field component gets color screened in the exterior part of the core, outside of which the fields approach exponentially fast those of the electrovacuum Bonnor solutions with a circular magnetic field. In the far field zone the solutions are not asymptotically flat but tend to vacuum Kasner metrics.
Wilson Loops in Noncommutative Yang Mills
Ishibashi, N; Kawai, H; Kitazawa, Y; Ishibashi, Nobuyuki; Iso, Satoshi; Kawai, Hikaru; Kitazawa, Yoshihisa
2000-01-01
We study the correlation functions of the Wilson loops in noncommutative Yang-Mills theory based upon its equivalence to twisted reduced models. We point out that there is a crossover at the noncommutativity scale. At large momentum scale, the Wilson loops in noncommmutative Yang-Mills represent extended objects. They coincide with those in ordinary Yang-Mills theory in low energy limit. The correlation functions on D-branes in IIB matrix model exhibit the identical crossover behavior. It is observed to be consistent with the supergravity description with running string coupling. We also explain that the results of Seiberg and Witten can be simply understood in our formalism.
Yang-Mills origin of gravitational symmetries
Anastasiou, A; Duff, M J; Hughes, L J; Nagy, S
2014-01-01
By regarding gravity as the convolution of left and right Yang-Mills theories, we derive in linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincar\\'e. As a concrete example we focus on the new-minimal (12+12) off-shell version of simple four-dimensional supergravity obtained by tensoring the off-shell Yang-Mills multiplets (4 + 4, N_L = 1) and (3 + 0, N_R = 0).
Spectroscopy of two dimensional N=2 Super Yang Mills theory
August, Daniel; Wipf, Andreas
2016-01-01
Albeit the standard model is the most successful model of particles physics, it still has some theoretical shortcomings, for instance the hierarchy problem, the absence of dark matter, etc. Supersymmetric extensions of the standard model could be a possible solution to these problems. One of the building blocks of these supersymmetric models are supersymmetric gauge theories. It is expected that they exhibit interesting features like confinement, chiral symmetry breaking, magnetic monopoles and the like. We present new results on N=2 Super Yang Mills theory in two dimensions. The lattice action is derived by a dimensional reduction of the N=1 Super Yang Mills theory in four dimensions. By preserving the R symmetry of the four dimensional model we can exploit Ward identities to fine tune our parameters of the model to obtain the chiral and supersymmetric continuum limit. This allows us to calculate the mass spectrum at the physical point and compare these results with effective field theories.
Asymmetric condensed dark matter
Aguirre, Anthony; Diez-Tejedor, Alberto
2016-04-01
We explore the viability of a boson dark matter candidate with an asymmetry between the number densities of particles and antiparticles. A simple thermal field theory analysis confirms that, under certain general conditions, this component would develop a Bose-Einstein condensate in the early universe that, for appropriate model parameters, could survive the ensuing cosmological evolution until now. The condensation of a dark matter component in equilibrium with the thermal plasma is a relativistic process, hence the amount of matter dictated by the charge asymmetry is complemented by a hot relic density frozen out at the time of decoupling. Contrary to the case of ordinary WIMPs, dark matter particles in a condensate must be lighter than a few tens of eV so that the density from thermal relics is not too large. Big-Bang nucleosynthesis constrains the temperature of decoupling to the scale of the QCD phase transition or above. This requires large dark matter-to-photon ratios and very weak interactions with standard model particles.
Asymmetric condensed dark matter
Aguirre, Anthony
2015-01-01
We explore the viability of a boson dark matter candidate with an asymmetry between the number densities of particles and antiparticles. A simple thermal field theory analysis confirms that, under certain general conditions, this component would develop a Bose-Einstein condensate in the early universe that, for appropriate model parameters, could survive the ensuing cosmological evolution until now. The condensation of a dark matter component in equilibrium with the thermal plasma is a relativistic process, hence the amount of matter dictated by the charge asymmetry is complemented by a hot relic density frozen out at the time of decoupling. Contrary to the case of ordinary WIMPs, dark matter particles in a condensate can be very light, $10^{-22}\\,{\\rm eV} \\lesssim m \\lesssim 10^2\\,{\\rm eV}$; the lower limit arises from constraints on small-scale structure formation, while the upper bound ensures that the density from thermal relics is not too large. Big-Bang nucleosynthesis constrains the temperature of deco...
Einstein-Yang-Mills-Lorentz Black Holes
Cembranos, Jose A R
2015-01-01
Different black hole solutions of the coupled Einstein-Yang-Mills equations are well known from long time. They have attracted much attention from mathematicians and physicists from their discovery. In this work, we analyze black holes associated with the gauge Lorentz group. In particular, we study solutions which identify the gauge connection with the spin connection. This ansatz allows to find exact solutions to the complete system of equations. By using this procedure, we show the equivalence between the Yang-Mills-Lorentz model in curved space-time and a particular set of extended gravitational theories.
Supermembrane limit of Yang-Mills theory
Lechtenfeld, Olaf
2015-01-01
We consider Yang-Mills theory with $N{=}1$ super translation group in eleven auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold $\\Sigma_3\\times S^1$, where $\\Sigma_3$ is a three-dimensional Lorentzian manifold and $S^1$ is a circle. We show that in the infrared limit, when the metric on $S^1$ is scaled down, the Yang-Mills action supplemented by a Wess-Zumino-type term reduces to the action of an M2-brane.
Implementing the Gribov-Zwanziger framework in N=1 Super Yang-Mills in the Landau gauge
Capri, M A L; Guimaraes, M S; Justo, I F; Palhares, L F; Sorella, S P; Vercauteren, D
2014-01-01
The Gribov-Zwanziger framework accounting for the existence of Gribov copies is extended to N=1 Super Yang--Mills theories quantized in the Landau gauge. We show that the restriction of the domain of integration in the Euclidean functional integral to the first Gribov horizon can be implemented in a way to recover non-perturbative features of N=1 Super Yang--Mills theories, namely: the existence of the gluino condensate as well as the vanishing of the vacuum energy.
Numerical simulations of dynamical gluinos in SU(3) Yang-Mills theory: first results
Feo, Alessandra; Kirchner, Robert; Luckmann, Silke; Montvay, Istvan; Muenster, Gernot
2000-03-01
In a numerical Monte Carlo simulation of SU(3) Yang-Mills theory with dynamical gluinos we have investigated the behaviour of the expectation value of the scalar and pseudoscalar gluino condensates in order to determine the phase structure. Preliminary results are presented as a function of the hopping parameter.
Evidence for discrete chiral symmetry breaking in $N = 1$ supersymmetric Yang-Mills theory
Kirchner, R; Montvay, István; Spanderen, K; Westphalen, J
1999-01-01
In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with dynamical gauginos we find evidence for two degenerate ground states at the supersymmetry point corresponding to zero gaugino mass. This is consistent with the expected pattern of spontaneous discrete chiral symmetry breaking $Z_4 \\to Z_2$ caused by gaugino condensation.
Numerical simulations of dynamical gluinos in SU(3) Yang-Mills theory first results
Feo, A; Luckmann, S; Montvay, István; Münster, G; Feo, Alessandra; Kirchner, Robert; Luckmann, Silke; Montvay, Istvan; Münster, Gernot
2000-01-01
In a numerical Monte Carlo simulation of SU(3) Yang-Mills theory with dynamical gluinos we have investigated the behaviour of the expectation value of the scalar and pseudoscalar gluino condensates in order to determine the phase structure. Preliminary results are presented as a function of the hopping parameter.
Evidence for discrete chiral symmetry breaking in N=1 supersymmetric Yang-Mills theory
Desy-Münster Collaboration; Kirchner, R.; Montvay, I.; Westphalen, J.; Luckmann, S.; Spanderen, K.
1999-01-01
In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with dynamical gauginos we find evidence for two degenerate ground states at the supersymmetry point corresponding to zero gaugino mass. This is consistent with the expected pattern of spontaneous discrete chiral symmetry breaking Z4-->Z2 caused by gaugino condensation.
Numerical simulations of dynamical gluinos in SU (3) Yang-Mills theory: first results
Feo, Alessandra; Kirchner, Robert; Luckmann, Silke; Montvay, István; Münster, Gernot; DESY-Münster Collaboration
In a numerical Monte Carlo simulation of SU(3) Yang-Mills theory with dynamical gluinos we have investigated the behaviour of the expectation value of the scalar and pseudoscalar gluino condensates in order to determine the phase structure. Preliminary results are presented as a function of the hopping parameter.
Analytic representations of Yang-Mills amplitudes
Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L.; Damgaard, Poul H.; Feng, Bo
2016-12-01
Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space-fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Möbius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is the foundations of a systematic procedure to obtain analytic, covariant forms of Yang-Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.
Analytic Representations of Yang-Mills Amplitudes
Bjerrum-Bohr, N E J; Damgaard, Poul H; Feng, Bo
2016-01-01
Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space---fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Mobius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is a systematic procedure to obtain analytic, covariant forms of Yang-Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.
Lifting the Gribov ambiguity in Yang-Mills theories
Serreau, Julien
2013-01-01
We report on the work presented in Phys. Lett. B712 (2012) 97, where a new one-parameter family of Landau gauges has been proposed for Yang-Mills theories, inspired by an analogy with disordered systems in condensed matter physics. This is based on a particular average over Gribov copies which avoids the Neuberger zero problem of the standard Fadeev-Popov construction. The proposed gauge fixing can be formulated as a local renormalizable field theory in four dimensions and is well-suited for analytical calculations. A remarkable feature is that, for what concerns the calculation of ghost and gauge field correlators, the gauged-fixed action is perturbatively equivalent to a simple massive extension of the Faddeev-Popov action. The renormalization group flow of the theory admits infrared safe trajectories, with no Landau pole. The one-loop calculations of Yang-Mills two-point correlators show remarkable agreement with lattice simulations all the way to the deep infrared.
Higher derivative super Yang-Mills theories
Bergshoeff, E.; Rakowski, M.; Sezgin, E.
1987-01-01
The most general higher derivative Yang-Mills actions of the type (F^2 + Î±^2F^4) which are globally supersymmetric up to order Î±^2 in six- and ten-dimensional spacetimes are given. The F^4-terms turn out to occur in the combination Î±^2[tr F^4 - Â¼(tr F^2)^2], where the trace is over the Lorentz i
Twin Supergravities from Yang-Mills Squared
Anastasiou, A; Duff, M J; Hughes, M J; Marrani, A; Nagy, S; Zoccali, M
2016-01-01
We consider `twin supergravities' - pairs of supergravities with $\\mathcal{N}_+$ and $\\mathcal{N}_-$ supersymmetries, $\\mathcal{N}_+>\\mathcal{N}_-$, with identical bosonic sectors - in the context of tensoring super Yang-Mills multiplets. It is demonstrated that the pairs of twin supergravity theories are related through their left and right super Yang-Mills factors. This procedure generates new theories from old. In particular, the matter coupled $\\mathcal{N}_-$ twins in $D=3,5,6$ and the $\\mathcal{N}_-=1$ twins in $D=4$ have not, as far as we are aware, been obtained previously using the double-copy construction, adding to the growing list of double-copy constructible theories. The use of fundamental matter multiplets in the double-copy construction leads us to introduce a bi-fundamental scalar that couples to the well-known bi-adjoint scalar field. It is also shown that certain matter coupled supergravities admit more than one factorisation into left and right super Yang-Mills-matter theories.
Superstring limit of Yang-Mills theories
Lechtenfeld, Olaf; Popov, Alexander D.
2016-11-01
It was pointed out by Shifman and Yung that the critical superstring on X10 =R4 ×Y6, where Y6 is the resolved conifold, appears as an effective theory for a U(2) Yang-Mills-Higgs system with four fundamental Higgs scalars defined on Σ2 ×R2, where Σ2 is a two-dimensional Lorentzian manifold. Their Yang-Mills model supports semilocal vortices on R2 ⊂Σ2 ×R2 with a moduli space X10. When the moduli of slowly moving thin vortices depend on the coordinates of Σ2, the vortex strings can be identified with critical fundamental strings. We show that similar results can be obtained for the low-energy limit of pure Yang-Mills theory on Σ2 × Tp2, where Tp2 is a two-dimensional torus with a puncture p. The solitonic vortices of Shifman and Yung then get replaced by flat connections. Various ten-dimensional superstring target spaces can be obtained as moduli spaces of flat connections on Tp2, depending on the choice of the gauge group. The full Green-Schwarz sigma model requires extending the gauge group to a supergroup and augmenting the action with a topological term.
Dynamical Breaking of Generalized Yang-Mills Theory
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.
HEAT FLOW FOR YANG-MILLS-HIGGS FIELDS, PART I
无
2000-01-01
The Yang-Mills-Higgs field generalizes the Yang-Mills field. The authors establish the local existence and uniqueness of the weak solution to the heat flow for the Yang-Mills-Higgs field in a vector bundle over a compact Riemannian 4-manifold, and show that the weak solution is gauge-equivalent to a smooth solution and there are at most finite singularities at the maximum existing time.
Spontaneous breaking of color in N=1 Super Yang-Mills theory without matter
Diakonov, D; Diakonov, Dmitri; Petrov, Victor
2002-01-01
We argue that in the pure N=1 Super Yang-Mills theory gauge symmetry is spontaneously broken to the maximal Abelian subgroup. In particular, colored gluino condensate is nonzero. It invalidates, in a subtle way, the so-called strong-coupling instanton calculation of the (normal) gluino condensate and resolves the long-standing paradox why its value does not agree with that obtained by other methods.
Chiral symmetry and the Yang--Mills gradient flow
Lüscher, Martin
2013-01-01
In the last few years, the Yang--Mills gradient flow was shown to be an attractive tool for non-perturbative studies of non-Abelian gauge theories. Here a simple extension of the flow to the quark fields in QCD is considered. As in the case of the pure-gauge gradient flow, the renormalizability of correlation functions involving local fields at positive flow times can be established using a representation through a local field theory in 4+1 dimensions. Applications of the extended flow in lattice QCD include non-perturbative renormalization and O(a) improvement as well as accurate calculations of the chiral condensate and of the pseudo-scalar decay constant in the chiral limit.
String Scale in Noncommutative Yang-Mills
Ishibashi, N; Kawai, H; Kitazawa, Y
2000-01-01
We identify the effective string scale of noncommutative Yang-Mills theory (NCYM) with the noncommutativity scale through its dual supergravity description. We argue that Newton's force law may be obtained with 4 dimensional NCYM with maximal SUSY. It provides a nonperturbative compactification mechanism of IIB matrix model. We can associate NCYM with the von Neumann lattice by the bi-local representation. We argue that it is superstring theory on the von Neumann lattice. We show that our identification of its effective string scale is consistent with exact T-duality (Morita equivalence) of NCYM.
Duality in supersymmetric Yang-Mills theory
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.
Perturbative spacetimes from Yang-Mills theory
Luna, Andrés; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2017-04-12
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Landau gauge Yang-Mills correlation functions
Cyrol, Anton K.; Fister, Leonard; Mitter, Mario; Pawlowski, Jan M.; Strodthoff, Nils
2016-09-01
We investigate Landau gauge S U (3 ) Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalization group. Particular focus is put on the dynamical creation of the gluon mass gap at nonperturbative momenta and the consistent treatment of quadratic divergences. The nonperturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated self-consistently with the classical action as the only input. The apparent convergence of the expansion scheme is discussed and within the errors, our numerical results are in quantitative agreement with available lattice results.
Perturbative spacetimes from Yang-Mills theory
Luna, Andres; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2016-01-01
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
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.)
Deformations of Yang-Mills theory
Cofano, Marco; Krasnov, Kirill
2015-01-01
We introduce and study a new class of power-counting non-renormalisable gauge theories in four space-time dimensions. The Lagrangian is an arbitrary function of the self-dual part of the field strength. The resulting perturbation theory has the property that whenever two derivatives act on an internal line propagator, the result is a delta-function and the line collapses to a point. This means that there remains at most one derivative on each internal line, which gives improved ulta-violet behaviour. For many purposes, this class of theories behaves just like ordinary Yang-Mills theory. In particular, they all share the Yang-Mills theory MHV amplitudes. Moreover, these theories remain constructible in the sense that higher-point tree level scattering amplitudes can be obtained from the lower-point amplitudes using the BCFW recursion relations. Also, the square of these gauge-theory amplitudes gives the scattering amplitudes of "deformations" of General Relativity, at least for the low particle numbers that we...
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
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.
Quantum Yang-Mills field theory
Frasca, Marco
2017-01-01
We show that the Dyson-Schwinger set of equations for the Yang-Mills theory can be exactly solved till the two-point function. This is obtained given a set of nonlinear waves solving the classical equations of motion. Translation invariance is maintained by the proper choice of the solution of the equation for the two-point function as devised by Coleman. The computation of the Dyson-Schwinger equations is performed in the same way as devised by Bender, Milton and Savage providing a set of partial differential equations whose proof of existence of the solutions is standard. So, the correlation functions of the theory could be proved to exist and the two-point function manifests a mass gap.
Band Structure in Yang-Mills Theories
Bachas, Constantin
2016-01-01
We show how Yang-Mills theory on $S^3\\times R$ can exhibit a spectrum with continuous bands if coupled either to a topological 3-form gauge field, or to a dynamical axion with heavy Peccei-Quinn scale. The basic mechanism consists in associating winding histories to a bosonic zero mode whose role is to convert a circle in configuration space into a helix. The zero mode is, respectively, the holonomy of the 3-form field or the axion momentum. In these models different theta sectors coexist but are not mixed by local operators. Our analysis sheds light on, and extends Seiberg's proposal for modifying the topological sums in quantum field theories. It refutes a recent claim that $B+L$ violation at LHC is unsuppressed.
Perturbations of the Yang-Mills field in the universe
Wen Zhao
2009-01-01
It has been suggested that the Yang-Mills (YM) field can be a kind of candidate for the inflationary field at high energy scales or dark energy at very low energy scales, which can naturally give the equation of state -1 <ω< 0 or ω<-1. We discuss the zero order and first order Einstein equations and YM field kinetic energy equations of the free YM field models. From the zero order equations, we find that ω+1 ∝α-2, from which it follows that the equation of state of the YM field always goes to - 1, independent of the initial conditions. By solving the first order Einstein equations and the YM field equations, we find that in the YM field inflationary models, the scale-invariant primordial perturbation power spectrum cannot be generated. Therefore, only using this kind of YM field is not enough to account for inflationary sources. However, as a kind of candidate for dark energy, the YM field has the 'sound speed' cs2 = -1/3 < 0, which makes the perturbation φ have a damping behavior at large scales. This provides a way to distinguish the YM field dark energy models from other kinds of models.
The Parisi-Sourlas Mechanism in Yang-Mills Theory?
Magpantay, J A
2000-01-01
The Parisi-Sourlas mechanism is exhibited in pure Yang-Mills theory. Using the new scalar degrees of freedom derived from the non-linear gauge condition, we show that the non-perturbative sector of Yang-Mills theory is equivalent to a 4D O(1,3) sigma model in a random field. We then show that the leading term of this equivalent theory is invariant under supersymmetry transformations where (x^{2}+\\thetabar\\theta) is unchanged. This leads to dimensional reduction proving the equivalence of the non-perturbative sector of Yang-Mills theory to a 2D O(1,3) sigma model.
Noncommutative Yang-Mills in IIB Matrix Model
Aoki, H; Iso, S; Kawai, H; Kitazawa, Y; Tada, T
2000-01-01
We show that twisted reduced models can be interpreted as noncommutative Yang-Mills theory. Based upon this correspondence, we obtain noncommutative Yang-Mills theory with D-brane backgrounds in IIB matrix model. We propose that IIB matrix model with D-brane backgrounds serve as a concrete definition of noncommutative Yang-Mills. We investigate D-instanton solutions as local excitations on D3-branes. When instantons overlap, their interaction can be well described in gauge theory and AdS/CFT correspondence. We show that IIB matrix model gives us the consistent potential with IIB supergravity when they are well separated.
Yang-Mills Instanton Sheaves with Arbitrary Topological Charges
Lai, Sheng-Hong; Lai, I-Hsun
2016-01-01
We use a set of ADHM 3-instanton data to systematically construct a class of SU(2) Yang-Mills instanton solutions with arbitrary topological charges. Moreover, by using the biquaternion calculation with biconjugation operation developed recently, these new ADHM data are used to construct a class of SL(2,C) Yang-Mills instanton sheaves on CP^3 with arbitrary topological charges k greater than 3. This result extends the previous construction of Yang-Mills 2-instanton sheaves to arbitrary higher k-instanton sheaves.
Light Dilaton at Fixed Points and Ultra Light Scale Super Yang Mills
Antipin, Oleg; Mojaza, Matin; Sannino, Francesco
2012-01-01
We investigate the infrared dynamics of a nonsupersymmetric SU(X) gauge theory featuring an adjoint fermion, Nf Dirac flavors and an Higgs-like complex Nf x Nf scalar which is a gauge singlet. We first establish the existence of an infrared stable perturbative fixed point and then investigate...... the spectrum near this point. We demonstrate that this theory naturally features a light scalar degree of freedom to be identified with the dilaton and elucidate its physical properties. We compute the spectrum and demonstrate that at low energy the nonperturbative part of the spectrum of the theory is the one...... of pure supersymmetric Yang-Mills. We can therefore determine the exact nonperturbative fermion condensate and deduce relevant properties of the nonperturbative spectrum of the theory. We also show that the intrinsic scale of super Yang-Mills is exponentially smaller than the scale associated...
Infra-red structure of Yang-Mills theories
Cvitanovic, P
1976-01-01
An analysis of QCD magnetic moment shows that all infra-red divergences are contained in the coupling constant renormalization. They are controlled by the renormalization function beta for the pure Yang-Mills field. (21 refs).
Cylindrically symmetric Einstein-Yang-Mills-Higgs gauge configurations.
Mondaini, R. P.
1985-02-01
Two solutions are obtained for coupled Einstein-Yang-Mills-Higgs fields with cylindrical symmetry and rigid rotation. The Higgs fields are responsible for the creation of singularities and infinite energy densities at the cylinder's axis.
Gravity as the square of Yang-Mills?
Borsten, L
2016-01-01
In these lectures we review how the symmetries of gravitational theories may be regarded as originating from those of "Yang-Mills squared". We begin by motivating the idea that certain aspects of gravitational theories can be captured by the product, in some sense, of two distinct Yang-Mills theories, particularly in the context of scattering amplitudes. We then introduce a concrete dictionary for the covariant fields of (super)gravity in terms of the product of two (super) Yang-Mills theories. The dictionary implies that the symmetries of each (super) Yang-Mills factor generate the symmetries of the corresponding (super)gravity theory: general covariance, $p$-form gauge invariance, local Lorentz invariance, local supersymmetry, R-symmetry and U-duality.
Exact solutions for classical Yang-Mills fields
2014-01-01
We provide a set of exact solutions of the classical Yang-Mills equations. They have the property to satisfy a massive dispersion relation and hold in all gauges. These solutions can be used to describe the vacuum of the quantum Yang-Mills theory and so, they provide a general framework to build a quantum field theory. The components of the field become separated on a generic gauge but are all equal just in the Lorenz (Landau) gauge.
A QCD Model Using Generalized Yang-Mills Theory
WANG Dian-Fu; SONG He-Shan; KOU Li-Na
2007-01-01
Generalized Yang-Mills theory has a covariant derivative,which contains both vector and scalar gauge bosons.Based on this theory,we construct a strong interaction model by using the group U(4).By using this U(4)generalized Yang-Mills model,we also obtain a gauge potential solution,which can be used to explain the asymptotic behavior and color confinement.
On maximally supersymmetric Yang-Mills theories
Movshev, M
2004-01-01
We consider ten-dimensional supersymmetric Yang-Mills theory (10D SUSY YM theory) and its dimensional reductions, in particular, BFSS and IKKT models. We formulate these theories using algebraic techniques based on application of differential graded Lie algebras and associative algebras as well as of more general objects, L_{\\infty}- and A_{\\infty}- algebras. We show that using pure spinor formulation of 10D SUSY YM theory equations of motion and isotwistor formalism one can interpret these equations as Maurer-Cartan equations for some differential Lie algebra. This statement can be used to write BV action functional of 10D SUSY YM theory in Chern-Simons form. The differential Lie algebra we constructed is closely related to differential associative algebra Omega of (0, k)-forms on some supermanifold; the Lie algebra is tensor product of Omega and matrix algebra . We construct several other algebras that are quasiisomorphic to Omega and, therefore, also can be used to give BV formulation of 10D SUSY YM theory...
Simulations of supersymmetric Yang-Mills theory
Demmouche, K.; Farchioni, F.; Ferling, A.; Muenster, G.; Wuilloud, J. [Muenster Univ. (Germany); Montvay, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Scholz, E.E. [Fermi National Accelerator Lab., Batavia, IL (United States)
2009-11-15
Results of a numerical simulation concerning the low-lying spectrum of four-dimensional N = 1 SU(2) Supersymmetric Yang-Mills (SYM) theory on the lattice with light dynamical gluinos are reported. We use the tree-level Symanzik improved gauge action and Wilson fermions with stout smearing of the gauge links in the Wilson-Dirac operator. The configurations are produced with the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) algorithm. We performed simulations on lattices up to a size of 24{sup 3}.48 at {beta}=1.6. Using QCD units with the Sommer scale being set to r{sub 0}=0.5 fm, the lattice spacing is about a {approx_equal}0.09 fm, and the spatial extent of the lattice corresponds to 2.1 fm to control finite size effects. At the lightest simulated gluino mass our results indicate a mass for the lightest gluino-glue bound state, which is considerably heavier than the values obtained for its possible superpartners. Whether supermultiplets are formed remains to be studied in upcoming simulations. (orig.)
Curving Yang-Mills-Higgs Gauge Theories
Kotov, Alexei
2015-01-01
Established fundamental physics can be described by fields, which are maps. The source of such a map is space-time, which can be curved due to gravity. The map itself needs to be curved in its gauge field part so as to describe interaction forces like those mediated by photons and gluons. In the present article, we permit non-zero curvature also on the internal space, the target of the field map. The action functional and the symmetries are constructed in such a way that they reduce to those of standard Yang-Mills-Higgs (YMH) gauge theories precisely when the curvature on the target of the fields is turned off. For curved targets one obtains a new theory, a curved YMH gauge theory. It realizes in a mathematically consistent manner an old wish in the community: replacing structures constants by functions depending on the scalars of the theory. In addition, we provide a simple 4d toy model, where the gauge symmetry is abelian, but turning off the gauge fields, no rigid symmetry remains---another possible manife...
Generalisation of the Yang-Mills Theory
Savvidy, George
2015-01-01
We suggest an extension of the gauge principle which includes tensor gauge fields. In this extension of the Yang-Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The proposed extension is essentially based on the extension of the Poincar\\'e algebra and the existence of an appropriate transversal representations. The invariant Lagrangian is expressed in terms of new higher-rank field strength tensors. It does not contain higher derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with a dimensionless coupling constant. We calculated the scattering amplitudes of non-Abelian tensor gauge bosons at tree level, as well as their one-loop contribution into the Callan-Symanzik beta function. This contribution is negative and corresponds to the asymptotically free theory. Considering the contribution of tensorgluons of all spins into the beta function we found that it is leading to the theo...
Yang-Mills-Vlasov system in the temporal gauge. Systeme de Yang-Mills-Vlasov en jauge temporelle
Choquet-Bruhat, Y.; Noutchegueme, N. (Paris-6 Univ., 75 (FR))
1991-01-01
We prove a local in time existence theorem of a solution of the Cauchy problem for the Yang-Mills-Vlasov integrodifferential system. Such equations govern the evolution of plasmas, for instance of quarks and gluons (quagmas), where non abelian gauge fields and Yang-Mills charges replace the usual electromagnetic field and electric charge. We work with the temporal gauge and use functional spaces with appropriate weight on the momenta, but no fall off is required in the space direction.
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 Connections On Orientable and Nonorientable Surfaces
Ho, Nan-Kuo
2007-01-01
In math.SG/0605587, we studied Yang-Mills functional on the space of connections on a principal G_R-bundle over a closed, connected, nonorientable surface, where G_R is any compact connected Lie group. In this sequel, we generalize the discussion in "The Yang-Mills equations over Riemann surfaces" by Atiyah and Bott, and math.SG/0605587. We obtain explicit descriptions (as representation varieties) of Morse strata of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups SO(n) and Sp(n). It turns out to be quite different from the unitary case. In the orientable case, we give a slightly modified version of Laumon and Rapoport's solution to the Atiyah-Bott recursion relation, and use it to write down explicit formulas of rational equivariant Poincar\\'{e} series of the top stratum for SO(n) and Sp(n).
Exact, Schwarzschild-like solution for Yang-Mills theory
Singleton, D.
1995-04-01
Exploiting the connection between general relativity and Yang-Mills theory an exact, Schwarzchild-like solution is given for an SU(N) gauge field coupled to a scalar field in the Bogomolny, Prasad, Sommerfield limit. The SU(2) solution is found using the second order Euler-Lagrange formalism, while the SU(N) generalization is given using the first order Bogomolny formalism. In analogy with the Schwarzschild solution of general relativity, these Yang-Mills solutions possess an event horizon with respect to the SU(N) charge. It is conjectured that this may be the confinement mechanism for QCD, since just as a Schwarzschild black hole will permanently confine anything which carries the charge of general relativity (mass-energy), so this Yang-Mills solution will confine any particle which carries the SU(N) charge.
't Hooft Loops, Electric Flux Sectors and Confinement in SU(2) Yang-Mills Theory
De Forcrand, Philippe; Forcrand, Philippe de; Smekal, Lorenz von
2002-01-01
We use 't Hooft loops of maximal size on finite lattices to calculate the free energy in the sectors of SU(2) Yang-Mills theory with fixed electric flux as a function of temperature and (spatial) volume. Our results provide evidence for the mass gap. The confinement of electric fluxes in the low temperature phase and their condensation in the high temperature phase are demonstrated. In a surprisingly large scaling window around criticality, the transition is quantitatively well described by universal exponents and amplitude ratios relating the properties of the two phases.
Global symmetries of Yang-Mills squared in various dimensions
Anastasiou, A. [Theoretical Physics, Blackett Laboratory, Imperial College London,London SW7 2AZ (United Kingdom); Borsten, L. [Theoretical Physics, Blackett Laboratory, Imperial College London,London SW7 2AZ (United Kingdom); School of Theoretical Physics, Dublin Institute for Advanced Studies,10 Burlington Road, Dublin 4 (Ireland); Hughes, M.J. [Theoretical Physics, Blackett Laboratory, Imperial College London,London SW7 2AZ (United Kingdom); Nagy, S. [Theoretical Physics, Blackett Laboratory, Imperial College London,London SW7 2AZ (United Kingdom); Department of Mathematics, Instituto Superior Técnico,Av. Rovisco Pais, 1049-001 Lisbon (Portugal)
2016-01-25
Tensoring two on-shell super Yang-Mills multiplets in dimensions D≤10 yields an on-shell supergravity multiplet, possibly with additional matter multiplets. Associating a (direct sum of) division algebra(s) D with each dimension 3≤D≤10 we obtain a formula for the supergravity U-duality G and its maximal compact subgroup H in terms of the internal global symmetry algebras of each super Yang-Mills theory. We extend our analysis to include supergravities coupled to an arbitrary number of matter multiplets by allowing for non-supersymmetric multiplets in the tensor product.
All tree amplitudes of supersymmetric Einstein-Yang-Mills theory
Adamo, Tim; Roehrig, Kai A; Skinner, David
2015-01-01
We present a new formula for all tree amplitudes in four dimensional supergravity coupled to super Yang-Mills. Like the Cachazo-He-Yuan formula, our expression is supported on solutions of the scattering equations, but with momenta written in terms of spinor helicity variables. Supersymmetry and parity are both manifest. In the pure gravity and pure Yang-Mills sectors, it reduces to the known twistor-string formulae. We show that the formula behaves correctly under factorization. We sketch how these amplitudes may be obtained from a four-dimensional (ambi)twistor string.
Field-dependent BRST transformations in Yang-Mills theory
Lavrov, Peter M
2013-01-01
We find an explicit form for the Jacobian of arbitrary field-dependent BRST transformations in Yang-Mills theory. For the functional-integral representation of the (gauge-fixed) Yang-Mills vacuum functional, such transformations merely amount to a precise change in the gauge-fixing functional. This proves the independence of the vacuum functional under any field-dependent BRST transformation. We also give a formula for the transformation parameter functional which generates a prescribed change of gauge and evaluate it for connecting two arbitrary R_xi gauges.
Field-dependent BRST transformations in Yang-Mills theory
Lavrov, Peter M.; Lechtenfeld, Olaf
2013-10-01
We find an explicit form for the Jacobian of arbitrary field-dependent BRST transformations in Yang-Mills theory. For the functional-integral representation of the (gauge-fixed) Yang-Mills vacuum functional, such transformations merely amount to a precise change in the gauge-fixing functional. This proves the independence of the vacuum functional under any field-dependent BRST transformation. We also give a formula for the transformation parameter functional which generates a prescribed change of gauge and evaluate it for connecting two arbitrary Rξ gauges.
Equivariance on Discrete Space and Yang-Mills-Higgs Model
Ikemori, Hitoshi; Matsui, Yoshimitsu; Otsu, Hideharu; Sato, Toshiro
2015-01-01
We introduce the basic equivariant quantity $Q$ in the gauge theory on the noncommutative descrete $Z_{2}$ space, which plays an important role for the equivariant dimensional reduction. If the gauge configuration of the ground state on the extra dimensional space is described by the equivariant $Q$, then the extra dimensional space is invisible. Especially, using the equivariance principle, we show that the Yang-Mills theory on $R^{2}\\times Z_{2}$ space is equivalent to the Yang-Mills-Higgs model on $R^{2}$ space. It can be said that this model is the simplest model of this type.
Perturbation Theory of Massive Yang-Mills Fields
Veltman, M.
1968-08-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.
Phase structure of lattice N=4 super Yang-Mills
Catterall, Simon; Damgaard, Poul H.; DeGrand, Thomas;
2012-01-01
We make a first study of the phase diagram of four-dimensional N = 4 super Yang-Mills theory regulated on a space-time lattice. The lattice formulation we employ is both gauge invariant and retains at all lattice spacings one exactly preserved supersymmetry charge. Our numerical results are consi...
Yang-Mills analogues of the Immirzi ambiguity
Gambini, R; Pullin, J
1999-01-01
We draw parallels between the recently introduced ``Immirzi ambiguity'' of the Ashtekar-like formulation of canonical quantum gravity and other ambiguities that appear in Yang-Mills theories, like the $\\theta$ ambiguity. We also discuss ambiguities in the Maxwell case, and implication for the loop quantization of these theories.
Internal Structure of Einstein-Yang-Mills Black Holes
Donets, E. E.; Gal'tsov, D. V.; Zotov, M. Yu.
1996-01-01
It is shown that a generic black hole solution of the SU(2) Einstein-Yang-Mills equations develops a new type of an infinitely oscillating behavior near the singularity. Only for certain discrete values of the event horizon radius exceptional solutions exist, possessing an inner structure of the Schwarzschild or Reissner-Nordstrom type.
Internal Structure of Einstein-Yang-Mills Black Holes
Donets, E E; Zotov, M Yu
1996-01-01
Interior solutions for the SU(2) Einstein-Yang-Mills black holes are investigated. It is found that generically the metric does not possess inner Cauchy horizons and infinitely oscillates near the singularity. However, for certain discrete radii of the event horizon exceptional solutions exist with an inner structure of the Schwarzschild (n=1) or Reissner--Nordstrom (n=2,3,...) type.
Super Yang-Mills theory from nonlinear supersymmetry
Shima, Kazunari, E-mail: shima@sit.ac.j [Laboratory of Physics, Saitama Institute of Technology Fukaya, Saitama 369-0293 (Japan); Tsuda, Motomu, E-mail: tsuda@sit.ac.j [Laboratory of Physics, Saitama Institute of Technology Fukaya, Saitama 369-0293 (Japan)
2010-04-05
The relation between a nonlinear supersymmetric (NLSUSY) theory and a SUSY Yang-Mills (SYM) theory is studied for N=3 SUSY in two-dimensional space-time. We explicitly show the NL/L SUSY relation for the (pure) SYM theory by means of cancellations among Nambu-Goldstone fermion self-interaction terms.
Coset space dimensional reduction of Einstein-Yang-Mills theory
Chatzistavrakidis, A. [Institute of Nuclear Physics, NCSR Demokritos, 15310 Athens (Greece); Physics Department, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece); Manousselis, P. [Physics Department, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece); Department of Engineering Sciences, University of Patras, 26110 Patras (Greece); Prezas, N. [Theory Unit, Physics Department, 1211 Geneva (Switzerland); Zoupanos, G.
2008-04-15
In the present contribution we extend our previous work by considering the coset space dimensional reduction of higher-dimensional Einstein-Yang-Mills theories including scalar fluctuations as well as Kaluza-Klein excitations of the compactification metric and we describe the gravity-modified rules for the reduction of non-abelian gauge theories. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
5D Maximally Supersymmetric Yang-Mills on the Lattice
Joseph, Anosh
2016-01-01
We provide details of the lattice construction of five-dimensional maximally supersymmetric Yang-Mills theory. The lattice theory is supersymmetric, gauge invariant and free from spectrum doublers. Such a supersymmetric lattice formulation is interesting as it can be used for non-perturbative explorations of the five-dimensional theory, which has a known gravitational dual.
S-duality in N=4 Yang-Mills theories
Girardello, L; Porrati, Massimo; Zaffaroni, A
1995-01-01
Evidence in favor of SL(2,Z) S-duality in N=4 supersymmetric Yang-Mills theories in four dimensions and with general compact, simple gauge groups is presented. (Contribution to the Proceedings of the Strings '95 conference, March 13-18, 1995, USC, and the Proceedings of the Trieste Conference on S-Duality and Mirror Symmetry June 5-9, 1995.)
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.
Eigenvalue spectrum of lattice N=4 super Yang-Mills
Weir, D.; Catterall, S.; Mehta, D. B.
We present preliminary results for the eigenvalue spectrum of four-dimensional ${\\cal N}=4$ super Yang-Mills theory on the lattice. In particular, by studying the the spectral density a measurement of the anomalous dimension is made and found to be consistent with zero.
Lagrangian multiplier and massive Yang-Mills fields
Li, Z.P.
1982-09-01
If we give appropriate constraint to the gauge invariant Lagrangian, the variation principle of the action convert to the variational problems with subsidiary condition. The effective Lagrangian which contains Lagrangian multiplier may have the mass term of the mesons. In that case we obtain naturally the massive Yang-Mills fields which was discussed by Nakanishi.
Perturbation theory of massive Yang-Mills fields
Veltman, M.J.G.
1968-01-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Primitive diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possib
Topological susceptibility for the SU(3) Yang--Mills theory
Del Debbio, Luigi; Giusti, Leonardo; Pica, Claudio
2004-01-01
We present the results of a computation of the topological susceptibility in the SU(3) Yang--Mills theory performed by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3), which corresponds to c...
Spinors, strings, integrable models, and decomposed Yang-Mills theory
Ioannidou, Theodora; Jiang, Ying; Niemi, Antti J.
2014-07-01
This paper deals with various interrelations between strings and surfaces in three-dimensional ambient space, two-dimensional integrable models, and two-dimensional and four-dimensional decomposed SU(2) Yang-Mills theories. Initially, a spinor version of the Frenet equation is introduced in order to describe the differential geometry of static three-dimensional stringlike structures. Then its relation to the structure of the su_(2) Lie algebra valued Maurer-Cartan one-form is presented, while by introducing time evolution of the string a Lax pair is obtained, as an integrability condition. In addition, it is shown how the Lax pair of the integrable nonlinear Schrödinger equation becomes embedded into the Lax pair of the time extended spinor Frenet equation, and it is described how a spinor-based projection operator formalism can be used to construct the conserved quantities, in the case of the nonlinear Schrödinger equation. Then the Lax pair structure of the time extended spinor Frenet equation is related to properties of flat connections in a two-dimensional decomposed SU(2) Yang-Mills theory. In addition, the connection between the decomposed Yang-Mills and the Gauß-Codazzi equation that describes surfaces in three-dimensional ambient space is presented. In that context the relation between isothermic surfaces and integrable models is discussed. Finally, the utility of the Cartan approach to differential geometry is considered. In particular, the similarities between the Cartan formalism and the structure of both two-dimensional and four-dimensional decomposed SU(2) Yang-Mills theories are discussed, while the description of two-dimensional integrable models as embedded structures in the four-dimensional decomposed SU(2) Yang-Mills theory are presented.
Reformulations of the Yang-Mills theory toward quark confinement and mass gap
Kondo, Kei-Ichi; Shinohara, Toru [Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522 (Japan); Kato, Seikou [Fukui National College of Technology, Sabae 916-8507 (Japan); Shibata, Akihiro [Computing Research Center, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801 (Japan)
2016-01-22
We propose the reformulations of the SU (N) Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the SU (N) Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulations can be combined with the SU (N) extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the SU (N) Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole with the stability group U (N− 1). This suggests the non-Abelian dual superconductivity picture for quark confinement. This should be compared with the maximal option: the restricted field is Abelian and involves only the Abelian magnetic monopoles with the stability group U(1){sup N−1}, just like the Abelian projection. We give some applications of this reformulation, e.g., the stability for the homogeneous chromomagnetic condensation of the Savvidy type, the large N treatment for deriving the dimensional transmutation and understanding the mass gap, and also the numerical simulations on a lattice which are given by Dr. Shibata in a subsequent talk.
Dark Energy Coupled with Relativistic Dark Matter in Accelerating Universe
张杨
2003-01-01
Recent observations favour an accelerating Universe dominated by the dark energy. We take the effective YangMills condensate as the dark energy and couple it to a relativistic matter which is created by the decaying condensate. The dynamic evolution has asymptotic behaviour with finite constant energy densities, and the fractional densities Ω∧～ 0.7 for dark energy and Ωm ～ 0.3 for relativistic matter are achieved at proper values of the decay rate. The resulting expansion of the Universe is in the de Sitter acceleration.
Exact solutions for classical Yang-Mills fields
Frasca, Marco
2014-01-01
Some years ago we displayed a set of classical solutions for the classical Yang-Mills field theory having the property to satisfy a dispersion relation typical of a massive theory. But such solutions seemed to be exact only in the Landau gauge making all the argument an asymptotic one for the most general case of a generic gauge. These solutions can be used to describe the vacuum of the quantum Yang-Mills theory and so, to prove that they are always exact can grant a general framework to build a quantum field theory. Here we show that these solutions are always exact changing just the normalization factor. The components of the field become separated on a generic gauge being all equal just in the Landau gauge.
Einstein-Yang-Mills solitons towards new degrees of freedom
Galtsov, D V
1998-01-01
A recent progress in obtaining non-spherical and non-static solitons in the four-dimensional Einstein--Yang--Mills (EYM) theory is discussed, and a non-perturbative formulation of the stationary axisymmetric problem is attempted. First a 2D dilaton gravity model is derived for the spherically symmetric time-dependent configurations. Then a similar Euclidean representation is constructed for the stationary axisymmetric non-circular SU(2) EYM system using the (2+1)+1 reduction scheme suggested by Maeda, Sasaki, Nakamura and Miyama. The crucial role in this reduction is played by the extra terms entering the reduced Yang--Mills and Kaluza--Klein two-forms similarly to Chern--Simons terms in the theories with higher rank antisymmetric tensor fields. We also derive a simple 2D action describing static axisymmetric magnetic EYM configurations and discuss a possibility of existence of cylindrical EYM sphalerons.
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...
(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 moduli space in the adiabatic limit
Lechtenfeld, Olaf
2015-01-01
We consider the Yang-Mills equations for a matrix gauge group $G$ inside the future light cone of 4-dimensional Minkowski space, which can be viewed as a Lorentzian cone $C(H^3)$ over the 3-dimensional hyperbolic space $H^3$. Using the conformal equivalence of $C(H^3)$ and the cylinder $R\\times H^3$, we show that, in the adiabatic limit when the metric on $H^3$ is scaled down, classical Yang-Mills dynamics is described by geodesic motion in the infinite-dimensional group manifold $C^\\infty (S^2_\\infty,G)$ of smooth maps from the boundary 2-sphere $S^2_\\infty=\\partial H^3$ into the gauge group $G$.
Towards a Loop Quantum Gravity and Yang-Mills unification
Alexander, Stephon, E-mail: stephonalexander@mac.com [Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755 (United States); Department of Physics and Astronomy, Haverford College, Haverford, PA 19041 (United States); Department of Physics, Princeton University, NJ 08544 (United States); Institute for Gravitation and the Cosmos, Department of Physics, Penn State, University Park, PA 16802 (United States); Marciano, Antonino [Department of Physics and Astronomy, Haverford College, Haverford, PA 19041 (United States); Department of Physics, Princeton University, NJ 08544 (United States); Tacchi, Ruggero Altair [Department of Physics, University of California, Davis, CA 95616 (United States)
2012-09-19
We propose a new method of unifying gravity and the Standard Model by introducing a spin-foam model. We realize a unification between an SU(2) Yang-Mills interaction and 3D general relativity by considering a constrained Spin(4){approx}SO(4) Plebanski action. The theory is quantized a la spin-foam by implementing the analogue of the simplicial constraints for the Spin(4) symmetry, providing a way to couple Yang-Mills fields to spin-foams. A natural 4D extension of the theory is introduced. We also present a way to recover 2-point correlation functions between the connections as a first way to implement scattering amplitudes between particle states, aiming to connect Loop Quantum Gravity to new physical predictions.
HYM-flation: Yang-Mills cosmology with Horndeski coupling
Davydov, E.; Gal'tsov, D.
2016-02-01
We propose new mechanism for inflation using classical SU (2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang-Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflationary scenario, in which the Planck-scale YM-generated inflation naturally prepares the desired initial conditions for the GUT-scale Higgs inflation.
HYM-flation: Yang-Mills cosmology with Horndeski coupling
Davydov, E
2016-01-01
We propose new mechanism for inflation using classical SU(2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang-Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflationary scenario, in which the Planck-scale YM-generated inflation naturally prepares the desired initial conditions for the GUT-scale Higgs inflation.
Currents and anomalies in topological Yang-Mills theory
Dahmen, H. D.; Marculescu, S.; Szymanowski, L.
1992-09-01
The quantum properties of topological Yang-Mills theory are investigated in the light of the N = 2 supersymmetry observed in flat space. We construct a unique system of covariantly (partially) conserved currents which develop anomalies while preserving BRS invariance of the theory. In particular, the one-loop renormalized energy-momentum tensor is free of purely gravitational contributions and can be written as a BRS variation. We study the consequences of changing the renormalization prescriptions inherited from the N = 2 supersymmetry to those consistent with BRS. Most of our conclusions are verified by explicit calculations. As a byproduct we derive the formula of Atiyah, Hitchin and Singer for the dimension of the moduli space of self-dual Yang-Mills fields. Finally strong arguments are given that the full system of Donaldson polynomials and the quantum BRS current are not renormalized beyond one-loop.
Special Geometries Emerging from Yang-Mills Type Matrix Models
Blaschke, Daniel N
2011-01-01
I review some recent results which demonstrate how various geometries, such as Schwarzschild and Reissner-Nordstroem, can emerge from Yang-Mills type matrix models with branes. Furthermore, explicit embeddings of these branes as well as appropriate Poisson structures and star-products which determine the non-commutativity of space-time are provided. These structures are motivated by higher order terms in the effective matrix model action which semi-classically lead to an Einstein-Hilbert type action.
Continuous Family of Einstein-Yang-Mills Wormholes
Donets, E E
1992-01-01
It is shown that for some particular value of the cosmological constant depending on the gauge coupling constant a continuous one-parameter family of Einstein-Yang-Mills wormholes exists which interpolates between the instanton and the gravitating meron solutions. In contradistinction with the previously known solutions the topological charge of these wormholes is not quantized. For all of them the contribution of gravity to the action exactly cancels that of the gauge field.
A Classical Solution of Massive Yang-Mills Fields
Mogami, Tsuguo
2016-01-01
Recent researches on the solution of Schwinger-Dyson equations, as well as lattice simulations of pure QCD, suggest that the gluon propagator is massive. In this letter, we assume that the classical counterpart of this massive gluon field may be represented with the equation of motion for Yang-Mills theory with a mass term added. A new classical solution is given for this equation. It is discussed that this solution may have some role in confinement.
Regge trajectories in {N} = 2 supersymmetric Yang-Mills theory
Córdova, Clay
2016-09-01
We demonstrate that {N} = 2 supersymmetric non-Abelian gauge theories have towers of BPS particles obeying a Regge relation, J ˜ m 2, between their angular momenta, J, and their masses, m. For SU( N) Yang-Mills theories, we estimate the slope of these Regge trajectories using a non-relativistic quiver quantum mechanics model. Along the way, we also prove various structure theorems for the quiver moduli spaces that appear in the calculation.
A Curious Relation Between Gravity and Yang-Mills Theories
Baulieu, L
2000-01-01
We find that Euclidian or Minkowski gravity in d dimensions can be formally expressed as the restriction to a slice of a supersymmetric Yang-Mills theory in d+1 dimensions with SO(d+1), SO(d,1) or SO(d-1,2) internal symmetry. We suggest that renormalization effects in the bulk imply a contraction of the latter symmetry into the Poincare group ISO(d) or ISO(d-1,1).
Dynamical CP violation of the generalized Yang-Mills model
WANG Dian-Fu; SUN Xiao-Yu; CHANG Xiao-Jing
2011-01-01
Starting from the generalized Yang-Mills model which contains, besides the vector part Vμ, also a scalar part S and a pseudoscalar part P. It is shown, in terms of the Nambu-Jona-Lasinio (NJL) mechanism,that CP violation can be realized dynamically. The combination of the generalized Yang-MiUs model and the NJL mechanism provides a new way to explain CP violation.
Multiscale Monte Carlo equilibration: pure Yang-Mills theory
Endres, Michael G; Detmold, William; Orginos, Kostas; Pochinsky, Andrew V
2015-01-01
We present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.
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.
Slavnov determinants, Yang-Mills structure constants, and discrete KP
Foda, O
2012-01-01
Using Slavnov's scalar product of a Bethe eigenstate and a generic state in closed XXZ spin-1/2 chains, with possibly twisted boundary conditions, we obtain determinant expressions for tree-level structure constants in 1-loop conformally-invariant sectors in various planar (super) Yang-Mills theories. When certain rapidity variables are allowed to be free rather than satisfy Bethe equations, these determinants become discrete KP tau-functions.
BRST symmetric gaugeon formalism for Yang-Mills fields
Koseki, M; Endo, R
1995-01-01
Yokoyama's gaugeon formalism is knwon to admit q-number gauge transformation. We introduce BRST symmetries into the formalism for the Yang-Mills gauge field. Owing to the BRST symmetry, Yokoyama's physical subsidiary conditions are replaced by a single condition of the Kugo-Ojima type. Our physical subsidiary condition is invariant under the q-number gauge transformation. Thus, our physical subspace is gauge invariant.
Asymptotic freedom of Yang-Mills theory with gravity
Folkerts, Sarah; Pawlowski, Jan M
2011-01-01
We study the high energy behaviour of Yang-Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.
Asymptotic freedom of Yang-Mills theory with gravity
Folkerts, Sarah, E-mail: Sarah.Folkerts@physik.uni-muenchen.de [Institut f. Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); Litim, Daniel F. [Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH (United Kingdom); Pawlowski, Jan M. [Institut f. Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); ExtreMe Matter Inst. EMMI, GSI, Planckstr. 1, 64291 Darmstadt (Germany)
2012-03-19
We study the behaviour of Yang-Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.
The local renormalization of super-Yang-Mills theories
Gillioz, Marc
2016-01-01
We show how to consistently renormalize $\\mathcal{N} = 1$ and $\\mathcal{N} = 2$ super-Yang-Mills theories in flat space with a local (i.e. space-time-dependent) renormalization scale in a holomorphic scheme. The action gets enhanced by a term proportional to derivatives of the holomorphic coupling. In the $\\mathcal{N} = 2$ case, this new action is exact at all orders in perturbation theory.
Magnetic Yang-Mills Theory of the Gluon Plasma
Baker, M
2009-01-01
We propose magnetic SU(N) pure gauge theory as an effective field theory describing the long distance nonperturbative magnetic response of the deconfined phase of Yang-Mills theory. The magnetic non-Abelian Lagrangian, unlike that of electrodynamics where there is exact electromagnetic duality, is not known explicitly, but here we regard the magnetic SU(N) Yang-Mills Lagrangian as the leading term in the long distance effective gauge theory of the plasma phase. In this treatment, which is applicable for a range of temperatures in the interval T_c < T < 3 T_c accessible in heavy ion experiments, formation of the magnetic energy profile around a spatial Wilson loop in the deconfined phase parallels the formation of an electric flux tube in the confined phase. We use the effective theory to calculate spatial Wilson loops and the magnetic charge density induced in the plasma by the corresponding color electric current loops. These calculations suggest that the deconfined phase of Yang-Mills theory has the p...
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.
New relations for Einstein-Yang-Mills amplitudes
Stieberger, Stephan; Taylor, Tomasz R.
2016-12-01
We obtain new relations between Einstein-Yang-Mills (EYM) amplitudes involving N gauge bosons plus a single graviton and pure Yang-Mills amplitudes involving N gauge bosons plus one additional vector boson inserted in a way typical for a gauge boson of a "spectator" group commuting with the group associated to original N gauge bosons. We show that such EYM amplitudes satisfy U(1) decoupling relations similar to Kleiss-Kuijf relations for Yang-Mills amplitudes. We consider a D-brane embedding of EYM amplitudes in the framework of disk amplitudes involving open and closed strings. A new set of monodromy relations is derived for mixed open-closed amplitudes with one closed string inserted on the disk world-sheet and a number of open strings at the boundary. These relations allow expressing the latter in terms of pure open string amplitudes and, in the field-theory limit, they yield the U(1) decoupling relations for EYM amplitudes.
New Results on N=4 SuperYang-Mills Theory
Baulieu, L; Baulieu, Laurent; Bossard, Guillaume
2005-01-01
The N=4 SuperYang--Mills theory is covariantly determined by a U(1) \\times SU(2) \\subset SL(2,R) \\times SU(2) internal symmetry and two scalar and one vector BRST topological symmetry operators. This determines an off-shell closed sector of N=4 SuperYang-Mills, with 6 generators, which is big enough to fully determine the theory, in a Lorentz covariant way. This reduced algebra derives from horizontality conditions in four dimensions. The horizontality conditions only depend on the geometry of the Yang-Mills fields. They also descend from a genuine horizontality condition in eight dimensions. In fact, the SL(2,R) symmetry is induced by a dimensional reduction from eight to seven dimensions, which establishes a ghost-antighost symmetry, while the SU(2) symmetry occurs by dimensional reduction from seven to four dimensions. When the four dimensional manifold is hyperKahler, one can perform a twist operation that defines the N=4 supersymmetry and its SL(2,H)\\sim SU(4) R-symmetry in flat space. (For defining a TQ...
Notes on theta dependence in holographic Yang-Mills
Bigazzi, Francesco [INFN - Sezione di Pisa,Largo B. Pontecorvo 3, I-56127 Pisa (Italy); Cotrone, Aldo L. [Dipartimento di Fisica e Astronomia, Università di Firenze and INFN - Sezione di Firenze,Via G. Sansone 1, I-50019 Sesto Fiorentino, Firenze (Italy); Sisca, Roberto [Università di Pisa, Dipartimento di Fisica “E. Fermi' ,Largo Bruno Pontecorvo 3, I-56127 Pisa (Italy)
2015-08-18
Effects of the θ parameter are studied in Witten’s model of holographic 4d Yang-Mills, where θ is the coefficient of the CP-breaking topological term. First, the gravity background, including the full backreaction of the RR form dual to the θ 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,θ) phase diagram — and the entanglement entropy. A simple rule is provided to derive the θ 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 θ regime, are given up to very few powers of θ{sup 2}. The corresponding holographic results agree qualitatively with available lattice data and signal an overall mass scale reduction by θ. Moreover, being exact in θ, they provide a benchmark for higher order corrections in Yang-Mills.
A global solution of the Einstein-Yang-Mills equation on the conformal space
LU; Qikeng(陆启铿)
2002-01-01
The method used to construct the SU(2) Yang-Mills field on a compactified Minkowski space-M(which is equivalent to the conformal space) is generalized to construct an SU(N)(N > 2) Yang-Mills fieldFjκ on M. It is proved that both Fjκ and the invariant metric tensor gjκ of M satisfy the Einstein-Yang-Mills equation. The case of N →∞ is also discussed.
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
Pereira, A.D. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Potsdam (Germany); UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); Sobreiro, R.F. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Sorella, S.P. [UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil)
2016-10-15
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi:10.1103/PhysRevD.92.045039. arXiv:1506.06995 [hepth], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions. (orig.)
Integrability in N=4 super Yang-Mills theory
Eden, B. [ITF and Spinoza Institute, University of Utrecht, Minnaertgebouw, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)
2008-10-15
We use the Bethe ansatz to calculate the cusp anomalous dimension in planar N=4 super Yang-Mills theory as an exact function of the coupling constant. The calculation allows us to fix the remaining ambiguities in the integrable system describing the spectrum of operators/string energy levels in the AdS/CFT correspondence. The cusp anomalous dimension is not affected by finite size effects, which in general remain ill-understood. We suggest a method for computing the lowest example of an anomalous dimension modified by such corrections.
Width of the confining string in Yang-Mills theory.
Gliozzi, F; Pepe, M; Wiese, U-J
2010-06-11
We investigate the transverse fluctuations of the confining string connecting two static quarks in (2+1)D SU(2) Yang-Mills theory using Monte Carlo calculations. The exponentially suppressed signal is extracted from the large noise by a very efficient multilevel algorithm. The resulting width of the string increases logarithmically with the distance between the static quark charges. Corrections at intermediate distances due to universal higher-order terms in the effective string action are calculated analytically. They accurately fit the numerical data.
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.
Super-Yang-Mills theories on S4 x R
Kim, Jungmin; Lee, Kimyeong; Park, Jaemo
2014-01-01
We construct super-Yang-Mills theories on S4 x R, S4 x S1 and S4 x interval with the field content of maximal SYM, coupled to boundary degrees in the last case. These theories provide building blocks of the `5d uplifts' of gauge theories on S4, obtained by compactifying the 6d (2,0) theory. We pay special attention to the N=2* theory on S4. We also explain how to construct maximal SYM on S5 x R, and clarify when SYM theories can be put on S^n x R.
Callan-Symanzik approach to infrared Yang-Mills theory
Weber Axel
2014-01-01
Full Text Available Dyson-Schwinger equations are the most common tool for the determination of the correlation functions of Landau gauge Yang-Mills theory in the continuum, in particular in the infrared regime. We shall argue that the use of Callan-Symanzik renormalization group equations has distinctive advantages over the Dyson-Schwinger equations, in particular for the vertex functions. We present a generalization of the infrared safe renormalization scheme proposed by Tissier and Wschebor in 2011. The comparison with the existing lattice data for the gluon and ghost propagators can be used to determine the most appropriate renormalization scheme.
Fate of Yang-Mills black hole in early Universe
Nakonieczny, Lukasz; Rogatko, Marek [Institute of Physics Maria Curie-Sklodowska University 20-031 Lublin, pl. Marii Curie-Sklodowskiej 1 (Poland)
2013-02-21
According to the Big Bang Theory as we go back in time the Universe becomes progressively hotter and denser. This leads us to believe that the early Universe was filled with hot plasma of elementary particles. Among many questions concerning this phase of history of the Universe there are questions of existence and fate of magnetic monopoles and primordial black holes. Static solution of Einstein-Yang-Mills system may be used as a toy model for such a black hole. Using methods of field theory we will show that its existence and regularity depend crucially on the presence of fermions around it.
A Curious Truncation of N=4 Yang-Mills
Basu, A; Sethi, S; Basu, Anirban; Sethi, Savdeep
2004-01-01
The coupling constant dependence of correlation functions of BPS operators in N=4 Yang-Mills can be expressed in terms of integrated correlation functions. We approximate these integrated correlators by using a truncated OPE expansion. This leads to differential equations for the coupling dependence. When applied to a particular sixteen point correlator, the coupling dependence we find agrees with the corresponding amplitude computed via the AdS/CFT correspondence. We conjecture that this truncation becomes exact in the large N and large 't Hooft coupling limit.
Ward identity implies recursion relations in Yang-Mills theory
Chen, Gang
2012-07-01
The Ward identity in gauge theory constrains the behavior of the amplitudes. We discuss the Ward identity for amplitudes with a pair of shifted lines with complex momenta. This will induce a recursion relation identical to Britto-Cachazo-Feng-Witten recursion relations at the finite poles of the complexified amplitudes. Furthermore, according to the Ward identity, it is also possible to transform the boundary term into a simple form, which can be obtained by a new recursion relation. For the amplitude with one off-shell line in pure Yang-Mills theory, we find this technique is effective for obtaining the amplitude even when there are boundary contributions.
Stabilizing Perturbative Yang-Mills Free Energy with Gribov Quantization
Fukushima, Kenji
2013-01-01
We evaluate the free energy of the Yang-Mills theory using the Gribov quantization that copes with non-perturbative resummation. The magnetic scale is automatically incorporated in the framework and we find it efficient to stabilize the perturbative expansion of the free energy. In the range of the temperature T=T_c~2T_c major uncertainty in our results comes from the non-perturbative running coupling that is adopted from the lattice simulation, while the convergence above 2T_c is impressively robust.
Maximally supersymmetric Yang-Mills on the lattice
Schaich, David
2015-01-01
We summarize recent progress in lattice studies of four-dimensional N=4 supersymmetric Yang--Mills theory and present preliminary results from ongoing investigations. Our work is based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, and we review a new procedure to regulate flat directions by modifying the moduli equations in a manner compatible with this supersymmetry. This procedure defines an improved lattice action that we have begun to use in numerical calculations. We discuss some highlights of these investigations, including the static potential and an update on the question of a possible sign problem in the lattice theory.
Transport coefficients in Yang-Mills theory and QCD
Strodthoff, Nils; Christiansen, Nicolai; Haas, Michael [Institut fuer Theoretische Physik, Heidelberg (Germany); Pawlowski, Jan M. [Institut fuer Theoretische Physik, Heidelberg (Germany); ExtreMe Matter Institute EMMI, Darmstadt (Germany)
2015-07-01
We calculate the shear viscosity over entropy density ratio η/s in Yang-Mills theory from the Kubo formula using an exact diagrammatic representation in terms of full propagators and vertices using gluon spectral functions as external input. We provide an analytic fit formula for the temperature dependence of η/s over the whole temperature range from a glueball resonance gas at low temperatures, to a high-temperature regime consistent with perturbative results. Subsequently we provide a first estimate for η/s in QCD.
Lectures on Supersymmetric Yang-Mills Theory and Integrable Systems
D'Hoker, Eric; Phong, D. H.
Introduction Supersymmetry and the Standard Model Supersymmetry and Unification of Forces Supersymmetric Yang-Mills Dynamics Supersymmetric Yang-Mills in 4 Dimensions Supersymmetry Algebra Massless Particle Representations Massive Particle Representations Field Contents of Supersymmetric Field Theories N = 1 Supersymmetric Lagrangians N = 1 Superfield Methods Irreducible Superfields of N = 1 General N = 1 Susy Lagrangians via Superfields Renormalizable N = 2,4 Susy Lagrangians N = 2 Superfield Methods: Unconstrained Superspace N = 2 Superfield Methods: Harmonic/Analytic Superspaces Seiberg-Witten Theory Wilson Effective Couplings and Actions Holomorphicity and Nonrenormalization Low Energy Dynamics of N = 2 Super-Yang-Mills Particle and Field Contents Form of the N = 2 Low Energy Effective Lagrangian Physical Properties of the Prepotential Electric-Magnetic Duality Monodromy via Elliptic Curves for SU(2) Gauge Group Physical Interpretation of Singularities Hypergeometric Function Representation More General Gauge Groups, Hypermultiplets Model of Riemann Surfaces Identifying Seiberg-Witten and Riemann Surface Data SU(N) Gauge Algebras, Fundamental Hypermultiplets Classical Gauge Algebras, Fundamental Hypermultiplets Mechanical Integrable Systems Lax Pairs with Spectral Parameter-Spectral Curves The Toda Systems The Calogero-Moser Systems for SU(N) Relation between Calogero-Moser and Toda for SU(N) Relations with KdV and KP Systems Calogero-Moser Systems for General Lie Algebras Scaling of Calogero-Moser to Toda for General Lie Algebras Calogero-Moser Lax Pairs for General Lie Algebras Lax Pairs with Spectral Parameter for Classical Lie Algebras The General Ansatz Lax Pairs for Untwisted Calogero-Moser Systems Lax Pairs for Twisted Calogero-Moser Systems Scaling Limits of Lax Pairs Super-Yang-Mills and Calogero-Moser Systems Correspondence of Seiberg-Witten and Integrable Systems Calogero-Moser and Seiberg-Witten Theory for SU(N) Four Fundamental Theorems Partial
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.
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.
Aspects of lattice N=4 supersymmetric Yang--Mills
Schaich, David
2015-01-01
Non-perturbative investigations of $\\mathcal N = 4$ supersymmetric Yang--Mills theory formulated on a space-time lattice have advanced rapidly in recent years. Large-scale numerical calculations are currently being carried out based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing. A recent development is the creation of an improved lattice action through a new procedure to regulate flat directions in a manner compatible with this supersymmetry, by modifying the moduli equations. In this proceedings I briefly summarize this new procedure and discuss the parameter space of the resulting improved action that is now being employed in numerical calculations.
Latest results from lattice N=4 supersymmetric Yang--Mills
Schaich, David; Damgaard, Poul H; Giedt, Joel
2016-01-01
We present some of the latest results from our numerical investigations of N=4 supersymmetric Yang--Mills theory formulated on a space-time lattice. Based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, we recently developed an improved lattice action that is now being employed in large-scale calculations. Here we update our studies of the static potential using this new action, also applying tree-level lattice perturbation theory to improve the analysis of the potential itself. Considering relatively weak couplings, we obtain results for the Coulomb coefficient that are consistent with continuum perturbation theory.
Topological susceptibility for the SU(3) Yang--Mills theory
Del Debbio, L; Pica, C; Debbio, Luigi Del; Giusti, Leonardo; Pica, Claudio
2005-01-01
We present the results of a computation of the topological susceptibility in the SU(3) Yang--Mills theory performed by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3), which corresponds to chi=(191 \\pm 5 MeV)^4 if F_K is used to set the scale. Our result supports the Witten--Veneziano explanation for the large mass of the eta'.
Loop formulation of supersymmetric Yang-Mills quantum mechanics
Steinhauer, Kyle
2014-01-01
We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.
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.
Supersymmetric Yang Mills Fields and Black Holes ; In Ten Dimensional Unified Field Theory
Patwardhan, Ajay
2007-01-01
The Ten dimensional Unified field theory has a 4 dimensional Riemannian spacetime and six dimensional Calabi Yau space structure. The supersymmetric Yang Mills fields and black holes are solutions in these theories. The formation of primordial black holes in early universe, the collapse to singularity of stellar black holes, the Hawking evaporation of microscopic black holes in LHC are topics of observational and theoretical interest. The observation of gamma ray bursts and creation of spectrum of particles and radiation of dark and normal matter occur due to primordial and microscopic black holes. The approach to singularity in black hole interior solutions, require the Bogoliubov transforms of SUSY YM fields in black hole geometries; both during formation and in evaporation. The Hawking effect of radiating black holes is applicable for all the fields. Invariants can be defined to give the conditions for these processes.
Dark matter and dark energy induced by condensates
Capolupo, Antonio
2016-01-01
It is shown that the vacuum condensate induced by many phenomena behaves as a perfect fluid which, under particular conditions, has zero or negative pressure. In particular, the condensates of thermal states, of fields in curved space and of mixed particles have been analyzed. It is shown that the thermal states with the cosmic microwave radiation temperature, the Unruh and the Hawking radiations give negligible contributions to the critical energy density of the universe, while the thermal vacuum of the intercluster medium could contribute to the dark matter, together with the vacuum energy of fields in curved space-time and of mixed neutrinos. Moreover, a component of the dark energy can be represented by the vacuum of axion-like particles mixed with photons and superpartners of neutrinos. The formal analogy among the systems characterized by the condensates can open new scenarios in the possibility to detect the dark components of the universe in table top experiments.
Dark Matter and Dark Energy Induced by Condensates
Antonio Capolupo
2016-01-01
Full Text Available It is shown that the vacuum condensate induced by many phenomena behaves as a perfect fluid which, under particular conditions, has zero or negative pressure. In particular, the condensates of thermal states of fields in curved space and of mixed particles have been analyzed. It is shown that the thermal states with the cosmic microwave radiation temperature and the Unruh and the Hawking radiations give negligible contributions to the critical energy density of the universe, while the thermal vacuum of the intercluster medium could contribute to the dark matter, together with the vacuum energy of fields in curved space-time and of mixed neutrinos. Moreover, a component of the dark energy can be represented by the vacuum of axion-like particles mixed with photons and superpartners of neutrinos. The formal analogy among the systems characterized by the condensates can open new scenarios in the possibility of detecting the dark components of the universe in table top experiments.
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...
Emergent Yang-Mills theories from universal extra dimensions
Chkareuli, J. L.; Kepuladze, Z.
2017-02-01
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 (5D) non-Abelian gauge theory is shown to lead to spontaneous violation of an underlying spacetime symmetry and generate vector pseudo-Goldstone modes as conventional four-dimensional (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 also appeared spontaneously broken to its diagonal subgroups. This breaking originates from the extra vector field components playing the role of some adjoint scalar field multiplet in the 4D spacetime. So, one naturally has the Higgs effect without a specially introduced scalar field multiplet. Remarkably, when applied to Grand Unified Theories (GUTs), this results in an automatic breakdown of emergent GUTs down to the Standard Model (SM) just at the 5D Lorentz violation scale M.
The Metric on the Space of Yang-Mills Configurations
Orland, P
1996-01-01
A distance function on the set of physical equivalence classes of Yang-Mills configurations considered by Feynman and by Atiyah, Hitchin and Singer is studied for both the $2+1$ and $3+1$-dimensional Hamiltonians. This set equipped with this distance function is a metric space, and in fact a Riemannian manifold as Singer observed. Furthermore, this manifold is complete. Gauge configurations can be used to parametrize the manifold. The metric tensor without gauge fixing has zero eigenvalues, but is free of ambiguities on the entire manifold. In $2+1$ dimensions the problem of finding the distance from any configuration to a pure gauge configuration is an integrable system of two-dimensional differential equations. A calculus of manifolds with singular metric tensors is developed and the Riemann curvature is calculated using this calculus. The Laplacian on Yang-Mills wave functionals has a slightly different form from that claimed earlier. In $3+1$-dimensions there are field configurations an arbitrarily large ...
Yang-Mills correlators across the deconfinement phase transition
Reinosa, U.; Serreau, J.; Tissier, M.; Tresmontant, A.
2017-02-01
We compute the finite temperature ghost and gluon propagators of Yang-Mills theory in the Landau-DeWitt gauge. The background field that enters the definition of the latter is intimately related with the (gauge-invariant) Polyakov loop and serves as an equivalent order parameter for the deconfinement transition. We use an effective gauge-fixed description where the nonperturbative infrared dynamics of the theory is parametrized by a gluon mass which, as argued elsewhere, may originate from the Gribov ambiguity. In this scheme, one can perform consistent perturbative calculations down to infrared momenta, which have been shown to correctly describe the phase diagram of Yang-Mills theories in four dimensions as well as the zero-temperature correlators computed in lattice simulations. In this article, we provide the one-loop expressions of the finite temperature Landau-DeWitt ghost and gluon propagators for a large class of gauge groups and present explicit results for the SU(2) case. These are substantially different from those previously obtained in the Landau gauge, which corresponds to a vanishing background field. The nonanalyticity of the order parameter across the transition is directly imprinted onto the propagators in the various color modes. In the SU(2) case, this leads, for instance, to a cusp in the electric and magnetic gluon susceptibilities as well as similar signatures in the ghost sector. We mention the possibility that such distinctive features of the transition could be measured in lattice simulations in the background field gauge studied here.
Thermodynamics of SU(2 quantum Yang-Mills theory and CMB anomalies
Hofmann Ralf
2014-04-01
-vortex loops in confining phases of SU(2 Yang-Mills theories neutrino mass mν solely arises by interactions with an environment. Cosmologically, the CMB represents this environment, and thus one would expect that mν = ξT where ξ = O(1. In this model cosmic neutrinos are a small dark-matter contribution, conserved only together with the CMB fluid, influencing Baryonic Acoustic Oscillations during CMB decoupling.
Effective Lagrangian of SU(2) Yang-Mills Theory in the Presence of Fermions
FAN Ji-Yang; JIANG Ying; ZHU Zhong-Yuan
2002-01-01
We derive the one-loop effective action of SU(2) Yang Mills theory in the presence of fermions in the lowenergy limit. This result is presented by separating the topological degrees, which describe the non-Abelian monopolesfrom the dynamical degrees of the gauge potential and integrate out all the dynamical degrees and fermions in SU(2)Yang-Mills theory.
N=2 SYM Action as a BRST Exact Term, Topological Yang Mills and Instantons
Ulker, K
2003-01-01
By defining an extended BRST operator that includes the chiral part of N=2 global supersymmetry, it is shown that the full N=2 off-shell Super Yang Mills Action can be represented as an exact BRST term. The action written in this form suggests that the fields of the Topological Yang Mills theory can be defined in terms of composite fields of supersymmetry ghosts and N=2 fields in a natural way. Topological Yang Mills theory is obtained from the ordinary Euclidean N=2 SYM directly as field redefinitions without using twisting procedure. With the help of these results, relation between the recent instanton calculations in N=2 Super Yang Mills and Topological Yang Mills theories is also discussed.
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.
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.
Covariant gauges without Gribov ambiguities in Yang-Mills theories
Serreau, Julien; Tresmontant, Andréas
2013-01-01
We propose a formulation of a certain class of nonlinear covariant gauges as an extremization procedure that can be implemented on the lattice. At high energies, where the Gribov ambiguities can be ignored, this reduces to the Curci-Ferrari-Delbourgo-Jarvis gauges. We further propose a continuum formulation in terms of a local action which is free of Gribov ambiguities and avoids the Neuberger zero problem of the standard Faddeev-Popov construction. This involves an averaging over Gribov copies with a nonuniform weight, which introduces a new gauge-fixing parameter. We show that the proposed gauge-fixed action is perturbatively renormalizable in four dimensions and we provide explicit expressions of the renormalization factors at one loop. We discuss the possible implications of the present proposal for the calculation of Yang-Mills correlators.
Lifting the Gribov ambiguity in Yang-Mills theories
Serreau, J., E-mail: serreau@apc.univ-paris7.fr [APC, AstroParticule et Cosmologie, Universite Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cite, 10, rue Alice Domon et Leonie Duquet, 75205 Paris Cedex 13 (France); Tissier, M. [LPTMC, Laboratoire de Physique Theorique de la Matiere Condensee, CNRS UMR 7600, Universite Pierre et Marie Curie, boite 121, 4 pl. Jussieu, 75252 Paris Cedex 05 (France)
2012-05-30
We propose a new one-parameter family of Landau gauges for Yang-Mills theories which can be formulated by means of functional integral methods and are thus well suited for analytic calculations, but which are free of Gribov ambiguities and avoid the Neuberger zero problem of the standard Faddeev-Popov construction. The resulting gauge-fixed theory is perturbatively renormalizable in four dimensions and, for what concerns the calculation of ghost and gauge field correlators, it reduces to a massive extension of the Faddeev-Popov action. We study the renormalization group flow of this theory at one-loop and show that it has no Landau pole in the infrared for some - including physically relevant - range of values of the renormalized parameters.
Lifting the Gribov ambiguity in Yang-Mills theories
Serreau, Julien
2012-01-01
We propose a new one-parameter family of Landau gauges for Yang-Mills theories which can be formulated by means of functional integral methods and are thus well suited for analytic calculations, but which are free of Gribov ambiguities and avoid the Neuberger zero problem of the standard Fadeev-Popov construction. The resulting gauge-fixed theory is perturbatively renormalizable in four dimensions and, for what concerns the calculation of ghost and gauge field correlators, it reduces to a massive extension of the Fadeev-Popov action. We study the renormalization group flow of this theory at one-loop and show that it has no Landau pole in the infrared for some - including physically relevant - range of values of the renormalized parameters.
Lifting the Gribov ambiguity in Yang-Mills theories
Serreau, J.; Tissier, M.
2012-05-01
We propose a new one-parameter family of Landau gauges for Yang-Mills theories which can be formulated by means of functional integral methods and are thus well suited for analytic calculations, but which are free of Gribov ambiguities and avoid the Neuberger zero problem of the standard 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.
Covariant gauges without Gribov ambiguities in Yang-Mills theories
Serreau, J.; Tissier, M.; Tresmontant, A.
2014-06-01
We propose a one-parameter family of nonlinear covariant gauges which can be formulated as an extremization procedure that may be amenable to lattice implementation. At high energies, where the Gribov ambiguities can be ignored, this reduces to the Curci-Ferrari-Delbourgo-Jarvis gauges. We further propose a continuum formulation in terms of a local action which is free of Gribov ambiguities and avoids the Neuberger zero problem of the standard Faddeev-Popov construction. This involves an averaging over Gribov copies with a nonuniform weight, which introduces a new gauge-fixing parameter. We show that the proposed gauge-fixed action is perturbatively renormalizable in four dimensions and we provide explicit expressions of the renormalization factors at one loop. We discuss the possible implications of the present proposal for the calculation of Yang-Mills correlators.
Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
Anastasiou, C; Dixon, L; Kosower, D A
2003-01-01
The collinear factorization properties of two-loop scattering amplitudes in dimensionally-regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point amplitudes. The simplicity of the relation is consistent with intuition based on the AdS/CFT correspondence that the form of the large N_c L-loop amplitudes should be simple enough to allow a resummation to all orders.
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 ...
Renormalization of the Yang-Mills spectral action
van Suijlekom, Walter D
2011-01-01
We prove renormalizability of the full spectral action for the Yang-Mills system on a flat 4-dimensional background manifold. Interpreting the spectral action as a higher-derivative gauge theory, a power-counting argument shows that it is superrenormalizable. We determine the counterterms at one-loop using zeta function regularization in a background field gauge and establish their gauge invariance. Consequently, the spectral action can be renormalized by a simple shift of the coefficients appearing in the asymptotic expansion of the spectral action. This manuscript provides more details than the shorter companion paper, where we have used a (formal) quantum action principle to arrive at gauge invariance of the counterterms. Here, we give in addition an explicit expression for the gauge propagator.
Confinement in a three-dimensional Yang-Mills theory
Frasca, Marco
2017-04-15
We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining theory. The potential we obtain agrees fairly well with preceding findings in the literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depend on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory and is now fully justified. The agreement obtained with the lattice results for the ground state of the theory is well below 1% at any value of the degree of the group. (orig.)
Confinement in a three-dimensional Yang-Mills theory
Frasca, Marco
2016-01-01
We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a confining theory. The potential we obtain agrees fairly well with preceding findings in literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depends on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory.
Lifshitz black holes in Einstein-Yang-Mills theory
Devecioglu, Deniz Olgu
2014-01-01
We find that the four dimensional cosmological Einstein-Yang-Mills theory with $SU(2)$ gauge group admits Lifshitz spacetime as a base solution for the dynamical exponent $z>1$. Motivated by this, we next demonstrate numerically that the field equations admit black hole solutions which behave regularly on the horizon and at spatial infinity for different horizon topologies. The solutions depend on one parameter, the strength of the gauge field at the horizon, which is fine-tuned to capture the Lifshitz asymptotics at infinity. We also discuss the behavior of solutions and the change in Hawking temperature for black holes that are large or small with respect to the length scale $L$, which is itself fixed by the value of the cosmological constant.
Function group approach to unconstrained Hamiltonian Yang-Mills theory
Salmela, A
2004-01-01
Starting from the temporal gauge Hamiltonian for classical pure Yang-Mills theory with the gauge group SU(2) a canonical transformation is initiated by parametrising the Gauss law generators with three new canonical variables. The construction of the remaining variables of the new set proceeds through a number of intermediate variables in several steps, which are suggested by the Poisson bracket relations and the gauge transformation properties of these variables. The unconstrained Hamiltonian is obtained from the original one by expressing it in the new variables and then setting the Gauss law generators to zero. This Hamiltonian turns out to be local and it decomposes into a finite Laurent series in powers of the coupling constant.
Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory
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....
Fluxes, Tadpoles and Holography for N=1 Super Yang Mills
Gómez, C; Resco, P; Gomez, Cesar; Montanez, Sergio; Resco, Pedro
2004-01-01
We study non perturbative superpotentials for N=1 super Yang Mills from the point of view of large $N$ dualities. Starting with open topological strings we work out the relation between the closed string sector dilaton tadpole, which appears in the annulus amplitude, and NSNS fluxes in the closed string dual on the resolved conifold. For the mirror closed string dual version on the deformed conifold we derive, for a non vanishing $G_{3}$ form, the $N$ supersymmetric vacua and the transformations of $G_{3}$ through domain walls. Finally, as an extension of Fischler Susskind mechanism we find a direct relation between the dilaton tadpole and the geometric warping factors induced by the gravitational backreaction of NSNS fluxes.
Brownian Motion in Non-Commutative Super-Yang-Mills
Fischler, Willy; Garcia, Walter Tangarife
2012-01-01
Using the gauge/gravity correspondence, we study the dynamics of a heavy quark in strongly-coupled non-commutative Super-Yang-Mills at finite temperature. We propose a Langevin equation that accounts for the effects of non-commutativity and resembles the structure of Brownian motion in the presence of a magnetic field. As expected, fluctuations along non-commutative directions are generically correlated. Our results show that the viscosity of the plasma is smaller than the commutative case and that the diffusion properties of the quark are unaffected by non-commutativity. Finally, we compute the random force autocorrelator and verify that the fluctuation-dissipation theorem holds in the presence of non-commutativity.
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.
Step scaling and the Yang-Mills gradient flow
Lüscher, Martin
2014-01-01
The use of the Yang-Mills gradient flow in step-scaling studies of lattice QCD is expected to lead to results of unprecedented precision. Step scaling is usually based on the Schr\\"odinger functional, where time ranges over an interval [0,T] and all fields satisfy Dirichlet boundary conditions at time 0 and T. In these calculations, potentially important sources of systematic errors are boundary lattice effects and the infamous topology-freezing problem. The latter is here shown to be absent if Neumann instead of Dirichlet boundary conditions are imposed on the gauge field at time 0. Moreover, the expectation values of gauge-invariant local fields at positive flow time (and of other well localized observables) that reside in the center of the space-time volume are found to be largely insensitive to the boundary lattice effects.
Perturbative study of Yang-Mills theory in the infrared
Siringo, Fabio
2015-01-01
Pure Yang-Mills SU(N) theory is studied in four dimensional space and Landau gauge by a double perturbative expansion based on a massive free-particle propagator. By dimensional regularization, all diverging mass terms cancel exactly in the double expansion, without the need to include mass counterterms that would spoil the symmetry of the original Lagrangian. The emerging perturbation theory is safe in the infrared and shares the same behaviour of the standard perturbation theory in the UV. At one-loop, Gluon and ghost propagators are found in excellent agreement with the data of lattice simulations and an infrared-safe running coupling is derived. A natural scale m=0.5-0.6 GeV is extracted from the data for N=3.
Confinement in a three-dimensional Yang-Mills theory
Frasca, Marco
2017-04-01
We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining theory. The potential we obtain agrees fairly well with preceding findings in the literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depend on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory and is now fully justified. The agreement obtained with the lattice results for the ground state of the theory is well below 1% at any value of the degree of the group.
Residual Confinement in High-Temperature Yang-Mills Theory
Maas, A; Gruter, B; Alkofer, R; Maas, Axel; Wambach, Jochen; Gruter, Burghard; Alkofer, Reinhard
2004-01-01
The infrared behavior of Landau gauge gluon and ghost propagators are investigated in Yang-Mills theory at non-vanishing temperatures. Self-consistent solutions are presented for temperatures below the presumed phase transition and in the infinite temperature limit. Gluon confinement is manifest in the infrared behavior of these propagators. As expected confinement prevails below the phase transition. In the infinite-temperature limit a qualitative change is observed: the chromoelectric sector exhibits a near-perturbative behavior while long-range chromomagnetic interactions, mediated by soft ghost modes, are still present. The latter behavior is in agreement with corresponding lattice results. It furthermore implies that part of the gluons are still confined.
Residual Confinement in High-Temperature Yang-Mills Theory
Maas, A.; Wambach, J.; Grüter, B.; Alkofer, R.
2005-01-01
The infrared behavior of Landau gauge gluon and ghost propagators are investigated in Yang-Mills theory at non-vanishing temperatures. Self-consistent solutions are presented for temperatures below the presumed phase transition and in the infinite temperature limit. Gluon confinement is manifest in the infrared behavior of these propagators. As expected confinement prevails below the phase transition. In the infinite-temperature limit a qualitative change is observed: the chromoelectric sector exhibits a near-perturbative behavior while long-range chromomagnetic interactions, mediated by soft ghost modes, are still present. The latter behavior is in agreement with corresponding lattice results. It furthermore implies that part of the gluons are still confined.
Condensation of galactic cold dark matter
Visinelli, Luca
2016-07-01
We consider the steady-state regime describing the density profile of a dark matter halo, if dark matter is treated as a Bose-Einstein condensate. We first solve the fluid equation for ``canonical'' cold dark matter, obtaining a class of density profiles which includes the Navarro-Frenk-White profile, and which diverge at the halo core. We then solve numerically the equation obtained when an additional ``quantum pressure'' term is included in the computation of the density profile. The solution to this latter case is finite at the halo core, possibly avoiding the ``cuspy halo problem'' present in some cold dark matter theories. Within the model proposed, we predict the mass of the cold dark matter particle to be of the order of Mχ c2 ≈ 10-24 eV, which is of the same order of magnitude as that predicted in ultra-light scalar cold dark matter models. Finally, we derive the differential equation describing perturbations in the density and the pressure of the dark matter fluid.
Thermal Yang-Mills theory in the Einstein universe
Avramidi, Ivan G.; Collopy, Samuel
2012-09-01
We study the stability of a non-Abelian chromomagnetic vacuum in Yang-Mills theory in Euclidean Einstein universe S1 × S3. We assume that the gauge group is a simple compact group G containing the group SU(2) as a subgroup and consider static covariantly constant gauge fields on S3 taking values in the adjoint representation of the group G and forming a representation of the group SU(2). We compute the heat kernel for the Laplacian acting on fields on S3 in an arbitrary representation of SU(2) and use this result to compute the heat kernels for the gluon and the ghost operators and the one-loop effective action. We show that the only configuration of the covariantly constant Yang-Mills background that is stable is the one that contains only spinor (fundamental) representations of the group SU(2); all other configurations contain negative modes and are unstable. For the stable configuration we compute the asymptotics of the effective action, the energy density, the entropy and the heat capacity in the limits of low/high temperature and small/large volume and show that the energy density has a non-trivial minimum at a finite value of the radius of the sphere S3. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.
Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy
Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; Roiban, Radu
2017-07-01
Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + ϕ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism. Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.
Solitonic axion condensates modeling dark matter halos
Castañeda Valle, David, E-mail: casvada@gmail.com; Mielke, Eckehard W., E-mail: ekke@xanum.uam.mx
2013-09-15
Instead of fluid type dark matter (DM), axion-like scalar fields with a periodic self-interaction or some truncations of it are analyzed as a model of galaxy halos. It is probed if such cold Bose–Einstein type condensates could provide a viable soliton type interpretation of the DM ‘bullets’ observed by means of gravitational lensing in merging galaxy clusters. We study solitary waves for two self-interacting potentials in the relativistic Klein–Gordon equation, mainly in lower dimensions, and visualize the approximately shape-invariant collisions of two ‘lump’ type solitons. -- Highlights: •An axion model of dark matter is considered. •Collision of axion type solitons are studied in a two dimensional toy model. •Relations to dark matter collisions in galaxy clusters are proposed.
Yang-Mills theory in terms of gauge invariant dual variables
Diakonov, D
2002-01-01
Quantum Yang-Mills theory and the Wilson loop can be rewritten identically in terms of local gauge-invariant variables being directly related to the metric of the dual space. In this formulation, one reveals a hidden high local symmetry of the Yang-Mills theory, which mixes up fields with spins up to J=N for the SU(N) gauge group. In the simplest case of the SU(2) group the dual space seems to tend to the de Sitter space in the infrared region. This observation suggests a new mechanism of gauge-invariant mass generation in the Yang-Mills theory.
Stabilization of the Yang-Mills chaos in non-Abelian Born-Infeld theory
Galtsov, D V
2003-01-01
We investigate dynamics of the homogeneous time-dependent SU(2) Yang-Mills fields governed by the non-Abelian Born-Infeld lagrangian which arises in superstring theory as a result of summation of all orders in the string slope parameter $\\alpha'$. It is shown that generically the Born-Infeld dynamics is less chaotic than that in the ordinary Yang-Mills theory, and at high enough field strength the Yang-Mills chaos is stabilized. More generally, a smothering effect of the string non-locality on behavior of classical fields is conjectured.
Geometry and off-shell nilpotency for N = 1 supersymmetric Yang-Mills theory
Meziane, A
2015-01-01
We show that for N = 1 supersymmetric Yang-Mills theory it is possible to build an off-shell nilpotent BRST and anti-BRST algebra in terms of a BRST superspace formalism. This is based on the introduction of the basic fields of the quantized theory together with an auxiliary real field via the lowest components of the superfield components of a superYang-Mills connection. Here, the associated supercurvature is constrained by horizontality conditions as in ordinary Yang-Mills theory. We also show how the off-shell BRST-invariant quantum action can be constructed starting from a gauge-fixed superaction.
A Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry
WANG Dian-Fu; SONG He-Shan
2005-01-01
A generalized Yang-Mills model, which contains, besides the vector part Vμ, also a scalar part S, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of Nambu-Jona-Lasinio (NJL) mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills model. The combination of the generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.
Sandbrink, Dirk
2015-01-26
One of the most promising candidates to describe the physics beyond the standard model is the so-called supersymmetry. This work was created in the context of the DESY-Muenster-Collaboration, which studies in particular the N=1 supersymmetric Yang-Mills theory (SYM). SYM is a comparatively simple theory, which is therefore well-suited to study the expected properties of a supersymmetric theory with the help of Monte Carlo simulations on the lattice. This thesis is focused on the numerical determination of the quarkpotential, the glueball masses and the phase structur of the N=1 supersymmetric Yang-Mills theory. The quarkpotential is used to calculate the Sommer scale, which in turn is needed to convert the dimensionless lattice spacing into physical units. Glueballs are hypothetical particles built out of gluons, their masses are relatively hard to determine in lattice simulations due to their pure gluonic nature. For this reason, various methods are studied to reduce the uncertainties of the mass determination. The focus lies on smearing methods and their use in variational smearing as well as on the use of different glueball operators. Lastly, a first look is taken at the phase diagram of the model at finite temperature. Various simulations have been performed at finite temperature in parallel to those performed at temperature zero to analyse the behaviour of the Polyakov loop and the gluino condensate in greater detail.
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.
Mechanism by which spatially homogeneous Yang-Mills fields become stochastic
Avakyan, A.R.; Arutyunyan, S.G.; Baseyan, G.Z.
1982-11-20
A mechanical system with a nonzero angular momentum, corresponding to spatially homogeneous Yang-Mills fields, is analyzed. Numerical simulations have been carried out. A mechanism by which the fields become stochastic is found.
Kaehler transformations and the coupling of matter and Yang-Mills fields to supergravity
Binetruy, P.; Girardi, G.; Grimm, R.; Mueller, M.
1987-04-30
It is demonstrated that a geometric interpretation of Kaehler transformations in superspace allows to construct the full action for matter and Yang-Mills fields coupled to supergravity in a concise way, both in terms of superfields and component fields.
Future applications of the Yang-Mills gradient flow in lattice QCD
Lüscher, Martin
2013-01-01
The Yang--Mills gradient flow has many interesting applications in lattice QCD. In this talk, some recent and possible future uses of the flow are discussed, emphasizing the underlying theoretical concepts rather than any computational aspects.
Non-perturbative Solutions to N=2 Supersymmetric Yang-Mills Theories Progress and Perspective
Ohta, Y
1999-01-01
This note reviews the progress on the low energy dynamics of N=2 supersymmetric Yang-Mills theories after the works of Seiberg and Witten. Specifically, the theory of prepotential for non-specialists is reviewed.
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.
N=4 Super-Yang-Mills Theory, QCD and Collider Physics
Bern, Z; Kosower, D A
2004-01-01
We review how (dimensionally regulated) scattering amplitudes in N=4 super-Yang-Mills theory provide a useful testing ground for perturbative QCD calculations relevant to collider physics, as well as another avenue for investigating the AdS/CFT correspondence. We describe the iterative relation for two-loop scattering amplitudes in N=4 super-Yang-Mills theory found in C. Anastasiou et al., Phys. Rev. Lett. 91:251602 (2003), and discuss recent progress toward extending it to three loops.
One-dimensional structures behind twisted and untwisted super Yang-Mills theory
Baulieu, Laurent [CERN, Geneve (Switzerland). Theoretical Div.; Toppan, Francesco, E-mail: baulieu@lpthe.jussieu.f, E-mail: toppan@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
2010-07-01
We give a one-dimensional interpretation of the four-dimensional twisted N = 1 super Yang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N = 1 super Yang-Mills theory. (author)
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.
Park, J S
1992-01-01
We re-examine the geometry and algebraic structure of BRST's of Topological Yang-Mills theory based on the universal bundle formalism of Atiyah and Singer. This enables us to find a natural generalization of the {\\it Russian formula and descent equations\\/}, which can be used as algebraic method to find the non-Abelian anomalies counterparts in Topological Yang-Mills theory. We suggest that the presence of the non-Abelian anomaly obstructs the proper definition of Donaldson's invariants.
The deconfinement phase transition in Yang-Mills theory with general Lie group G
Holland, K; Wiese, U J
2004-01-01
We present numerical results for the deconfinement phase transition in Sp(2) and Sp(3) Yang-Mills theories in (2+1)-D and (3+1)-D. We then make a conjecture on the order of this phase transition in Yang-Mills theories with general Lie groups G = SU(N), SO(N), Sp(N) and with exceptional groups G = G(2), F(4), E(6), E(7), E(8).
An exploratory study of Yang-Mills three-point functions at non-zero temperature
Huber, Markus Q
2016-01-01
Results for three-point functions of Landau gauge Yang-Mills theory at non-vanishing temperature are presented and compared to lattice results. It is found that the three-gluon vertex is enhanced for temperatures below the phase transition. At very low momenta it becomes negative for all temperatures. Furthermore, truncation effects in functional equations are discussed at the example of three-dimensional Yang-Mills theory for which a self-contained solution is presented.
Topological Quantization of Instantons in SU(2) Yang-Mills Theory
ZHONG Wo-Jun; DUAN Yi-Shi
2008-01-01
By decomposing SU(2) gauge potential in four-dimensional Euclidean SU(2) Yang-Mills theory in a new way,we find that the instanton number related to the isospin defects of a doublet order parameter can be topologically quantized by the Hopf index and Brouwer degree.It is also shown that the instanton number is just the sum of the topological charges of the isospin defects in the non-trivial sector of Yang-Mills theory.
Integrability in Yang-Mills theory on the light cone beyond leading order
Belitsky, A V; Müller, D
2004-01-01
The one-loop dilatation operator in Yang-Mills theory possesses a hidden integrability symmetry in the sector of maximal helicity Wilson operators. We calculate two-loop corrections to the dilatation operator and demonstrate that while integrability is broken for matter in the fundamental representation of the SU(3) gauge group, for the adjoint SU(N_c) matter it survives the conformal symmetry breaking and persists in supersymmetric N=1, N=2 and N=4 Yang-Mills theories.
Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic
Douglas, M R; Lukic, S; Reinbacher, R; Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene
2007-01-01
We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P^2. In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic.
A U(4) QCD Model Using Generalized Yang-Mills Theory
WANG Dian-Fu; ZHONG Hai-Yang
2008-01-01
Generalized Yang-Mills theory has a covariant derivative which contains both vector and pseudoscalar gauge bosons.Based on this theory,we construct a U(4) strong interaction model By using this U(4) generalized Yang-Mills model,we obtain that mesons can be realized as the colorless pseudoscalar gauge bosons.We also obtain a gauge potential solution which can be used to explain the asymptotic behavior and color confinement.
One-dimensional structures behind twisted and untwisted superYang-Mills theory
Baulieu, Laurent
2011-01-01
We give a one-dimensional interpretation of the four-dimensional twisted N=1 superYang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N=1 superYang-Mills theory.
Surface-Invariants in 2D Classical Yang-Mills Theory
Díaz, R; Leal, L; D\\'{\\i}az, Rafael; Leal, Lorenzo
2006-01-01
We study a method to obtain invariants under area-preserving diffeomorphisms associated to closed curves in the plane from classical Yang-Mills theory in two dimensions. Taking as starting point the Yang-Mills field coupled to non dynamical particles carrying chromo-electric charge, and by means of a perturbative scheme, we obtain the first two contributions to the on shell action, which are area-invariants. A geometrical interpretation of these invariants is given.
Static Spherically Symmetric Solutions of the SO(5) Einstein Yang-Mills Equations
Bartnik, Robert A.; Fisher, Mark; Oliynyk, Todd A.
2009-01-01
Globally regular (ie. asymptotically flat and regular interior), spherically symmetric and localised ("particle-like") solutions of the coupled Einstein Yang-Mills (EYM) equations with gauge group SU(2) have been known for more than 20 years, yet their properties are still not well understood. Spherically symmetric Yang--Mills fields are classified by a choice of isotropy generator and SO(5) is distinguished as the simplest model with a \\emph{non-Abelian} residual (little) group, $SU(2)\\times...
Observables in Topological Yang-Mills Theories With Extended Shift Supersymmetry
Constantinidis, C P; Spalenza, W; Constantinidis, Clisthenis P.; Piguet, Olivier; Spalenza, Wesley
2006-01-01
We present a complete classification, at the classical level, of the observables of topological Yang-Mills theories with an extended shift supersymmetry of N generators, in any space-time dimension. The observables are defined as the Yang-Mills BRST cohomology classes of shift supersymmetry invariants. These cohomology classes turn out to be solutions of an N-extension of Witten's equivariant cohomology. This work generalizes results known in the case of shift supersymmetry with a single generator.
An exploratory study of Yang-Mills three-point functions at non-zero temperature
Huber, Markus Q.
2017-03-01
Results for three-point functions of Landau gauge Yang-Mills theory at non-vanishing temperature are presented and compared to lattice results. It is found that the three-gluon vertex is enhanced for temperatures below the phase transition. At very low momenta it becomes negative for all temperatures. Furthermore, truncation effects in functional equations are discussed at the example of three-dimensional Yang-Mills theory for which a self-contained solution is presented.
Yang--Mills Glueballs as Closed Bosonic Strings
Dubovsky, Sergei
2016-01-01
We put forward the Axionic String Ansatz (ASA), which provides a unified description for the worldsheet dynamics of confining strings in pure Yang--Mills theory both in $D=3$ and $D=4$ space-time dimensions. The ASA is motivated by the excitation spectrum of long confining strings, as measured on a lattice, and by recently constructed integrable axionic non-critical string models. According to the ASA, pure gluodynamics in 3D is described by a non-critical bosonic string theory without any extra local worldsheet degrees of freedom. We argue that this assumption fixes the set of quantum numbers (spins, $P$- and $C$-parities) of almost all glueball states. We confront the resulting predictions with the properties of approximately $1^2+2^2+3^2+5^2=39$ lightest glueball states measured on a lattice and find a good agreement. On the other hand, the spectrum of low lying glueballs in 4D gluodynamics suggests the presence of a massive pseudoscalar mode on the string worldsheet, in agreement with the ASA and lattice ...
Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
Bern, Z; Johansson, H; Kosower, D A
2007-01-01
We present an ansatz for the planar five-loop four-point amplitude in maximally supersymmetric Yang-Mills theory in terms of loop integrals. This ansatz exploits the recently observed correspondence between integrals with simple conformal properties and those found in the four-point amplitudes of the theory through four loops. We explain how to identify all such integrals systematically. We make use of generalized unitarity in both four and D dimensions to determine the coefficients of each of these integrals in the amplitude. Maximal cuts, in which we cut all propagators of a given integral, are an especially effective means for determining these coefficients. The set of integrals and coefficients determined here will be useful for computing the five-loop cusp anomalous dimension of the theory which is of interest for non-trivial checks of the AdS/CFT duality conjecture. It will also be useful for checking a conjecture that the amplitudes have an iterative structure allowing for their all-loop resummation, w...
Yang-Mills glueballs as closed bosonic strings
Dubovsky, Sergei; Hernández-Chifflet, Guzmán
2017-02-01
We put forward the Axionic String Ansatz (ASA), which provides a unified description for the worldsheet dynamics of confining strings in pure Yang-Mills theory both in D = 3 and D = 4 space-time dimensions. The ASA is motivated by the excitation spectrum of long confining strings, as measured on a lattice, and by recently constructed integrable axionic non-critical string models. According to the ASA, pure gluodynamics in 3D is described by a non-critical bosonic string theory without any extra local worldsheet degrees of freedom. We argue that this assumption fixes the set of quantum numbers (spins, P-and C-parities) of almost all glueball states. We confront the resulting predictions with the properties of approximately 12 + 22 + 32 + 52 = 39 lightest glueball states measured on a lattice and find a good agreement. On the other hand, the spectrum of low lying glueballs in 4D gluodynamics suggests the presence of a massive pseudoscalar mode on the string worldsheet, in agreement with the ASA and lattice data for long strings.
A novel renormalizable representation of the Yang-Mills theory
Dubin, A Yu
2007-01-01
For a generic gauge-invariant correlator _{A}, we reformulate the standard D=4 Yang-Mills theory as a renormalizable system of two interacting fields a_{\\mu} and B_{\\mu} which faithfully represent high- and low-energy degrees of freedom of the single gauge field A_{\\mu} in the original formulation. It opens a possibility to synthesize an infrared-nonsingular weak-coupling series, employed to integrate over a_{\\mu} for a given background B_{\\mu}, with qualitatively different methods. These methods are to be applied to evaluate the resulting (after the a_{\\mu}-integration) representation of _{A} in terms of gauge-invariant generically non-local low-energy observables, like Wilson loops. The latter observables are averaged over B_{\\mu} with respect to a gauge-invariant Wilsonean effective action S_{eff}[B]. To avoid a destructive dissipation between the high- and low-energy excitations, we implement a specific fine-tuning of the interaction between the pair of the fields: prior to the integration over B_{\\mu}, t...
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...
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...
Magnetic Monopoles in the Einstein-Yang-Mills-Higgs System
Viet, N A; Viet, Nguyen Ai; Wali, Kameshwar C.
1995-01-01
We study the Yang-Mills-Higgs system within the framework of general relativity. In the static situation, using Bogomol'nyi type analysis, we derive a positive-definite energy functional which has a lower bound. Specializing to the gauge group $SU(2)$ and the t'Hooft-Polyakov ansatz for the gauge and Higgs fields, we seek static, spherically symmetric solutions to the coupled system of equations in both the isotropic and standard coordinate systems. In both cases, in the spontaneously broken symmetry situation, we find great simplications reducing the solutions of the coupled system to the solution of a single non-linear differential equation, different one in each case, but well-known in other contexts of physics. We find abelian and non-abelian monopole solutions with gravitational fields playing the role of Higgs fields in providing attraction that balances the repulsion due to the gauge fields. Numerical solutions indicate the possibility of blackhole horizons inside the monopoles enclosing the singularit...
The Yang-Mills gradient flow in finite volume
Fodor, Zoltan; Kuti, Julius; Nogradi, Daniel; Wong, Chik Him
2012-01-01
The Yang-Mills gradient flow is considered on the four dimensional torus T^4 for SU(N) gauge theory coupled to N_f flavors of massless fermions in arbitrary representations. The small volume dynamics is dominated by the constant gauge fields. The expectation value of the field strength tensor squared is calculated for positive flow time t by treating the non-zero gauge modes perturbatively and the zero modes exactly. The finite volume correction to the infinite volume result is found to contain both algebraic and exponential terms. The leading order result is then used to define a one parameter family of running coupling schemes in which the coupling runs with the linear size of the box. The new scheme is tested numerically in SU(3) gauge theory coupled to N_f = 4 flavors of massless fundamental fermions. The calculations are performed at several lattice spacings with a controlled continuum extrapolation. The continuum result agrees with the perturbative 2-loop prediction for small renormalized coupling as ex...
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.
Dark Energy Coupled with Dark Matter in the Accelerating Universe
ZHANG Yang
2004-01-01
@@ To model the observed Universe containing both dark energy and dark matter, we study the effective Yang-Mills condensate model of dark energy and add a non-relativistic matter component as the dark matter, which is generated out of the decaying dark energy at a constant rate Г, a parameter of our model. For the Universe driven by these two components, the dynamic evolution still has asymptotic behaviour: the expansion of the Universe is accelerating with an asymptotically constant rate H, and the densities of both components approach to finite constant values. Moreover, ΩA≈ 0.7 for dark energy and Ωm ≈ 0.3 for dark matter are achieved if the decay rate Г is chosen such that Г/H～ 1.
Gauge Coupling Field, Currents, Anomalies and N=1 Super-Yang-Mills Effective Actions
Ambrosetti, Nicola; Derendinger, Jean-Pierre; Hartog, Jelle
2016-01-01
Working with a gauge coupling field in a linear superfield, we construct effective Lagrangians for N=1 super-Yang-Mills theory fully compatible with the expected all-order behaviour or physical quantities. Using the one-loop dependence on its ultraviolet cutoff and anomaly matching or cancellation of R and dilatation anomalies, we obtain the Wilsonian effective Lagrangian. With similar anomaly matching or cancellation methods, we derive the effective action for gaugino condensates, as a function of the real coupling field. Both effective actions lead to a derivation of the NSVZ beta function from algebraic arguments only. The extension of results to N=2 theories or to matter systems is briefly considered. The main tool for the discussion of anomalies is a generic supercurrent structure with 16_B+16_F operators (the S multiplet), which we derive using superspace identities and field equations for a fully general gauge theory Lagrangian with the linear gauge coupling superfield, and with various U(1)_R currents...
Gauge coupling field, currents, anomalies and N = 1 super-Yang-Mills effective actions
Ambrosetti, Nicola; Arnold, Daniel; Derendinger, Jean-Pierre; Hartong, Jelle
2017-02-01
Working with a gauge coupling field in a linear superfield, we construct effective Lagrangians for N = 1 super-Yang-Mills theory fully compatible with the expected all-order behavior or physical quantities. Using the one-loop dependence on its ultraviolet cutoff and anomaly matching or cancellation of R and dilatation anomalies, we obtain the Wilsonian effective Lagrangian. With similar anomaly matching or cancellation methods, we derive the effective action for gaugino condensates, as a function of the real coupling field. Both effective actions lead to a derivation of the NSVZ β function from algebraic arguments only. The extension of results to N = 2 theories or to matter systems is briefly considered. The main tool for the discussion of anomalies is a generic supercurrent structure with 16B +16F operators (the S multiplet), which we derive using superspace identities and field equations for a fully general gauge theory Lagrangian with the linear gauge coupling superfield, and with various U(1)R currents. As a byproduct, we show under which conditions the S multiplet can be improved to contain the Callan-Coleman-Jackiw energy-momentum tensor whose trace measures the breaking of scale invariance.
WANG Dian-Fu; SUN Xiao-Yu; CHANG Xiao-Jing
2011-01-01
Starting from the generalized Yang-Mills model which contains, besides the vector part Vμ, also a scalar part S and a pseudoscalar part P. It is shown, in terms of the Nambu-Jona-Lasinio （NJL） mechanism, that CP violation can be realized dynamically. The
Field-dependent BRST-antiBRST transformations in Yang-Mills and Gribov-Zwanziger theories
Moshin, Pavel Yu.; Reshetnyak, Alexander A.
2014-11-01
Yang-Mills theories. In Section 5, the Gribov horizon functional in an arbitrary Rξ-like gauge, and generally in any differentiable gauge, is determined with the help of respective finite field-dependent BRST-antiBRST transformations. In Discussion, we make an overview of our results and outline some open problems. In particular, we discuss an extension of finite BRST-antiBRST transformations to the case of general gauge theories and present an ansatz for such transformations. In Appendix A, we study the group properties of finite field-dependent BRST-antiBRST transformations. In Appendix B, we present a detailed calculation of the Jacobian corresponding to the finite, both global (Appendix B.1) and field-dependent (Appendix B.2), BRST-antiBRST transformations. Appendix C is devoted to calculations involving the BRST-antiBRST invariant Yang-Mills action in Rξ-gauges.We use DeWitt's condensed notations [40]. By default, derivatives with respect to the fields are taken from the right, and those with respect to the corresponding antifields are taken from the left; otherwise, left-hand and right-hand derivatives are labeled by the subscripts “l” and “r”, respectively; F,A stands for the right-hand derivative δF/δϕA of a functional F=F(ϕ) with respect to ϕA. The raising and lowering of Sp(2) indices, sa=εsb, sa=εabsb, is carried out with the help of a constant antisymmetric second-rank tensor ε, εεcb=δba, subject to the normalization condition ε12=1. The Grassmann parity and ghost number of a quantity A, assumed to be homogeneous with respect to these characteristics, are denoted by ε(A), gh(A), respectively.
One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
Brandhuber, A; Travaglini, G; Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele
2004-01-01
We propose a new, twistor string theory inspired formalism to calculate loop amplitudes in N=4 super Yang-Mills theory. In this approach, maximal helicity violating (MHV) tree amplitudes of N=4 super Yang-Mills are used as vertices, using an off-shell prescription introduced by Cachazo, Svrcek and Witten, and combined into effective diagrams that incorporate large numbers of conventional Feynman diagrams. As an example, we apply this formalism to the particular class of MHV one-loop scattering amplitudes with an arbitrary number of external legs in N=4 super Yang-Mills. Remarkably, our approach naturally leads to a representation of the amplitudes as dispersion integrals, which we evaluate exactly. Our results for the MHV amplitudes are in precise agreement with the expressions for this class of amplitudes obtained previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.
One-Loop Self-Dual and N=4 Super Yang-Mills
Bern, Z; Dunbar, D C; Kosower, D A
1997-01-01
We conjecture a simple relationship between the one-loop maximally helicity violating gluon amplitudes of ordinary QCD (all helicities identical) and those of N=4 supersymmetric Yang-Mills (all but two helicities identical). Because the amplitudes in self-dual Yang Mills have been shown to be the same as the maximally helicity violating ones in QCD, this conjecture implies that they are also related to the maximally helicity violating ones of N=4 supersymmetric Yang-Mills. We have an explicit proof of the relation up to the six-point amplitude; for amplitudes with more external legs, it remains a conjecture. A similar conjecture relates amplitudes in self-dual gravity to maximally helicity violating N=8 supergravity amplitudes.
Explicit Derivation of Yang-Mills Self-Dual Solutions on non-Commutative Harmonic Space
Belhaj, A; Sahraoui, E L; Saidi, E H
2001-01-01
We develop the noncommutative harmonic space (NHS) analysis to study the problem of solving the non-linear constraint eqs of noncommutative Yang-Mills self-duality in four-dimensions. We show that this space, denoted also as NHS($\\eta,\\theta$), has two SU(2) isovector deformations $\\eta^{(ij)}$ and $\\theta^{(ij)}$ parametrising respectively two noncommutative harmonic subspaces NHS($\\eta,0$) and NHS($0,\\theta$) used to study the self-dual and anti self-dual noncommutative Yang-Mills solutions. We formulate the Yang-Mills self-dual constraint eqs on NHS($\\eta,0$) by extending the idea of harmonic analyticity to linearize them. Then we give a perturbative self-dual solution recovering the ordinary one. Finally we present the explicit computation of an exact self-dual solution.
Nonsymmetric unified theory of gravitation, electromagnetism and Yang-Mills field
Ragusa, S [Departamento de Fisica e Informatica, Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, CP 369, 13560-970 Sao Carlos, SP (Brazil)
2002-12-07
The recently studied new variation of Einstein's metric nonsymmetric unified field theory of gravitation and electromagnetism is enlarged to include the Yang-Mills field theory. It is shown that the antisymmetric part of the metric tensor, now a 2x2 matrix, can be made to describe both a field obeying Maxwell's equations and a field obeying Yang-Mills's field equations in the flat space linear approximation, thereby making its identification with the sum of a generalized electromagnetic and isotopic field strength tensors a possibly consistent procedure. The theory is shown to be free of unphysical ghost-negative energy radiative modes even when expanded on a curved Riemannian background. The Einstein-Maxwell-Yang-Mills theory is contained in the first approximation of the field equations on a curved general relativity background.
Gauge-covariant decomposition and magnetic monopole for G(2) Yang-Mills field
Matsudo, Ryutaro
2016-01-01
We give a gauge-covariant decomposition of the Yang-Mills field with an exceptional gauge group $G(2)$, which extends the field decomposition invented by Cho, Duan-Ge, and Faddeev-Niemi for the $SU(N)$ Yang-Mills field. As an application of the decomposition, we derive a new expression of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of $G(2)$. The resulting new form is used to define gauge-invariant magnetic monopoles in the $G(2)$ Yang-Mills theory. Moreover, we obtain the quantization condition to be satisfied by the resulting magnetic charge. The method given in this paper is general enough to be applicable to any semi-simple Lie group other than $SU(N)$ and $G(2)$.
Maximally Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry
无
2006-01-01
A maximally generalized Yang-Mills model, which contains, besides the vector part Vμ, also an axial-vector part Aμ, a scalar part S, a pseudoscalar part P, and a tensor part Tμv, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of the Nambu-Jona-Lasinio mechanism, that the gauge symmetry breaking can be realized dynamically in the maximally generalized Yang-Mills model. The combination of the maximally generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.
Confinement, Holonomy and Correlated Instanton-Dyon Ensemble I: SU(2) Yang-Mills Theory
Lopez-Ruiz, Miguel Angel; Liao, Jinfeng
2016-01-01
The mechanism of confinement in Yang-Mills theories remains a challenge to our understanding of nonperturbative gauge dynamics. While it is widely perceived that confinement may arise from chromo-magnetically charged gauge configurations with nontrivial topology, it is not clear what types of configurations could do that and how, in pure Yang-Mills and QCD-like (non-supersymmetric) theories. Recently a promising approach has emerged, based on statistical ensembles of dyons/anti-dyons that are constituents of instanton/anti-instanton solutions with nontrivial holonomy where the holonomy plays a vital role as an effective "Higgsing" mechanism. We report a thorough numerical investigation of the confinement dynamics in SU(2) Yang-Mills theory by constructing such a statistical ensemble of correlated instanton-dyons.
The global existence of Yang-Mills fields on curved space-times
Ghanem, Sari
2013-01-01
This is an introductory chapter in a series in which we take a systematic study of the Yang-Mills equations on curved space-times. In this first, we provide standard material that consists in writing the proof of the global existence of Yang-Mills fields on arbitrary curved space-times using the Klainerman-Rodnianski parametrix combined with suitable Gr\\"onwall type inequalities. While the Chru\\'sciel-Shatah argument requires a simultaneous control of the $L^{\\infty}_{loc}$ and the $H^{2}_{loc}$ norms of the Yang-Mills curvature, we can get away by controlling only the $H^{1}_{loc}$ norm instead, and write a new gauge independent proof on arbitrary, fixed, sufficiently smooth, globally hyperbolic, curved 4-dimensional Lorentzian manifolds. This manuscript is written in an expository way in order to provide notes to Master's level students willing to learn mathematical General Relativity.
Yang-Mills Solutions and Dyons on Cylinders over Coset Spaces with Sasakian Structure
Tormählen, Maike
2014-01-01
We present solutions of the Yang-Mills equation on cylinders $\\mathbb R\\times G/H$ over coset spaces with Sasakian structure and odd dimension $2m+1$. The gauge potential is assumed to be $SU(m)$-equivariant, parametrized by two real, scalar-valued functions. Yang-Mills theory with torsion in this setup reduces to the Newtonian mechanics of a point particle moving in $\\mathbb R^2$ under the influence of an inverted potential. We analyze the critical points of this potential and present an analytic as well as several numerical finite-action solutions. Apart from the Yang-Mills solutions that constitute $SU(m)$-equivariant instanton configurations, we construct periodic sphaleron solutions on $S^1\\times G/H$ and dyon solutions on $i\\mathbb R\\times G/H$.
Spatially compact solutions and stabilization in Einstein-Yang-Mills-Higgs theories.
Forgács, Péter; Reuillon, Sébastien
2005-08-01
New solutions to the static, spherically symmetric Einstein-Yang-Mills-Higgs equations with the Higgs field in the triplet (doublet) representation are presented. They form continuous families parametrized by alpha = M(W)/M(Pl) [M(W) (M(Pl)) denoting the W boson (the Planck) mass]. The corresponding space-times are regular and have spatially compact sections. A particularly interesting class with the Yang-Mills amplitude being nodeless is exhibited and is shown to be linearly stable with respect to spherically symmetric perturbations. For some solutions with nodes of the Yang-Mills amplitude a new stabilization phenomenon is found, according to which their unstable modes disappear as alpha increases (for the triplet) or decreases (for the doublet).
Nonlinear Schrodinger solitons in massive Yang-Mills theory and partial localization of Dirac matter
Maintas, X N; Diakonos, F K; Frantzeskakis, D J
2013-01-01
We investigate the classical dynamics of the massive SU(2) Yang-Mills field in the framework of multiple scale perturbation theory. We show analytically that there exists a subset of solutions having the form of a kink soliton, modulated by a plane wave, in a linear subspace transverse to the direction of free propagation. Subsequently, we explore how these solutions affect the dynamics of a Dirac field possessing an SU(2) charge. We find that this class of Yang-Mills configurations, when regarded as an external field, leads to the localization of the fermion along a line in the transverse space. Our analysis reveals a mechanism for trapping SU(2) charged fermions in the presence of an external Yang-Mills field indicating the non-abelian analogue of Landau localization in electrodynamics.
The Configuration Space of Low-dimensional Yang-Mills Theories
Pause, T
1998-01-01
We discuss the construction of the physical configuration space for Yang-Mills quantum mechanics and Yang-Mills theory on a cylinder. We explicitly eliminate the redundant degrees of freedom by either fixing a gauge or introducing gauge invariant variables. Both methods are shown to be equivalent if the Gribov problem is treated properly and the necessary boundary identifications on the Gribov horizon are performed. In addition, we analyze the significance of non-generic configurations and clarify the relation between the Gribov problem and coordinate singularities.
A Twistor Approach to One-Loop Amplitudes in N=1 Supersymmetric Yang-Mills Theory
Bedford, J; Spence, B; Travaglini, G; Bedford, James; Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele
2004-01-01
We extend the twistor string theory inspired formalism introduced in hep-th/0407214 for calculating loop amplitudes in N=4 super Yang-Mills theory to the case of N=1 (and N=2) super Yang-Mills. Our approach yields a novel representation of the gauge theory amplitudes as dispersion integrals, which are surprisingly simple to evaluate. As an application we calculate one-loop maximally helicity violating (MHV) scattering amplitudes with an arbitrary number of external legs. The result we obtain agrees precisely with the expressions for the N=1 MHV amplitudes derived previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.
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.
Linear Broadening of the Confining String in Yang-Mills Theory at Low Temperature
Gliozzi, F; Wiese, U -J
2010-01-01
The logarithmic broadening predicted by the systematic low-energy effective field theory for the confining string has recently been verified in numerical simulations of (2+1)-d SU(2) lattice Yang-Mills theory at zero temperature. The same effective theory predicts linear broadening of the string at low non-zero temperature. In this paper, we verify this prediction by comparison with very precise Monte Carlo data. The comparison involves no additional adjustable parameters, because the low-energy constants of the effective theory have already been fixed at zero temperature. It yields very good agreement between the underlying Yang-Mills theory and the effective string theory.
Perturbative running of the twisted Yang-Mills coupling in the gradient flow scheme
Bribian, Eduardo I
2016-01-01
We report on our ongoing computation of the perturbative running of the Yang-Mills coupling using gradient flow techniques. In particular, we use the gradient flow method with twisted boundary conditions to perform a perturbative expansion of the expectation value of the Yang-Mills energy density up to fourth order in the coupling at finite flow time. We regularise the resulting integrals using dimensional regularisation, and reproduce the universal coefficient of the 1/{\\epsilon} term in the relation between bare and renormalised couplings. The computation of the finite part leading to a determination of the {\\Lambda} parameter in this scheme is underway.
Model of Polyakov duality: String field theory Hamiltonians from Yang-Mills theories
Periwal, Vipul
2000-08-01
Polyakov has conjectured that Yang-Mills theory should be equivalent to a noncritical string theory. I point out, based on the work of Marchesini, Ishibashi, Kawai and collaborators, and Jevicki and Rodrigues, that the loop operator of the Yang-Mills theory is the temporal gauge string field theory Hamiltonian of a noncritical string theory. The consistency condition of the string interpretation is the zig-zag symmetry emphasized by Polyakov. I explicitly show how this works for the one-plaquette model, providing a consistent direct string interpretation of the unitary matrix model for the first time.
Fifty Years of Yang-Mills Theory and my Contribution to it
Jackiw, Roman W
2004-01-01
On the fiftieth anniversary of Yang-Mills theory, I review the contribution to its understanding by my collaborators and me. Contents: 1.Gauge Theories and Quantum Anomalies; 2.Mathematical Connections; 3. Gauge Field Dynamics other than Yang-Mills; 4. Gauge Formalism for General Relativity Variables; A. Christoffel connection as a gauge potential, B. Gravitational Chern-Simons term from gauge theory Chern-Simons term, C. Coordinate transformations in general relativity and gauge theory, (i) Response to changes in coordinates (ii) Invariant fields and constants of motion. References.
Quantum Metamorphosis of Conformal Transformation in D3-Brane Yang-Mills Theory
Jevicki, A; Yoneya, T
1998-01-01
We show how the linear special conformal transformation in four-dimensional N=4 super Yang-Mills theory is metamorphosed into the nonlinear and field-dependent transformation for the collective coordinates of Dirichlet 3-branes, which agrees with the transformation law for the space-time coordinates in the anti-de Sitter (AdS) space-time. Our result provides a new and strong support for the conjectured relation between AdS supergravity and super conformal Yang-Mills theory (SYM). Furthermore, our work sheds elucidating light on the nature of the AdS/SYM correspondence.
Superspace gauge fixing in Yang-Mills matter-coupled conformal supergravity
Kugo, Taichiro; Yokokura, Ryo; Yoshioka, Koichi
2016-09-01
In D=4, N=1 conformal superspace, the Yang-Mills matter-coupled supergravity system is constructed where the Yang-Mills gauge interaction is introduced by extending the superconformal group to include the Kähler isometry group of chiral matter fields. There are two gauge-fixing procedures to get to the component Poincaré supergravity: one via the superconformal component formalism and the other via the Poincaré superspace formalism. These two types of superconformal gauge-fixing conditions are analyzed in detail and their correspondence is clarified.
Yang-Mills gauge fields conserving symmetry algebra of Dirac equation in homogeneous space
Breev, A I
2014-01-01
We consider the Dirac equation with external Yang-Mills gauge field in a homogeneous space with invariant metric. The Yang-Mills fields for which the motion group of the space serves as symmetry group of the Dirac equation are found by comparison of the Dirac equation with a invariant matrix differential operator of the first order. General constructions are illustrated by the example of de Sitter space. The basis of eigenfunctions and corresponding spectrum are obtained for the Dirac equation in the space $\\mathbb{R}^2 \\times \\mathbb{S}^2$ in the framework of the noncommutative integration method.
Plane wave matrix theory vs. N=4 D=4 super Yang-Mills
Kim, N. [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, 14476 Golm (Germany)
2004-06-01
A mass deformed, supersymmetric, Yang-Mills quantum mechanics has been introduced recently as the matrix model of M-theory on plane-wave backgrounds. Here we point out that the massive matrix model can be obtained as a dimensional reduction of N=4, D=4 Super Yang-Mills theory on S{sup 3}. The hamiltonian of the matrix model can be matched with the dilatation operator of the conformal field theory, and we discuss how they behave in the perturbative computations. (Abstract Copyright [2004], Wiley Periodicals, Inc.)
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.
Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories
Caselle, Michele; Panero, Marco
2015-01-01
We present a high-precision lattice calculation of the equation of state in the confining phase of SU(2) Yang-Mills theory. We show that the results are described very well by a gas of massive, non-interacting glueballs, provided one assumes an exponentially growing Hagedorn spectrum. The latter can be derived within an effective bosonic closed-string model, leading to a parameter-free theoretical prediction, which is in perfect agreement with our lattice results. Furthermore, when applied to SU(3) Yang-Mills theory, this effective model accurately describes the lattice results reported by Bors\\'anyi et al. in JHEP 07 (2012) 056.
Hagedorn spectrum and equation of state of Yang-Mills theories
Caselle, Michele; Panero, Marco
2015-01-01
We present a novel lattice calculation of the equation of state of SU(2) Yang-Mills theory in the confining phase. We show that a gas of massive, non-interacting glueballs describes remarkably well the results, provided that a bosonic closed-string model is used to derive an exponentially growing Hagedorn spectrum for the heavy glueball states with no free parameters. This effective model can be applied to SU(3) Yang-Mills theory and the theoretical prediction agrees nicely with the lattice results reported by Bors\\'anyi et al. in JHEP 07 (2012) 056.
Self-Dual Yang-Mills and the Hamiltonian Structures of Integrable Systems
Schiff, J
1992-01-01
In recent years it has been shown that many, and possibly all, integrable systems can be obtained by dimensional reduction of self-dual Yang-Mills. I show how the integrable systems obtained this way naturally inherit bihamiltonian structure. I also present a simple, gauge-invariant formulation of the self-dual Yang-Mills hierarchy proposed by several authors, and I discuss the notion of gauge equivalence of integrable systems that arises from the gauge invariance of the self-duality equations (and their hierarchy); this notion of gauge equivalence may well be large enough to unify the many diverse existing notions.
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.
Dark matter as a condensate: Deduction of microscopic properties
Gutierrez, Sergio; Camacho, Abel
2016-01-01
In the present work we model dark matter as a Bose-Einstein condensate and the main goal is the deduction of the microscopic properties, namely, mass, number of particles, and scattering length, related to the particles comprised in the corresponding condensate. This task is done introducing in the corresponding model the effects of the thermal cloud of the system. Three physical conditions are imposed, i.e., mechanical equilibrium of the condensate, explanation of the rotation curves of stars belonging to dwarf galaxies, and, finally, the deflection of light due to the presence of dark matter. These three aforementioned expressions allow us to cast the features of the particles in terms of detectable astrophysical variables. Finally, the model is contrasted against observational data and in this manner we obtain values for the involved microscopic parameters of the condensate. The deduced results are compared with previous results in which dark matter has not been considered a condensate. The main conclusion...
Power spectrum for the Bose-Einstein condensate dark matter
Velten, Hermano, E-mail: velten@physik.uni-bielefeld.de [Departamento de Fisica, UFES, Vitoria, 29075-910 Espirito Santo (Brazil); Fakultaet fuer Physik, Universitaet Bielefeld, Postfach 100131, 33501 Bielefeld (Germany); Wamba, Etienne [Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon)
2012-03-13
We assume that dark matter is composed of scalar particles that form a Bose-Einstein condensate (BEC) at some point during the cosmic evolution. Afterwards, cold dark matter is in the form of a condensate and behaves slightly different from the standard dark matter component. We study the large scale perturbative dynamics of the BEC dark matter in a model where this component coexists with baryonic matter and cosmological constant. The perturbative dynamics is studied using neo-Newtonian cosmology (where the pressure is dynamically relevant for the homogeneous and isotropic background) which is assumed to be correct for small values of the sound speed. We show that BEC dark matter effects can be seen in the matter power spectrum if the mass of the condensate particle lies in the range 15 MeV
Power spectrum for the Bose-Einstein condensate dark matter
Velten, Hermano
2011-01-01
We assume that dark matter is composed of scalar particles that form a Bose-Einstein condensate (BEC) at some point during the cosmic evolution. Afterwards, cold dark matter is in the form of a condensate and behaves slightly different from the standard dark matter component. We study the large scale perturbative dynamics of the BEC dark matter in a model where this component coexists with baryonic matter and cosmological constant. The perturbative dynamics is studied using neo- Newtonian cosmology (where the pressure is dynamically relevant for the homogeneous and isotropic background) which is assumed to be correct for small values of the sound speed. We show that BEC dark matter effects can be seen in the matter power spectrum if the mass of the condensate particle lies in the range 15meV < m < 700meV leading to a small, but perceptible, excess of power at large scales.
2PI Effective Action and Evolution Equations of N = 4 super Yang-Mills
Smolic, Jelena
2011-01-01
We employ nPI effective action techniques to study N = 4 super Yang-Mills, and write down the 2PI effective action of the theory. We also supply the evolution equations of two-point correlators within the theory.
Freedom and confinement in lattice Yang-Mills theories. A case for divorce
Colangelo, P.; Cosmai, L.; Pellicoro, M.; Preparata, G.
1986-03-01
We present evidence that nonperturbative effects in lattice gauge theories do not obey at small coupling constant (large ..beta..) asymptotic scaling, but they rather behave as suggested by a recent result in continuum Yang-Mills theories. We also discuss the possible impact of these results on our understanding of QCD.
A note on the Coulomb branch of susy Yang-Mills
Kabat, D; Kabat, Daniel; Lifschytz, Gilad
2006-01-01
We compute the force between oppositely charged W bosons in the large N limit of Yang-Mills with 16 supercharges broken to SU(N) x U(1) by a finite Higgs vev. We clarify some issues regarding Wilson line computations and show that there is a regime in which the force between W bosons is independent of separation distance.
A note on the Coulomb branch of susy Yang-Mills
Kabat, Daniel [Department of Physics, Columbia University, New York, NY 10027 (United States)]. E-mail: kabat@phys.columbia.edu; Lifschytz, Gilad [Department of Mathematics and Physics, University of Haifa at Oranim, Tivon 36006 (Israel)]. E-mail: giladl@research.haifa.ac.il
2006-02-16
We compute the force between oppositely charged W bosons in the large N limit of Yang-Mills with 16 supercharges broken to SU(N)xU(1) by a finite Higgs vev. We clarify some issues regarding Wilson line computations and show that there is a regime in which the force between W bosons is independent of separation distance.
Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
Caron Huot, Simon; He, Song
2013-01-01
We study the S-matrix of planar = 4 supersymmetric Yang-Mills theory when external momenta are restricted to a two-dimensional subspace of Minkowski space. We find significant simplifications and new, interesting structures for tree and loop amplitudes in two-dimensional kinematics, in particular...
Existence of axially symmetric solutions in SU(2)-Yang-Mills and related theories
Hannibal, L; Hannibal, Ludger; Ossietzky, Carl von
1999-01-01
It is shown that the static axially symmetric solutions of SU(2) Einstein-Yang-Mills-Dilaton theory constructed by Kleihaus and Kunz are gauge-equivalent to two-parameter families of embedded abelian solutions, characterized by mass and magnetic dipole moment. The existence of other particle-like solutions is excluded.
The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces
Driver, Bruce K; Hall, Brian C; Kemp, Todd
2016-01-01
We prove the Makeenko-Migdal equation for two-dimensional Euclidean Yang-Mills theory on an arbitrary compact surface, possibly with boundary. In particular, we show that two of the proofs given by the first, third, and fourth authors for the plane case extend essentially without change to compact surfaces.
Challifour, John L.; Timko, Edward J.
2016-06-01
Using a Krein indefinite metric in Fock space, the Hamiltonian for cut-off models of canonically quantized Higgs-Yang-Mills fields interpolating between the Gupta-Bleuler-Feynman and Landau gauges is shown to be essentially maximal accretive and essentially Krein selfadjoint.
Classical and semi-classical solutions of the Yang--Mills theory. [Review
Jackiw, R.; Nohl, C.; Rebbi, C.
1977-12-01
This review summarizes what is known at present about classical solutions to Yang-Mills theory both in Euclidean and Minkowski space. The quantal meaning of these solutions is also discussed. Solutions in Euclidean space expose multiple vacua and tunnelling of the quantum theory. Those in Minkowski space-time provide a semi-classical spectrum for a conformal generator.
Two-loop Feynman Diagrams in Yang-Mills Theory from Bosonic String Amplitudes
Körs, B; Kors, Boris; Schmidt, Michael G.
2000-01-01
We present intermediate results of an ongoing investigation which attempts a generalization of the well known one-loop Bern Kosower rules of Yang-Mills theory to higher loop orders. We set up a general procedure to extract the field theoretical limit of bosonic open string diagrams, based on the sewing construction of higher loop world sheets. It is tested with one- and two-loop scalar field theory, as well as one-loop and two-loop vacuum Yang-Mills diagrams, reproducing earlier results. It is then applied to two-loop two-point Yang-Mills diagrams in order to extract universal renormalization coefficients that can be compared to field theory. While developing numerous technical tools to compute the relevant contributions, we hit upon important conceptual questions: Do string diagrams reproduce Yang-Mills Feynman diagrams in a certain preferred gauge? Do they employ a certain preferred renormalization scheme? Are four gluon vertices related to three gluon vertices? Unfortunately, our investigations remained in...
Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
Chiodaroli, Marco; Johansson, Henrik; Roiban, Radu
2015-01-01
We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian and Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which th...
Exact Solutions of the SU(2) Yang-Mills-Higgs Theory
Teh, R
2001-01-01
Some exact static solutions of the SU(2) Yang-Mills-Higgs theory are presented. These solutions do not satisfy the first order Bogomol'nyi equations, and do not possess finite energy. They are axially symmetric and could possibly represent monopoles and an antimonopole sitting on the z-axis.
Generalized Riccati equations for self-dual Yang--Mills fields
Chau, L.; Yen, H.C.
1987-05-01
It is shown that although no Riccati equations in the strict sense are likely to exist for the self-dual Yang--Mills fields, certain ''generalized Riccati equations'' derivable from the Baecklund transformation do exist, and are capable of reproducing the linear system when a certain contraint is imposed.
2PI effective action and evolution equations of N=4 super Yang-Mills
Smolic, Jelena; Smolic, Milena [University of Amsterdam, Institute for Theoretical Physics, Amsterdam (Netherlands)
2012-08-15
We employ nPI effective action techniques to study N=4 super Yang-Mills, and write down the 2PI effective action of the theory to two-loop order in the symmetric phase. We also supply the evolution equations of two-point correlators within the theory. (orig.)
The low-lying spectrum of N=1 supersymmetric Yang-Mills theory
Bergner, Georg; Montvay, Istvan; Muenster, Gernot; Piemonte, Stefano
2015-01-01
The spectrum of the lightest bound states in N=1 supersymmetric Yang-Mills theory with SU(2) gauge group, calculated on the lattice, is presented. The masses have first been extrapolated towards vanishing gluino mass and then to the continuum limit. The final picture is consistent with the formation of degenerate supermultiplets.
WANG Dian-Fu
2008-01-01
In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Yang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.
Massive and mass-less Yang-Mills and gravitational fields
Veltman, M.J.G.; Dam, H. van
1970-01-01
Massive and mass-less Yang-Mills and gravitational fields are considered. It is found that there is a discrete difference between the zero-mass theories and the very small, but non-zero mass theories. In the case of gravitation, comparison of massive and mass-less theories with experiment, in
The complete one-loop spin chain for N=2 Super-Yang-Mills
Vecchia, P D
2004-01-01
We show that the complete planar one-loop mixing matrix of the N=2 Super Yang--Mills theory can be obtained from a reduction of that of the N=4 theory. For composite operators of scalar fields, this yields an anisotropic XXZ spin chain, whose spectrum of excitations displays a mass gap.
Eigenvalue spectrum of lattice $\\mathcal{N}=4$ super Yang-Mills
Weir, David J; Mehta, Dhagash
2013-01-01
We present preliminary results for the eigenvalue spectrum of four-dimensional ${\\cal N}=4$ super Yang-Mills theory on the lattice. In particular, by studying the the spectral density a measurement of the anomalous dimension is made and found to be consistent with zero.
Microscopic- versus Effective Coupling in N=2 Yang-Mills With Four Flavours
Sachs, I; Sachs, Ivo; Weir, Billy
2000-01-01
We determine the instanton corrections to the effective coupling in SU(2), N=2 Yang-Mills theory with four flavours to all orders. Our analysis uses the S(2,Z)-invariant curve and the two instanton contribution obtained earlier to fix the higher order contributions uniquely.
Monte Carlo simulation of SU(2) Yang-Mills theory with light gluinos
Campos, I; Kirchner, R; Luckmann, S; Montvay, István; Münster, G; Spanderen, K; Westphalen, J
1999-01-01
In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with light dynamical gluinos the low energy features of the dynamics as confinement and bound state mass spectrum are investigated. The motivation is supersymmetry at vanishing gluino mass. The performance of the applied two-step multi-bosonic dynamical fermion algorithm is discussed.
Monte Carlo simulation of SU(2) Yang-Mills theory with light gluinos
Campos, I.; Kirchner, R.; Montvay, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Feo, A.; Luckmann, S.; Muenster, G.; Spanderen, K. [Muenster Univ. (Germany). Inst. fuer Theoretische Physik 1
1999-12-01
In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with light dynamical gluinos the low energy features of the dynamics as confinement and bound state mass spectrum are investigated. The motivation is supersymmetry at vanishing gluino mass. The performance of the applied two-step multi-bosonic dynamical fermion algorithm is discussed. (orig.)
N=1 Super-Yang-Mills on the Lattice Weak and Strong Coupling Limits
Gabrielli, E
1999-01-01
We present a general review about the N=1 supersymmetric SU(Nc) Yang-Mills on the lattice focusing our attention on the quenched approximation in supersymmetry. Finally we analyse and discuss the recent results obtained at strong coupling and large Nc for the mesonic and fermionic propagators and spectrum.
Generalized WDVV equations for $F_4$ pure N=2 Super-Yang-Mills theory
Hoevenaars, L.K.; Kersten, P.H.M.; Martini, R.
2000-01-01
An associative algebra of holomorphic differential forms is constructed associated with pure N=2 Super-Yang-Mills theory for the Lie algebra $F_4$ . Existence and associativity of this algebra, combined with the general arguments in the work of Marshakov, Mironov and Morozov, proves that the prepote
Notes on equivalences and Higgs branches in N=2 supersymmetric Yang-Mills theory
Danielsson, U H; Danielsson, Ulf H; Stjernberg, Par
1996-01-01
In this paper we investigate how various equivalences between effective field theories of N=2 SUSY Yang-Mills theory with matter can be understood through Higgs breaking, i.e. by giving expectation values to squarks. We give explicit expressions for the flat directions for a wide class of examples.
Massive and mass-less Yang-Mills and gravitational fields
Veltman, M.J.G.; Dam, H. van
1970-01-01
Massive and mass-less Yang-Mills and gravitational fields are considered. It is found that there is a discrete difference between the zero-mass theories and the very small, but non-zero mass theories. In the case of gravitation, comparison of massive and mass-less theories with experiment, in partic
The Hamiltonian structure of Yang-Mills theories and instantons II
Bergvelt, M. J.; De Kerf, E. A.
1986-11-01
The formalism of constraints, reviewed in paper I, is applied to Yang-Mills theory to determine the physical phase space. This turns out to be the cotangent bundle of orbit space, the space of gauge inequivalent potentials. Self-dual configurations are not Hamiltonian with respect to the symplectic structure inherited from the general system.
Chau, L.L.
1983-01-01
Integrable properties, i.e., existence of linear systems, infinite number of conservation laws, Reimann-Hilbert transforms, affine Lie algebra of Kac-Moody, and Bianchi-Baecklund transformation, are discussed for the constraint equations of the supersymmetric Yang-Mills fields. For N greater than or equal to 3 these constraint equations give equations of motion of the fields. These equations of motion reduce to the ordinary Yang-Mills equations as the spinor and scalar fields are eliminated. These understandings provide a possible method to solve the full Yang-Mills equations. Connections with other non-linear systems are also discussed. 53 references.
Füzfa, A
2002-01-01
The general hamiltonian formalism for time-dependent Einstein-Yang-Mills equations is presented and then applied to the well studied case of spherically symmetric su(2)-valued Yang-Mills fields. Here, we focus on by far less known time dependent solutions of these equations, and especially on perturbations of Friedmann-Lemaitre homogeneous solutions. By analysing the hamiltonian constraints, we present numerical evidences that the non abelian Yang-Mills fields are more sensitive to inhomogeneity (at least in the expansion rate) than their scalar (inflaton) and abelian (Maxwell) counterparts. Interesting consequences on the process of gravitational instability are briefly outlined here and will be developped in a forthcoming paper.
The Rethermalizing Bose-Einstein Condensate of Dark Matter Axions
Banik, Nilanjan; Sikivie, Pierre; Todarello, Elisa Maria
2015-01-01
The axions produced during the QCD phase transition by vacuum realignment, string decay and domain wall decay thermalize as a result of their gravitational self-interactions when the photon temperature is approximately 500 eV. They then form a Bose-Einstein condensate (BEC). Because the axion BEC rethermalizes on time scales shorter than the age of the universe, it has properties that distinguish it from other forms of cold dark matter. The observational evidence for caustic rings of dark matter in galactic halos is explained if the dark matter is axions, at least in part, but not if the dark matter is entirely WIMPs or sterile neutrinos.
Dark matter and dark energy induced by condensates
Antonio Capolupo
2016-01-01
It is shown that the vacuum condensate induced by many phenomena behaves as a perfect fluid which, under particular conditions, has zero or negative pressure. In particular, the condensates of thermal states of fields in curved space and of mixed particles have been analyzed. It is shown that the thermal states with the cosmic microwave radiation temperature and the Unruh and the Hawking radiations give negligible contributions to the critical energy density of the universe, while the thermal...
Domain Walls in Supersymmetric Yang-Mills Theories
Kaplunovsky, V S; Yankielowicz, Shimon; Kaplunovsky, Vadim S.; Sonnenschein, Jacob; Yankielowicz, Shimon
1999-01-01
We study BPS saturated domain walls in the supersymmetric SU(2) gauge theory. For a theory with a very light adjoint scalar (mass <~ Lambda/400) we use the perturbed N=2 Seiberg-Witten theory to calculate the actual field configuration of the domain wall. The wall has a sandwich-like five-layer structure of three distinct phases -- electric confinement, Coulomb and oblique confinement -- separated by two separate transition regions. For larger scalar masses, the three-phase structure disappears and the Seiberg-Witten theory becomes inadequate because of two major problems: First, the higher-derivative interactions between the light fields become relevant and second, both the magnetic monopole condensate and the dyon condensate show up in the same region of space, a phenomenon indescribable in terms of a local field theory. Nevertheless, we argue that the BPS saturated domain wall continues to exist in this regime and give a qualitative description of the scalar and gaugino condensates. Finally, we discuss ...
Accurate Determination of Reference Scales for Wilson Gauge Action from Yang--Mills Gradient Flow
Asakawa, Masayuki; Iritani, Takumi; Itou, Etsuko; Kitazawa, Masakiyo; Suzuki, Hiroshi
2015-01-01
A high precision parametrization of the lattice spacing ($a$) in terms of the bare coupling ($\\beta$) for the SU(3) Yang--Mills theory with the Wilson gauge action is given in a wide range of $\\beta$ with high accuracy. The Yang--Mills gradient flow with respect to the flow time $t$ for the dimensionless observable, $t\\frac{d}{dt}t^2\\langle E(t)\\rangle$, is utilized to determine the parametrization. With fine lattice spacings ($6.3\\le\\beta\\le7.5$) and large lattice volumes ($N_{\\rm s}=64$--$128$), the discretization and finite-volume errors are significantly reduced to the same level as the statistical error. With this lattice setup, the lattice and perturbative estimates of $t^2\\langle E\\rangle$ are also compared as a function of $t$.
Yang-Mills matrix models with ghosts and derivations of the graded shuffle algebra
Krishnaswami, Govind S
2007-01-01
We consider large-N multi-matrix models that are inspired by the action of Yang-Mills theory including gauge-fixing and ghost terms. We show that the factorized Schwinger-Dyson loop equations of such matrix models have a special algebraic property not shared by generic matrix models. When expressed in terms of the generating series of gluon and ghost correlations G(xi), they are quadratic equations S^i G = G xi^i G in concatenation of correlations. We express S^i in terms of the left annihilation operator and show that it is a derivation of the graded-shuffle product of correlation tensors. A corresponding property of Yang-Mills theory was observed by Makeenko and Migdal in the Wilson loop formulation, where S^i was expressed in terms of the path and area derivatives.
Topics In N = 4 Yang-mills And The Self-dual String
Basu, A
2005-01-01
We analyze some systematics of the coupling constant dependence of correlators in N = 4 Yang- Mills, which is the world-volume theory on D3-branes. We use the fact that the operator Ot that generates infinitesimal changes of the coupling constant in this theory sits in the same supermultiplet as the superconformal currents. We show how superconformal current Ward identities determine a class of terms in the operator product expansion of Ot with any other operator. In certain cases, this leads to constraints on the coupling dependence of correlation functions in N = 4 Yang-Mills. As an application, we demonstrate the exact non-renormalization of two and certain three-point correlation functions of BPS operators. We next approximate these integrated correlators by using a truncated OPE expansion. This leads to differential equations for the coupling dependence. When applied to a particular sixteen point correlator, the coupling dependence we find agrees with the corresponding amplitude computed via the Ad...
Renormalization aspects of N = 1 Super Yang-Mills theory in the Wess-Zumino gauge
Capri, M.A.L.; Granado, D.R.; Guimaraes, M.S.; Justo, I.F.; Sorella, S.P.; Vercauteren, D. [UERJ-Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Instituto de Fisica, Maracana, Rio de Janeiro (Brazil); Mihaila, L. [Karlsruhe Institute of Technology (KIT), Institut fuer Theoretische Teilchenphysik, Karlsruhe (Germany)
2014-04-15
The renormalization of N = 1 Super Yang-Mills theory is analyzed in the Wess-Zumino gauge, employing the Landau condition. An all-orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field, and gluino renormalization. The nonrenormalization theorem of the gluon-ghost-antighost vertex in the Landau gauge is shown to remain valid in N = 1 Super Yang-Mills. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino. These features are explicitly checked through a three-loop calculation. (orig.)
Hedgehogs in Wilson loops and phase transition in SU(2) Yang-Mills theory
Belavin, V A; Kozlov, I E
2006-01-01
We suggest that the gauge-invariant hedgehogs-like structures in the Wilson loops are physically interesting degrees of freedom in the Yang-Mills theory. The trajectories of these hedgehogs are closed curves which correspond to center-valued (untraced) Wilson loops and are characterized by the center charge and by the winding number. We show numerically in SU(2) Yang-Mills theory that the density of the hedgehogs in the thermal Wilson-Polyakov line is very sensitive to the finite temperature phase transition. The (additively normalized) hedgehog density behaves as an order parameter: the density is almost independent of the temperature in the confinement phase and changes substantially as the system gets into the deconfinement phase. Our results suggest in particular that the (static) hedgehogs may be relevant degrees of freedom around the deconfinement transition, and thus affect evolution of the quark-gluon plasma in high-energy heavy ion collisions.
On the spherically symmetric Einstein-Yang-Mills-Higgs equations in Bondi coordinates
Tadmon, Calvin
2012-01-01
We revisit and generalize, to the Einstein-Yang-Mills-Higgs system, previous results of D. Christodoulou and D. Chae concerning global solutions for the Einstein-scalar field and the Einstein-Maxwell-Higgs equations. The novelty of the present work is twofold. For one thing the assumption on the self-interaction potential is improved. For another thing explanation is furnished why the solutions obtained here and those proved by Chae for the Einstein-Maxwell-Higgs decay more slowly than those established by Christodoulou in the case of self-gravitating scalar fields. Actually this latter phenomenon stems from the non-vanishing local charge in Einstein-Maxwell-Higgs and Einstein-Yang-Mills-Higgs models.
Excluded-volume effects for a hadron gas in Yang-Mills theory
Alba, Paolo; Nada, Alessandro; Panero, Marco; Stöcker, Horst
2016-01-01
When the multiplicities of particles produced in heavy-ion collisions are fitted to the hadron-resonance-gas model, excluded-volume effects play a significant role. In this work, we study the impact of such effects onto the equation of state of pure Yang-Mills theory at low temperatures, comparing the predictions of the statistical model with lattice results. In particular, we present a detailed analysis of the SU(2) and SU(3) Yang-Mills theories: we find that, for both of them, the best fits to the equilibrium thermodynamic quantities are obtained when one assumes that the volume of different glueball states is inversely proportional to their mass. The implications of these findings for QCD are discussed.
Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories
Caselle, Michele; Nada, Alessandro; Panero, Marco [Department of Physics, University of Turin & INFN,Via Pietro Giuria 1, I-10125 Turin (Italy)
2015-07-27
We present a high-precision lattice calculation of the equation of state in the confining phase of SU(2) Yang-Mills theory. We show that the results are described very well by a gas of massive, non-interacting glueballs, provided one assumes an exponentially growing Hagedorn spectrum. The latter can be derived within an effective bosonic closed-string model, leading to a parameter-free theoretical prediction, which is in perfect agreement with our lattice results. Furthermore, when applied to SU(3) Yang-Mills theory, this effective model accurately describes the lattice results reported by Borsányi et al. in http://dx.doi.org/10.1007/JHEP07(2012)056.
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...
Amplitude relations in heterotic string theory and Einstein-Yang-Mills
Schlotterer, Oliver
2016-11-01
We present all-multiplicity evidence that the tree-level S-matrix of gluons and gravitons in heterotic string theory can be reduced to color-ordered single-trace amplitudes of the gauge multiplet. Explicit amplitude relations are derived for up to three gravitons, up to two color traces and an arbitrary number of gluons in each case. The results are valid to all orders in the inverse string tension α' and generalize to the ten-dimensional superamplitudes which preserve 16 supercharges. Their field-theory limit results in an alternative proof of the recently discovered relations between Einstein-Yang-Mills amplitudes and those of pure Yang-Mills theory. Similarities and differences between the integrands of the Cachazo-He-Yuan formulae and the heterotic string are investigated.
Tree amplitudes of noncommutative U(N) Yang-Mills theory
Huang Jiahui [Center of Mathematical Science, Zhejiang University, Hangzhou (China); Huang Rijun; Jia Yin, E-mail: huangjh19@gmail.com [Physics Department, Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou (China)
2011-10-21
Following the spirit of the S-matrix program, we propose a modified Britto-Cachazo-Feng-Witten recursion relation for tree amplitudes of noncommutative U(N) Yang-Mills theory. Starting from three-point amplitudes, one can use this modified BCFW recursion relation to compute or analyze color-ordered tree amplitudes without relying on any detailed information of noncommutative Yang-Mills theory. After clarifying the color structure of noncommutative tree amplitudes, we write down the noncommutative analogies of Kleiss-Kuijf and Bern-Carrasco-Johansson relations for color-ordered tree amplitudes and prove them using the modified BCFW recursion relation. This checks the consistency of the relation. (paper)
Tree amplitudes of noncommutative U(N) Yang-Mills theory
Huang, Jia-Hui; Huang, Rijun; Jia, Yin
2011-10-01
Following the spirit of the S-matrix program, we propose a modified Britto-Cachazo-Feng-Witten recursion relation for tree amplitudes of noncommutative U(N) Yang-Mills theory. Starting from three-point amplitudes, one can use this modified BCFW recursion relation to compute or analyze color-ordered tree amplitudes without relying on any detailed information of noncommutative Yang-Mills theory. After clarifying the color structure of noncommutative tree amplitudes, we write down the noncommutative analogies of Kleiss-Kuijf and Bern-Carrasco-Johansson relations for color-ordered tree amplitudes and prove them using the modified BCFW recursion relation. This checks the consistency of the relation.
Boundary behaviors for general off-shell amplitudes in Yang-Mills theory
Zhang, Yun; Chen, Gang
2013-07-01
The boundary behavior of amplitudes—the amplitudes’ behavior under a large Britto-Cachazo-Feng-Witten (BCFW) momenta deformation for a pair of legs—in Yang-Mills theory is of great interest recently. In this article we analyze the boundary behavior of off-shell Yang-Mills amplitudes in Feynman gauge. The deformed legs can be either adjacent or nonadjacent. We find that a set of reduced vertices can be used to simplify the analysis and calculation of the boundary behavior of amplitudes. Boundary behavior for amplitudes with adjacent BCFW deformation is read off from the reduced vertices. Then we discover a relationship between a permutation sum with fixed color ordering of the legs and the improved boundary behavior for the off-shell amplitudes with a nonadjacent BCFW momenta deformation. Based on the boundary behavior, we generalize the BCFW recursion relation to calculate general tree-level off-shell amplitudes and analyze the relations between them.
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.
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.
Dual-color decompositions at one-loop level in Yang-Mills theory
Du, Yi-Jian; Fu, Chih-Hao
2014-01-01
In this work, we extend the construction of dual color decomposition in Yang-Mills theory to one-loop level, i.e., we show how to write one-loop integrands in Yang-Mills theory to the dual DDM-form and the dual trace-form. In dual forms, integrands are decomposed in terms of color-ordered one-loop integrands for color scalar theory with proper dual color coefficients.In dual DDM decomposition, The dual color coefficients can be obtained directly from BCJ-form by applying Jacobi-like identities for kinematic factors. In dual trace decomposition, the dual trace factors can be obtained by imposing one-loop KK relations, reflection relation and their relation with the kinematic factors in dual DDM-form.
Numerical Hermitian Yang-Mills connections and vector bundle stability in heterotic theories
Anderson, Lara B.; Braun, Volker; Karp, Robert L.; Ovrut, Burt A.
2010-06-01
A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.
Amplitude relations in heterotic string theory and Einstein-Yang-Mills
Schlotterer, Oliver
2016-01-01
We present all-multiplicity evidence that the tree-level S-matrix of gluons and gravitons in heterotic string theory can be reduced to color-ordered single-trace amplitudes of the gauge multiplet. Explicit amplitude relations are derived for up to three gravitons, up to two color traces and an arbitrary number of gluons in each case. The results are valid to all orders in the inverse string tension alpha' and generalize to the ten-dimensional superamplitudes which preserve 16 supercharges. Their field-theory limit results in an alternative proof of the recently discovered relations between Einstein-Yang-Mills amplitudes and those of pure Yang-Mills theory. Similarities and differences between the integrands of the Cachazo-He-Yuan formulae and the heterotic string are investigated.
Numerical Hermitian Yang-Mills Connections and Vector Bundle Stability in Heterotic Theories
Anderson, Lara B; Karp, Robert L; Ovrut, Burt A
2010-01-01
A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.
Hedgehogs in Wilson loops and phase transition in SU(2) Yang-Mills theory
Belavin, V.A. [Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, RU-117259 Moscow (Russian Federation); Chernodub, M.N. [Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, RU-117259 Moscow (Russian Federation) and Department of Theoretical Physics, Uppsala University, P.O. Box 803, S-75108 Uppsala (Sweden)]. E-mail: maxim.chernodub@itep.ru; Kozlov, I.E. [Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, RU-117259 Moscow (Russian Federation); Faculty of Physics, Moscow State University, RU-119992 Moscow (Russian Federation)
2006-08-07
We suggest that the gauge-invariant hedgehog-like structures in the Wilson loops are physically interesting degrees of freedom in the Yang-Mills theory. The trajectories of these 'hedgehog loops' are closed curves corresponding to center-valued (untraced) Wilson loops and are characterized by the center charge and winding number. We show numerically in the SU(2) Yang-Mills theory that the density of hedgehog structures in the thermal Wilson-Polyakov line is very sensitive to the finite-temperature phase transition. The (additively normalized) hedgehog line density behaves like an order parameter: The density is almost independent of the temperature in the confinement phase and changes substantially as the system enters the deconfinement phase. In particular, our results suggest that the (static) hedgehog lines may be relevant degrees of freedom around the deconfinement transition and thus affect evolution of the quark-gluon plasma in high-energy heavy-ion collisions.
Structure constants of planar N =4 Yang Mills at one loop
Alday, L F; Gava, E; Narain, K S; Alday, Luis F.; David, Justin R.; Gava, Edi
2005-01-01
We study structure constants of gauge invariant operators in planar N=4 Yang-Mills at one loop with the motivation of determining features of the string dual of weak coupling Yang-Mills. We derive a simple renormalization group invariant formula characterizing the corrections to structure constants of any primary operator in the planar limit. Applying this to the scalar SO(6) sector we find that the one loop corrections to structure constants of gauge invariant operators is determined by the one loop anomalous dimension Hamiltonian in this sector. We then evaluate the one loop corrections to structure constants for scalars with arbitrary number of derivatives in a given holomorphic direction. We find that the corrections can be characterized by suitable derivatives on the four point tree function of a massless scalar with quartic coupling. We show that individual diagrams violating conformal invariance can be combined together to restore it using a linear inhomogeneous partial differential equation satisfied ...
Infrared Behaviour of Landau Gauge Yang-Mills Theory with a Fundamentally Charged Scalar Field
Fister, Leonard
2010-01-01
The infrared behaviour of the n-point functions of a Yang-Mills theory with a charged scalar field in the fundamental representation of SU(N) is studied in the formalism of Dyson-Schwinger equations. Assuming a stable skeleton expansion solutions in form of power laws for the Green functions are obtained. For a massless scalar field the uniform limit is sufficient to describe the infrared scaling behaviour of vertices. Not taking into account a possible Higgs-phase it turns out that kinematic singularities play an important role for the scaling solutions of massive scalars. On a qualitative level scalar Yang-Mills theory yields similar scaling solutions as recently obtained for QCD.
Some Comments on the String Singularity of the Yang-Mills-Higgs Theory
Lim, Kok-Geng; Teh, Rosy
2010-07-01
We are going to make use of the regulated polar angle which had been introduced by Boulware et al.. to show that in the SU(2) Yang-Mills-Higgs theory when the magnetic monopole is carried by the gauge field, the Higgs field does not carry the monopole and vice versa. In the Yang-Mills-Higgs theory, our solution shows that when the parameter ɛ ≠ 0, the monopole is carried by the gauge field and there is a string singularity in the gauge field. When the parameter ɛ → 0, the monopole is transferred from the gauge field to the Higgs field and the string singularity disappeared. The solution is only singular at the origin, that is at r = 0 as it becomes the Wu-Yang monopole.
Matsuura, So; Ohta, Kazutoshi
2014-01-01
We define supersymmetric Yang-Mills theory on an arbitrary two-dimensional lattice (polygon decomposition) with preserving one supercharge. When a smooth Riemann surface $\\Sigma_g$ with genus $g$ emerges as an appropriate continuum limit of the generic lattice, the discretized theory becomes topologically twisted $\\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory on $\\Sigma_g$. If we adopt the usual square lattice as a special case of the discretization, our formulation is identical with Sugino's lattice model. Although the tuning of parameters is generally required while taking the continuum limit, the number of the necessary parameters is at most two because of the gauge symmetry and the supersymmetry. In particular, we do not need any fine-tuning if we arrange the theory so as to possess an extra global $U(1)$ symmetry ($U(1)_{R}$ symmetry) which rotates the scalar fields.
Yang-Mills equation for the nuclear geometrical collective model connexion
Sparks, N.; Rosensteel, G.
2017-01-01
The Bohr-Mottelson collective model of rotations and quadrupole vibrations is a foundational model in nuclear structure physics. A modern formulation using differential geometry of bundles builds on this legacy collective model to allow a deformation-dependent interaction between rotational and vortical degrees of freedom. The interaction is described by the bundle connexion. This article reports the Yang-Mills equation for the connexion. For a class of solutions to the Yang-Mills equation, the differential geometric collective model attains agreement between experiment and theory for the moments of inertia of deformed isotopes. More generally, the differential geometric framework applies to models of emergent phenomena in which two interacting sets of degrees of freedom must be unified.
N=4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole
Huang, Xing
2014-01-01
We construct four-dimensional N=4 super-Yang-Mills theories on a conic sphere with various background R-symmetry gauge fields. We study free energy and supersymmetric Renyi entropy using heat kernel method as well as localization technique. We find that the universal contribution to the partition function in the free field limit is the same as that in the strong coupling limit, which implies that it may be protected by supersymmetry. Based on the fact that, the conic sphere can be conformally mapped to $S^1\\times H^3$ and the R-symmetry background fields can be supported by the R-charges of black hole, we propose that the holographic dual of these theories are five-dimensional, supersymmetric STU topological black holes. We demonstrate perfect agreement between N=4 super-Yang-Mills theories in the planar limit and the STU topological black holes.
The thermodynamics of quantum Yang-Mills theory theory and applications
Hofmann, Ralf
2016-01-01
This latest edition enhances the material of the first edition with a derivation of the value of the action for each of the Harrington-Shepard calorons/anticalorons that are relevant for the emergence of the thermal ground state. Also included are discussions of the caloron center versus its periphery, the role of the thermal ground state in U(1) wave propagation, photonic particle-wave duality, and calculational intricacies and book-keeping related to one-loop scattering of massless modes in the deconfining phase of an SU(2) Yang-Mills theory. Moreover, a derivation of the temperature-redshift relation of the CMB in deconfining SU(2) Yang-Mills thermodynamics and its application to explaining an apparent early re-ionization of the Universe are given. Finally, a mechanism of mass generation for cosmic neutrinos is proposed.
Universal aspects in the equation of state for Yang-Mills theories
Nada, Alessandro
2015-01-01
We present high-precision lattice calculations of the thermodynamics of Yang-Mills theories with different gauge groups. In the confining phase, we show that the equation of state is described remarkably well by a gas of massive, non-interacting glueballs, provided that an effective bosonic closed-string model is used to derive an exponentially growing Hagedorn spectrum for the heavy states. In particular, this model describes very accurately the results for the SU(3) theory reported by Bors\\'anyi et al. in JHEP 07 (2012) 056, as well as a novel set of lattice data for the SU(2) theory. In addition, we also also show that the equation of state in the deconfined phase exhibits a near perfect proportionality to the number of gluon degrees of freedom, including for the Yang-Mills theory based on the exceptional, center-less gauge group $G_2$.
Transport properties of N=4 supersymmetric Yang-Mills theory at finite coupling
Benincasa, P; Benincasa, Paolo; Buchel, Alex
2006-01-01
Gauge theory-string theory duality describes strongly coupled N=4 supersymmetric SU(n) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-n N=4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation for the shear and the sound wave lowest quasinormal modes in the leading order alpha'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the alpha'-corrected nonextremal black branes in string theory.
On the sign problem in 2D lattice super Yang--Mills
Catterall, Simon; Joseph, Anosh; Mehta, Dhagash
2011-01-01
In recent years a new class of supersymmetric lattice theories have been proposed which retain one or more exact supersymmetries for non-zero lattice spacing. Recently there has been some controversy in the literature concerning whether these theories suffer from a sign problem. In this paper we address this issue by conducting simulations of the N=(2, 2) and N=(8, 8) supersymmetric Yang--Mills theories in two dimensions for the U(N) theories with N=2,3,4, using the new twisted lattice formulations. Our results provide evidence that these theories do not suffer from a sign problem in the continuum limit. These results thus boost confidence that the new lattice formulations can be used successfully to explore non-perturbative aspects of four-dimensional N=4 supersymmetric Yang--Mills theory.
Correspondence between Einstein-Yang-Mills-Lorentz systems and dynamical torsion models
Cembranos, Jose A R
2016-01-01
In the framework of Einstein-Yang-Mills theories, we study the gauge Lorentz group and establish a particular equivalence between this case and a certain class of theories with torsion within Riemann-Cartan space-times. This relation is specially useful in order to simplify the problem of finding exact solutions to the Einstein-Yang-Mills equations. Solutions for non-vanishing torsion with rotation and reflection symmetries are presented by the explicit use of this correspondence. Although these solutions were found in previous literature by a different approach, our method provides an alternative way to obtain them and it may be used in future research to find other exact solutions within this theory.
A solution to the non-linear equations of D=10 super Yang-Mills theory
Mafra, Carlos R
2015-01-01
In this letter, we present a formal solution to the non-linear field equations of ten-dimensional super Yang--Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher mass dimensions are defined and their equations of motion spelled out.
Superspace Formulation of N=4 Super Yang-Mills Theory with a Central Charge
Saito, J
2005-01-01
A superspace formulation using superconnections and supercurvatures is specifically constructed for N=4 extended super Yang-Mills theory with a central charge in four dimensions, first proposed by Sohnius, Stelle and West long ago. We find that the constraints, almost uniquely derived from the possible spin structure of the multiplet, can be algebraically solved which results in an off-shell supersymmetric formulation of the theory on the superspace.
Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
Bern, Z; Kosower, D A; Roiban, R; Smirnov, V A
2006-01-01
We confirm by explicit computation the conjectured all-orders iteration of planar maximally supersymmetric N=4 Yang-Mills theory in the nontrivial case of five-point two-loop amplitudes. We compute the required unitarity cuts of the integrand and evaluate the resulting integrals numerically using a Mellin--Barnes representation and the automated package of ref.~[1]. This confirmation of the iteration relation provides further evidence suggesting that N=4 gauge theory is solvable.
Bassetto, A; Torrielli, A; Vian, F
2005-01-01
We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.
Power-law mass inflation in Einstein-Yang-Mills-Higgs black holes
Galtsov, D V
1997-01-01
Analytical formulas are presented describing a generic singularity inside the static spherically symmetric black holes in the SU(2) Einstein-Yang-Mills-Higgs theories with triplet or doublet Higgs field. The singularity is spacelike and exhibits a `power-low mass inflation'. Alternatively this asymptotic may be interpreted as a pointlike singularity with a non-vanishing shear in the Kantowski-Sachs anisotropic cosmology.
On the string actions for the generalized two-dimensional Yang-Mills theories
Sugawara, Y
1996-01-01
We study the structures of partition functions of the large N generalized two-dimensional Yang-Mills theories (gYM_2) by recasting the higher Casimirs. We clarify the appropriate interpretations of them and try to extend the Cordes-Moore-Ramgoolam's topological string model describing the ordinary YM_2 \\cite{CMR} to those describing gYM_2. The concept of ''deformed gravitational descendants'' will be introduced for this purpose.
Emergence of Yang Mills theory from the Non-Abelian Nambu Model
Escobar, C A
2016-01-01
The equivalence between the Non-Abelian Nambu model (NANM) and Yang Mills theory is proved, after demanding the Gauss laws at some initial time to the first one. Thereby, the Lorentz violation encoded into the constraint that defines the NANM is physically unobservable. As result, the Goldstone bosons in the NANM arising from the spontaneous symmetry breaking can be identified as the standard gauge fields.
Hamiltonian Formulation of the Yang-Mills field on the null-plane
Casana, R., E-mail: casana@ufma.b [Universidade Federal do Maranhao (UFMA), Departamento de Fisica, Campus Universitario do Bacanga, CEP 65085-580, Sao Luis - MA, Brasil. (Brazil); Pimentel, B.M., E-mail: pimentel@ift.unesp.b [Instituto de Fisica Teorica (IFT/UNESP), UNESP - Sao Paulo State University, Caixa Postal 70532-2, 01156-970, Sao Paulo, SP (Brazil); Zambrano, G.E.R., E-mail: gramos@ift.unesp.b [Instituto de Fisica Teorica (IFT/UNESP), UNESP - Sao Paulo State University, Caixa Postal 70532-2, 01156-970, Sao Paulo, SP (Brazil)
2010-02-15
We have studied the null-plane hamiltonian structure of the free Yang-Mills fields. Following the Dirac's procedure for constrained systems we have performed a detailed analysis of the constraint structure of the model and we give the generalized Dirac brackets for the physical variables. Using the correspondence principle in the Dirac's brackets we obtain the same commutators present in the literature and new ones.
Hamiltonian Formulation of the Yang-Mills field on the null-plane
Casana, R.; Pimentel, B. M.; Zambrano, G. E. R.
2010-02-01
We have studied the null-plane hamiltonian structure of the free Yang-Mills fields. Following the Dirac's procedure for constrained systems we have performed a detailed analysis of the constraint structure of the model and we give the generalized Dirac brackets for the physical variables. Using the correspondence principle in the Dirac's brackets we obtain the same commutators present in the literature and new ones.
Einstein and Yang-Mills theories in hyperbolic form without gauge-fixing
Abrahams, A M; Choquet-Bruhat, Y; York, J W
1995-01-01
The evolution of physical and gauge degrees of freedom in the Einstein and Yang-Mills theories are separated in a gauge-invariant manner. We show that the equations of motion of these theories can always be written in flux-conservative first-order symmetric hyperbolic form. This dynamical form is ideal for global analysis, analytic approximation methods such as gauge-invariant perturbation theory, and numerical solution.
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.
Relating Gribov-Zwanziger theory and Yang-Mills theory in Batalin-Vilkovisky formalism
Upadhyay, Sudhaker
2011-01-01
We consider the BRST invariant Gribov-Zwanziger theory with appropriate horizon term in Batalin-Vilkovisky formalism. The usual infinitesimal BRST transformation is generalized by considering the parameter finite and field dependent. We show that such finite field dependent BRST transformation with suitable choice of finite parameter relates the generating functional of Gribov-Zwanziger theory to that of the Yang-Mills theory.
Statistical mechanics for dilatations in N=4 super Yang--Mills theory
Sochichiu, C
2006-01-01
Matrix model describing the anomalous dimensions of composite operators in $\\mathcal{N}=4$ super Yang--Mills up to one-loop level theory is considered at finite temperature. We compute the thermal effective action for this model, which we define as the log of the partition function restricted to the states of given length and spin. The result is obtained in the limits of high and low temperature.
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.
Coupled equations for K\\"ahler metrics and Yang-Mills connections
Alvarez-Consul, Luis; Garcia-Prada, Oscar
2011-01-01
We study equations on a principal bundle over a compact complex manifold coupling connections on the bundle with K\\"ahler structures in the base. These equations generalize the conditions of constant scalar curvature for a K\\"ahler metric and Hermite-Yang-Mills for a connection. We provide a moment map interpretation of the equations and study obstructions for the existence of solutions, generalizing the Futaki invariant, Mabuchi functional and geodesic stability. We finish by giving some examples of solutions.
Geometry of the gauge algebra in noncommutative Yang-Mills theory
Lizzi, Fedele; Zampini, Alessandro; Szabo, Richard J.
2001-08-01
A detailed description of the infinite-dimensional Lie algebra of star-gauge transformations in non-commutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra u(∞), and of the C*-algebra of compact operators on a quantum mechanical Hilbert space. The spacetime and string interpretations are also elucidated.
Geometry of the Gauge Algebra in Noncommutative Yang-Mills Theory
Lizzi, F; Zampini, A
2001-01-01
A detailed description of the infinite-dimensional Lie algebra of star-gauge transformations in noncommutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra, and of the algebra of compact operators on a quantum mechanical Hilbert space. The spacetime and string interpretations are also elucidated.
Supersymmetry algebra and BPS states of super Yang-Mills theories on noncommutative tori
Konechny, Anatoly; Schwarz, Albert
1999-04-01
We consider 10-dimensional super Yang-Mills theory with topological terms compactified on a noncommutative torus. We calculate supersymmetry algebra and derive BPS energy spectra from it. The cases of d-dimensional tori with d=2,3,4 are considered in full detail. SO(d,d,Z)-invariance of the BPS spectrum and relation of new results to the previous work in this direction are discussed.
Supersymmetric Yang-Mills theory as higher Chern-Simons theory
Sämann, Christian; Wolf, Martin
2017-07-01
We observe that the string field theory actions for the topological sigma models describe higher or categorified Chern-Simons theories. These theories yield dynamical equations for connective structures on higher principal bundles. As a special case, we consider holomorphic higher Chern-Simons theory on the ambitwistor space of four-dimensional space-time. In particular, we propose a higher ambitwistor space action functional for maximally supersymmetric Yang-Mills theory.
A new sphaleron in SU(3) Yang-Mills-Higgs theory
Nagel, Pascal; Klinkhamer, Frans [Karlsruher Institut fuer Technologie (KIT), Karlsruhe (Germany)
2016-07-01
The sphaleron solution S is known to contribute to baryon-number violation within the electroweak Standard Model. To gain further insight into the nonperturbative dynamics of QCD (and GUTs), we study a new sphaleron solution of SU(3) Yang-Mills-Higgs theory, the solution S. Two independent numerical approaches yield solutions of the reduced field equations and a surprising structure of the energy barrier in configuration space.
Infrared Safe Observables in ${\\cal N}=4$ Super Yang-Mills Theory
Bork, L V; Vartanov, G S; Zhiboedov, A V
2009-01-01
The infrared structure of MHV gluon amplitudes in ${\\cal N}=4$ super Yang-Mills theory is considered in the next-to-leading order of PT. Explicit cancelation of the infrared divergencies in properly defined cross-sections is demonstrated. The remaining finite parts for some inclusive differential cross-sections are calculated analytically. In general, contrary to the virtual corrections, they do not reveal any simple structure.
Canonical simulations of supersymmetric SU(N) Yang-Mills quantum mechanics
Bergner, Georg; Wenger, Urs
2015-01-01
The fermion loop formulation naturally separates partition functions into their canonical sectors. Here we discuss various strategies to make use of this for supersymmetric SU(N) Yang-Mills quantum mechanics obtained from dimensional reduction in various dimensions and present numerical results for the separate canonical sectors with fixed fermion numbers. We comment on potential problems due to the sign of the contributions from the fermions and due to flat directions.
5D maximally supersymmetric Yang-Mills in 4D superspace. Applications
McGarrie, Moritz
2013-03-15
We reformulate 5D maximally supersymmetric Yang-Mills in 4D Superspace, for a manifold with boundaries. We emphasise certain features and conventions necessary to allow for supersymmetric model building applications. Finally we apply the holographic interpretation of a slice of AdS and show how to generate Dirac soft masses between external source fields, as well as kinetic mixing, as a boundary effective action.
Solutions to Yang-Mills field equations in eight dimensions and the last Hopf map
Grossman, B.; Kephart, T.W.; Stasheff, J.D.
1984-12-01
The authors show that the Hopf map S/sup 15/->S/sup 7/ S/sup 8/ admits a sourceless, topologically non-trivial gauge field. This result is cast in the form of a solution to eight dimensional Euclidean Yang-Mills field equations with topological charge Q=1. This solution is Spin (9) symmetric and leads to a new generalized duality condition FandF=+-(FandF)sup(*).
Coupling of Yang-Mills to N = 4, d = 4 supergravity
Bergshoeff, E.; Koh, I.G.; Sezgin, E.
1985-01-01
We couple N = 4, d = 4 supersymmetric Yang-Mills theory to supergravity. The scalars of the theory parametrize the coset (SO(n,6)/[SO(n)Ã—SO(6)])Ã—(SU(1,1)/U(1)). Keeping the composite local SO(n)Ã—SO(6)Ã—U(1) invariance intact, we gauge an (n + 6) parameter subgroup of SO(n,6) which is either (i) S
Black Hole Solution of Einstein-Born-Infeld-Yang-Mills Theory
Kun Meng
2017-01-01
Full Text Available A new four-dimensional black hole solution of Einstein-Born-Infeld-Yang-Mills theory is constructed; several degenerated forms of the black hole solution are presented. The related thermodynamical quantities are calculated, with which the first law of thermodynamics is checked to be satisfied. Identifying the cosmological constant as pressure of the system, the phase transition behaviors of the black hole in the extended phase space are studied.
The gluino-glue particle and relevant scales for the simulations of supersymmetric Yang-Mills theory
Bergner, Georg; Münster, Gernot; Sandbrink, Dirk; Özugurel, Umut D
2012-01-01
Supersymmetric Yang-Mills theory is in several respects different from QCD and pure Yang-Mills theory. Therefore, a reinvestigation of the scales, at which finite size effects and lattice artifacts become relevant, is necessary. Both, finite size effects and lattice artifacts, induce a breaking of supersymmetry. In view of the unexpected mass gap between bosonic and fermionic particles an estimation of these effects is essential.
An instability of hyperbolic space under the Yang-Mills flow
Gegenberg, Jack; Day, Andrew C.; Liu, Haitao; Seahra, Sanjeev S. [Department of Mathematics and Statistics, University of New Brunswick Fredericton, New Brunswick, E3B 5A3 (Canada)
2014-04-15
We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated Riemannian geometry is one of constant curvature. We analytically solve the linearized flow equations for a large class of perturbations to the fixed point corresponding to hyperbolic 3-space. These can be expressed as a linear superposition of distinct modes, some of which are exponentially growing along the flow. The growing modes imply the divergence of the (gauge invariant) perturbative torsion for a wide class of initial data, indicating an instability of the background geometry that we confirm with numeric simulations in the partially compactified case. There are stable modes with zero torsion, but all the unstable modes are torsion-full. This leads us to speculate that the instability is induced by the torsion degrees of freedom present in the Yang-Mills flow.
Reformulations of the Yang-Mills theory toward quark confinement and mass gap
Kondo, Kei-Ichi; Shibata, Akihiro; Shinohara, Toru
2014-01-01
We propose the reformulations of the $SU(N)$ Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the $SU(N)$ Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulations can be combined with the $SU(N)$ extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the $SU(N)$ Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole ...
Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay’s angle
Bouguerra, Yacine; Maamache, Mustapha; Ryeol Choi, Jeong
2017-06-01
Hannay’s angle is a classical analogue of the “geometrical phase factor” found by Berry in his research on the quantum adiabatic theorem. This classical analogue is defined if closed curves of constant action variables return to the same curves in phase space after an adaibatic evolution. Adiabatic evolution of Yang-Mills cosmology, which is described by a time-dependent quartic oscillator, is investigated. Phase properties of the Yang-Mills fields are analyzed and the corresponding Hannay’s angle is derived from a rigorous evaluation. The obtained Hannay’s angle shift is represented in terms of several observable parameters associated with such an angle shift. The time evolution of Hannay’s angle in Yang-Mills cosmology is examined from an illustration plotted on the basis of numerical evaluation, and its physical nature is addressed. Hannay’s angle, together with its quantum counterpart Berry’s phase, plays a pivotal role in conceptual understanding of several cosmological problems and indeed can be used as a supplementary probe for cosmic inflation. Supported by Basic Science Research Program through National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1A09919503)
Yelnykov, O V
2005-01-01
This thesis addresses three topics: calculation of the invariant measure for the pure Yang-Mills configuration space in (3 + 1) dimensions, Hamiltonian analysis of the pure Chern-Simons theory on the noncommutative plane and noncommutative quantum mechanics in the presence of singular potentials. In Chapter 1 we consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parameterized in terms of a matrix variable which facilitates the elimination of the gauge degrees of freedom. We develop an approximate calculation of the volume element on the gauge-invariant configuration space. We also make a rough estimate of the ratio of 0++ glueball mass and the square root of string tension by comparison with (2 + 1)-dimensional Yang-Mills theory. In Chapter 2 the Hamiltonian analysis of the pure Chern- Simons theory on the noncommutative plane is performed. We use the techniques of geometric quantization to show that the classical reduced phase space o...
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...
Deconfinement in Yang-Mills theory through toroidal compactification with deformation
Simic, Dusan
2010-01-01
We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double- trace deformation of toroidally compactified Yang-Mills theory on R2 \\times S1_L \\times S1_{\\beta}. At large N, fixed-L, and arbitrary {\\beta}, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N, small L and a range of {\\beta}, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak regarding the magnetic comp...
Quark confinement, new cosmic expansion and general Yang-Mills symmetry
Hsu, Jong-Ping
2017-01-01
We discuss a unified model of quark confinement and new cosmic expansion with linear potentials based on a general (SU 3)color×(U 1)baryon symmetry. The phase functions in the usual gauge transformations are generalized to new ‘action integrals’. The general Yang-Mills transformations have group properties and reduce to usual gauge transformations in special cases. Both quarks and ‘gauge bosons’ are permanently confined by linear potentials. In this unified model of particle-cosmology, physics in the largest cosmos and that in the smallest quark system appear to both be dictated by the general Yang-Mills symmetry and characterized by a universal length. The basic force between two baryons is independent of distance. However, the cosmic repulsive force exerted on a baryonic supernova by a uniform sphere of galaxies is proportional to the distance from the center of the sphere. The new general Yang-Mills field may give a field-theoretic explanation of the accelerated cosmic expansion. The prediction could be tested experimentally by measuring the frequency shifts of supernovae at different distances. Supported in part by the Jingshin Resealch Fund of the UMassD Foundation
Bose-Einstein condensation of dark matter axions.
Sikivie, P; Yang, Q
2009-09-11
We show that cold dark matter axions thermalize and form a Bose-Einstein condensate (BEC). We obtain the axion state in a homogeneous and isotropic universe, and derive the equations governing small axion perturbations. Because they form a BEC, axions differ from ordinary cold dark matter in the nonlinear regime of structure formation and upon entering the horizon. Axion BEC provides a mechanism for the production of net overall rotation in dark matter halos, and for the alignment of cosmic microwave anisotropy multipoles.
Dwarf spheroidal galaxies and Bose-Einstein condensate dark matter
Diez-Tejedor, Alberto; Profumo, Stefano
2014-01-01
We constrain the parameters of a self-interacting massive dark matter scalar particle in a condensate using the kinematics of the eight brightest dwarf spheroidal satellites of the Milky Way. For the case of an attractive self-interaction the condensate develops a mass density profile with a characteristic scale radius that is closely related to the fundamental parameters of the theory. We find that the velocity dispersion of dwarf spheroidal galaxies suggests a scale radius of the order of 1 kpc, in tension with previous results found using the rotational curve of low-surface-brightness and dwarf galaxies. We discuss the implications of our findings for the particle dark matter model and argue that a single classical coherent state cannot play, in general, a relevant role for the description of dark matter in galaxies.
Pedro Romano-Aportela
2011-01-01
Full Text Available Se analizan las interacciones electromagnéticas y nucleares débiles utilizando el principio fundamental de simetría en espacios abstractos denominados teoría de campos de Yang-Mills, también conocidos como campos de norma (gauge fields y el mecanismo de Higgs. Los campos de norma actúan como mediadores de las interacciones, cuyo alcance está determinado de manera directa por la masa. Por este motivo los campos de norma se unen al mecanismo de Higgs que genera masa a los portadores de las interacciones, manteniendo la teoría invariante bajo una transformación de norma. Esto se logra a través de un rompimiento espontaneo de simetría para finalmente aplicar esta metodología con la finalidad de unificar las teorías de las interacciones considerando el modelo estándar de Weinberg-Salam.The electromagnetic and weak nuclear interactions are analyzed using the fundamental principle of symmetry in abstract spaces named theory of Yang-Mills fields, also known as gauge fields, and Higgs's mechanism. Gauge fields are mediators of interactions, whose scope is determined directly by the mass. For this reason, gauge fields are joined with the Higgs mechanism that generates mass to the interaction carriers, maintaining the invariant theory under a gauge transformation. This is achieved through spontaneous symmetry breaking to finally applying this methodology in order to unify the theories of interactions considering the Weinberg-Salam standard model.
Dark Energy and Dark Matter from the same Vacuum Condensate
Sarfatti, Jack
2003-04-01
The micro-quantum Dirac negative energy electron Fermi sphere with Planck scale cutoff is unstable to the formation of off-mass-shell Cooper pairs of virtual electrons and positrons from their static Coulomb attraction. The resulting virtual BEC complex macro-quantum coherent local order parameter (0|e+e-|0) gives rise to both spin 2 gravity guv and spin 0 quintessence / from the Goldstone and Higgs oscillations respectively, Susskind's "world hologram" conjecture replaces the Planck scale Lp with Lp^2/3L^1/3 at scale L. Hagen Kleinert's strain tensor for the "world crystal" is Einstein's geometrodynamic field: guv = nuv + Lp^4/3L^2/3Du,Dvarg(0|e+e-|0)/2 nuv = Minkowski metric, = anti-commutator Du = ,u + TaAu^a is the spin 1 gauge covariant derivative for Lie group P with Lie algebra [Ta,Tb] = Cab^cTc / = Lp-4/3L-2/3[1 - Lp^2L|(0|e+e-|0)|^2] When L = size of visible universe 10^28 cm, Lp^2/3L^1/3 1 fermi / > 0 is anti-gravitating zero point vacuum dark energy, i.e. Kip Thorne's "exotic matter" for traversable wormhole time machines. / < 0 is gravitating zero point vacuum dark matter The non-perturbative BCS energy gap equation for a basic vacuum polarization closed loop with one virtual photon Feynman diagram is: z^2 = ge^-(1/gz) z = (Lp/L)^1/3 and the dimensionless coupling vertex is g^1/2 http://stardrive.org/Jack/nambu.pdf http://stardrive.org/Jack/Lambda1.pdf
Dark Lump Excitations in Bose-Einstein Condensates
黄国翔; 朱善华
2002-01-01
Key Laboratory for Optical and Magnetic Resonance Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062We investigate the dynamics of two-dimensional matter-wave pulses in a Bose-Einstein condensate with diskshaped traps. For the case ofrepulsive atom-atom interactions, a Kadomtsev-Petviashvili equation with positive dispersion is derived using the method of multiple scales. The results show that it is possible to excite dark lump-like two-dimensional nonlinear excitations in the Bose-Einstein condensate.
Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
Caporaso, N; Griguolo, L; Pasquetti, S; Seminara, D; Szabó, R J
2006-01-01
We study the relations between two-dimensional Yang-Mills theory on the torus, topological string theory on a Calabi-Yau threefold whose local geometry is the sum of two line bundles over the torus, and Chern-Simons theory on torus bundles. The chiral partition function of the Yang-Mills gauge theory in the large N limit is shown to coincide with the topological string amplitude computed by topological vertex techniques. We use Yang-Mills theory as an efficient tool for the computation of Gromov-Witten invariants and derive explicitly their relation with Hurwitz numbers of the torus. We calculate the Gopakumar-Vafa invariants, whose integrality gives a non-trivial confirmation of the conjectured nonperturbative relation between two-dimensional Yang-Mills theory and topological string theory. We also demonstrate how the gauge theory leads to a simple combinatorial solution for the Donaldson-Thomas theory of the Calabi-Yau background. We match the instanton representation of Yang-Mills theory on the torus with ...
Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
Caron Huot, Simon; He, Song
2013-01-01
, the higher-point amplitudes we consider can be obtained from those with lowest-points by a collinear uplifting. Based on a compact formula for one-loop N(2)MHV amplitudes, we use an equation proposed previously to compute, for the first time, the complete two-loop NMHV and three-loop MHV octagons, which we......We study the S-matrix of planar = 4 supersymmetric Yang-Mills theory when external momenta are restricted to a two-dimensional subspace of Minkowski space. We find significant simplifications and new, interesting structures for tree and loop amplitudes in two-dimensional kinematics, in particular...
Global dynamics of a Yang-Mills field on an asymptotically hyperbolic space
Bizoń, Piotr
2014-01-01
We consider a spherically symmetric (purely magnetic) SU(2) Yang-Mills field propagating on an ultrastatic spacetime with two asymptotically hyperbolic regions connected by a throat of radius $\\alpha$. Static solutions in this model are shown to exhibit an interesting bifurcation pattern in the parameter $\\alpha$. We relate this pattern to the Morse index of the static solution with maximal energy. Using a hyperboloidal approach to the initial value problem, we describe the relaxation to the ground state solution for generic initial data and unstable static solutions for initial data of codimension one, two, and three.
N=4 Supersymmetric Yang-Mills Theory on a Kaehler Surface
Dijkgraaf, R; Schroers, B J
1998-01-01
We study N=4 supersymmetric Yang-Mills theory on a Kaehler manifold with $b_2^+ \\geq 3$. Adding suitable perturbations we show that the partition function of the N=4 theory is the sum of contributions from two branches: (i) instantons, (ii) a special class of Seiberg-Witten monopoles. We determine the partition function for the theories with gauge group SU(2) and SO(3), using S-duality. This leads us to a formula for the Euler characteristic of the moduli space of instantons.
N=4 Supersymmetric Yang-Mills Theory on Orbifold-$T^4/{\\bf Z}_2$
Jinzenji, M; Jinzenji, Masao; Sasaki, Toru
2001-01-01
We derive the partition function of N=4 supersymmetric Yang-Mills theory on orbifold-$T^4/{\\bf Z}_2$. In classical geometry, K3 surface is constructed from the orbifold-$T^4/{\\bf Z}_2$. Along the same way as the orbifold construction, we construct the partition function of K3 surface from orbifold-$T^4/{\\bf Z}_2$. The partition function is given by the product of the contribution of the untwisted sector of $T^4/{\\bf Z}_2$, and that of the twisted sector of $T^4/{\\bf Z}_2$ i.e., ${\\cal O}(-2)$ curve blow-up formula.
Yang-Mills theory as bimetrical gravity: Polarization effects and finite-energy gluon clusters
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 configurations from 3D Riemann-Cartan geometry
Mielke, E W; Hehl, F W
1994-01-01
Recently, the {\\it spacelike} part of the SU(2) Yang--Mills equations has been identified with geometrical objects of a three--dimensional space of constant Riemann--Cartan curvature. We give a concise derivation of this Ashtekar type (``inverse Kaluza--Klein") {\\it mapping} by employing a (3+1)--decomposition of {\\it Clifford algebra}--valued torsion and curvature two--forms. In the subcase of a mapping to purely axial 3D torsion, the corresponding Lagrangian consists of the translational and Lorentz {\\it Chern--Simons term} plus cosmological term and is therefore of purely topological origin.
Towards a precise determination of the topological susceptibility in the SU(3) Yang-Mills theory
Giusti, Leonardo; Petrarca, Silvano
2009-01-01
An ongoing effort to compute the topological susceptibility for the SU(3) Yang-Mills theory in the continuum limit with a precison of about 2% is reported. The susceptibility is computed by using the definition of the charge suggested by Neuberger fermions for two values of the negative mass parameter s. Finite volume and discretization effects are estimated to meet this level of precision. The large statistics required has been obtained by using PCs of the INFN-GRID. Simulations with larger lattice volumes are necessary in order to better understanding the continuum limit at small lattice spacing values.
A novel computation of the thermodynamics of the SU(3) Yang-Mills theory
Giusti, Leonardo
2015-01-01
We present an accurate computation of the Equation of State of the SU(3) Yang-Mills theory using shifted boundary conditions in the temporal direction. In this framework, the entropy density s can be obtained in a simple way from the expectation value of the space-time components T0k of the energy-momentum tensor. At each given value of the temperature, s is measured in an independent way at several values of the lattice spacing. The extrapolation to the continuum limit shows small discretization effects with respect to the statistical errors of approximatively 0.5%.
From decay to complete breaking: pulling the strings in SU(2) Yang-Mills theory.
Pepe, M; Wiese, U-J
2009-05-15
We study {2Q+1} strings connecting two static charges Q in (2+1)D SU(2) Yang-Mills theory. While the fundamental {2} string between two charges Q=1/2 is unbreakable, the adjoint {3} string connecting two charges Q=1 can break. When a {4} string is stretched beyond a critical length, it decays into a {2} string by gluon pair creation. When a {5} string is stretched, it first decays into a {3} string, which eventually breaks completely. The energy of the screened charges at the ends of a string is well described by a phenomenological constituent gluon model.
Quantization Near Violent Singularities in Einstein-Yang-Mills Black Holes
Galtsov, D V
2001-01-01
Classical singularities inside black holes in the Einstein-Yang-Mills theory exhibit unusual features. Only for discrete values of the black hole mass one encounters singularities of the Schwarzschild type (timelike) and the Reissner-Nordstrom type (spacelike). For a generic mass the approach to singularity is not smooth: the metric oscillates with an infinitely growing amplitude and decreasing period. In spite of some similarity with the BKL oscillations, here the behavior is not chaotic. However the oscillation amplitude exceeds classical limits after few cycles, so the question arises how this behavior gets modified by quantum effects. We discuss this issue both in the framework of QFT and in the string theory.
Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields
Volkov, M S; Volkov, Mikhail S.; Galtsov, Dmitri V.
1999-01-01
We present a review of gravitating particle-like and black hole solutions with non-Abelian gauge fields. The emphasis is given to the description of the structure of the solutions and to the connection with the results of flat space soliton physics. We describe the Bartnik-McKinnon solitons and the non-Abelian black holes arising in the Einstein-Yang-Mills theory, and consider their various generalizations. These include axially symmetric and slowly rotating configurations, solutions with higher gauge groups, $\\Lambda$-term, dilaton, and higher curvature corrections. The stability issue is discussed as well. We also describe the gravitating generalizations for flat space monopoles, sphalerons, and Skyrmions.
Gravitational matter-antimatter asymmetry and four-dimensional Yang-Mills gauge symmetry
Hsu, J. P.
1981-01-01
A formulation of gravity based on the maximum four-dimensional Yang-Mills gauge symmetry is studied. The theory predicts that the gravitational force inside matter (fermions) is different from that inside antimatter. This difference could lead to the cosmic separation of matter and antimatter in the evolution of the universe. Moreover, a new gravitational long-range spin-force between two fermions is predicted, in addition to the usual Newtonian force. The geometrical foundation of such a gravitational theory is the Riemann-Cartan geometry, in which there is a torsion. The results of the theory for weak fields are consistent with previous experiments.
Analytical self-dual solutions in a nonstandard Yang-Mills-Higgs scenario
Casana, R.; Ferreira, M. M.; da Hora, E.; dos Santos, C.
2013-05-01
We have found analytical self-dual solutions within the generalized Yang-Mills-Higgs model introduced in R. Casana et al. (2012) [1]. Such solutions are magnetic monopoles satisfying Bogomol'nyi-Prasad-Sommerfield (BPS) equations and usual finite energy boundary conditions. Moreover, the new solutions are classified in two different types according to their capability of recovering (or not) the usual 't Hooft-Polyakov monopole. Finally, we compare the profiles of the solutions we found with the standard ones, from which we comment about the main features exhibited by the new configurations.
Analytical self-dual solutions in a nonstandard Yang-Mills-Higgs scenario
Casana, R; da Hora, E; Santos, C dos
2013-01-01
We have found analytical self-dual solutions within the generalized Yang-Mills-Higgs model introduced in Phys. Rev. D 86, 085034 (2012). Such solutions are magnetic monopoles satisfying Bogomol'nyi-Prasad-Sommerfield (BPS) equations and usual finite energy boundary conditions. Moreover, the new solutions are classified in two different types according to their capability of recovering (or not) the usual 't Hooft--Polyakov monopole. Finally, we compare the profiles of the solutions we found with the standard ones, from which we comment about the main features exhibited by the new configurations.
Renormalization aspects of N=1 Super Yang-Mills theory in the Wess-Zumino gauge
Capri, M A L; Guimaraes, M S; Justo, I F; Mihaila, L; Sorella, S P; Vercauteren, D
2014-01-01
The renormalization of N=1 Super Yang-Mills theory is analysed in the Wess-Zumino gauge, employing the Landau condition. An all orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field and gluino renormalization. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino, as explicitly shown through a three loop calculation.
Cut-and-join operators and N=4 super Yang-Mills
Brown, T.W. [DESY, Hamburg (Germany). Theory Group
2010-02-15
We show which multi-trace structures are compatible with the symmetrisation of local operators in N=4 super Yang-Mills when they are organised into representations of the global symmetry group. Cut-and-join operators give the non-planar expansion of correlation functions of these operators in the free theory. Using these techniques we find the 1/N corrections to the quarter-BPS operators which remain protected at weak coupling. We also present a new way of counting these chiral ring operators using the Weyl group S{sub N}. (orig.)
Coupled equations for K\\"ahler metrics and Yang-Mills connections (Thesis)
Garcia-Fernandez, Mario
2011-01-01
We study equations on a principal bundle over a compact complex manifold coupling connections on the bundle with K\\"ahler structures in the base. These equations generalize the conditions of constant scalar curvature for a K\\"ahler metric and Hermite-Yang-Mills for a connection. We provide a moment map interpretation of the equations and study obstructions for the existence of solutions, generalizing the Futaki character and the Mabuchi K-energy. We explain their relationship to the algebro-geometric moduli problem for pairs consisting of a polarized variety and a holomorphic vector bundle.
Global solutions of Yang-Mills equations on anti-de Sitter spacetime
Choquet-Bruhat, Y. (Paris Univ. (France). Mecanique Relativiste)
1989-12-01
Anti-de Sitter spacetime is a C{sup {infinity}} manifold diffeomorphic to R{sup 4}, endowed with a C{sup {infinity}} metric of hyperbolic signature. However this spacetime is not globally hyperbolic, and the known results about the solution of the Cauchy problem for wave equations on Lorentzian manifolds do not apply, even for a small interval of time and even for linear equations. We prove the global existence of a solution of the Cauchy problem for the Yang-Mills-Higgs equations on anti-de Sitter spacetime, under the condition that there is no radiation at timelike infinity, a condition that is explained mathematically. (author).
Goursat problem for the Yang-Mills-Vlasov system in temporal gauge
Marcel Dossa
2011-12-01
Full Text Available This article studies the characteristic Cauchy problem for the Yang-Mills-Vlasov (YMV system in temporal gauge, where the initial data are specified on two intersecting smooth characteristic hypersurfaces of Minkowski spacetime $(mathbb{R}^{4},eta $. Under a $mathcal{C}^{infty }$ hypothesis on the data, we solve the initial constraint problem and the evolution problem. Local in time existence and uniqueness results are established thanks to a suitable combination of the method of characteristics, Leray's Theory of hyperbolic systems and techniques developed by Choquet-Bruhat for ordinary spatial Cauchy problems related to (YMV systems.
A Duality for Yang-Mills Moduli Spaces on Noncommutative Manifolds
Takai, H
2004-01-01
Studied are the moduli spaces of Yang-Mills connections on finitely generated projective modules associated with noncommutative flows. It is actually shown that they are homeomorphic to those on the dual modules associated with the dual noncommutative flows. Moreover the result is also affirmative in the case of multiflows. As an important application, computed are the moduli spaces of the instanton bundles over the noncommutative Euclidean 4-space with respect to the canonical action of space translations without using the ADHM-construction.
The Width of the Confining String in Yang-Mills Theory
Gliozzi, F; Wiese, U -J
2010-01-01
We investigate the transverse fluctuations of the confining string connecting two static quarks in (2+1)-d SU(2) Yang-Mills theory using Monte Carlo calculations. The exponentially suppressed signal is extracted from the large noise by a very efficient multi-level algorithm. The resulting width of the string increases logarithmically with the distance between the static quark charges. Corrections at intermediate distances due to universal higher order terms in the effective string action are calculated analytically. They accurately fit the numerical data.
Wilson punctured network defects in 2D q-deformed Yang-Mills theory
Watanabe, Noriaki
2016-01-01
In the context of class S theories and 4D/2D duality relations there, we discuss the skein relations of general topological defects on the 2D side which are expected to be counterparts of composite surface-line operators in 4D class S theory. Such defects are geometrically interpreted as networks in a three dimensional space. We also propose a conjectural computational procedure for such defects in two dimensional SU(N) topological q-deformed Yang-Mills theory by interpreting it as a statistical mechanical system associated with ideal triangulations.
Fifty years of Yang-Mills Theories: a phenomenological point of view
De Rújula, Alvaro
2005-01-01
On the occasion of the celebration of the first half-century of Yang--Mills theories, I am contributing a personal recollection of how the subject, in its early times, confronted physical reality, that is, its "phenomenology". There is nothing original in this work, except, perhaps, my own points of view. But I hope that the older practitioners of the field will find here grounds for nostalgia, or good reasons to disagree with me. Younger addicts may learn that history does not resemble at all what is reflected in current textbooks: it was orders of magnitude more fascinating.
Comparing Pure Yang-Mills SU(2) and SU(3) Propagators
Cucchieri, Attilio; Silva, Paulo J
2007-01-01
The infrared behavior of gluon and ghost propagators in Yang-Mills gauge theories is of central importance for the understanding of confinement in QCD. While analytic studies using Schwinger-Dyson equations predict the same infrared exponents for the SU(2) and SU(3) gauge groups, lattice simulations usually assume that the two cases are different, although their qualitative infrared features may be the same. We carry out a comparative study of lattice (Landau) propagators for both gauge groups. Our data were especially produced with equivalent lattice parameters to allow a careful comparison of the two cases.
BPS Equations in Omega-deformed N=4 Super Yang-Mills Theory
Ito, Katsushi; Nakajima, Hiroaki; Sasaki, Shin
2015-01-01
We study supersymmetry of N=4 super Yang-Mills theory in four dimensions deformed in the Omega-background. We take the Nekrasov-Shatashvili limit of the background so that two-dimensional super Poincare symmetry is recovered. We compute the deformed central charge of the superalgebra and study the 1/2 and 1/4 BPS states. We obtain the Omega-deformed 1/2 and 1/4 BPS dyon equations from the deformed supersymmetry transformation and the Bogomol'nyi completion of the energy.
Twisted N=4 Super Yang-Mills Theory in Omega-background
Ito, Katsushi; Sasaki, Shin
2013-01-01
We study the twisted N=4 super Yang-Mills theories in the Omega-background with the constant R-symmetry Wilson line gauge field. Based on the classification of topological twists of N=4 supersymmetry (the half, the Vafa-Witten and the Marcus twists), we construct the deformed off-shell supersymmetry associated with the scalar supercharges for these twists. We find that the Omega-deformed action is written in the exact form with respect to the scalar supercharges as in the undeformed case.
The exact decomposition of gauge variables in lattice Yang-Mills theory
Shibata, Akihiro; Kondo, Kei-Ichi; Shinohara, Toru
2010-07-01
In this Letter, we consider lattice versions of the decomposition of the Yang-Mills field a la Cho-Faddeev-Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU (N) gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU (2) and SU (3). As a result, we obtain the general form of the decomposition for SU (N) gauge link variables and confirm the previous results obtained for SU (2) and SU (3).
On the Functional Renormalization Group approach for Yang-Mills fields
Lavrov, Peter M
2012-01-01
We explore the gauge dependence of the effective average action within the functional renormalization group (FRG) approach. It is shown that in the framework of standard definitions of FRG for the Yang-Mills theory, the effective average action remains gauge-dependent on-shell, independent on the use of truncation scheme. Furthermore, we propose a new formulation of the FRG, based on the use of composite operators. In this case one can provide on-shell gauge-invariance for the effective average action and universality of $S$-matrix.
On the functional renormalization group approach for Yang-Mills fields
Lavrov, Peter M.; Shapiro, Ilya L.
2013-06-01
We explore the gauge dependence of the effective average action within the functional renormalization group (FRG) approach. It is shown that in the framework of standard definitions of FRG for the Yang-Mills theory, the effective average action remains gauge-dependent on-shell, independent on the use of truncation scheme. Furthermore, we propose a new formulation of the FRG, based on the use of composite operators. In this case one can provide on-shell gauge-invariance for the effective average action and universality of S-matrix.
Gluon scattering in N=4 super-Yang-Mills theory fromweak to strong coupling
Dixon, Lance J.; /SLAC
2008-03-25
I describe some recent developments in the understanding of gluon scattering amplitudes in N = 4 super-Yang-Mills theory in the large-N{sub c} limit. These amplitudes can be computed to high orders in the weak coupling expansion, and also now at strong coupling using the AdS/CFT correspondence. They hold the promise of being solvable to all orders in the gauge coupling, with the help of techniques based on integrability. They are intimately related to expectation values for polygonal Wilson loops composed of light-like segments.
Local integrands for two-loop all-plus Yang-Mills amplitudes
Badger, Simon; Peraro, Tiziano
2016-01-01
We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4-2epsilon dimensions.
Real space renormalization group for twisted lattice N=4 super Yang-Mills
Catterall, Simon
2014-01-01
A necessary ingredient for our previous results on the form of the long distance effective action of the twisted lattice N=4 super Yang-Mills theory is the existence of a real space renormalization group which preserves the lattice structure, both the symmetries and the geometric interpretation of the fields. In this brief article we provide an explicit example of such a blocking scheme and illustrate its practicality in the context of a small scale Monte Carlo renormalization group calculation. We also discuss the implications of this result, and the possible ways in which to use it in order to obtain further information about the long distance theory.
Non-Abelian (2,0)-super-Yang-Mills coupled to linear {sigma}-models
Goes-Negrao, M.S.; Helayel-Neto, J.A.; Negrao, M.R. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]|[Universidade Catolica de Petropolis, RJ (Brazil). E-mail: negrao@cbpf.br; helayel@cbpf.br; guida@cbpf.br
2000-06-01
Considering a class of (2,0)-super-Yang-Mills multiplets that accommodate a pair of independent gauge potentials in connection with a single symmetry group, we present here non-Abelian coupling to ordinary matter and to non-linear {sigma}-models in (2,0)-superspace. The dynamics and the couplings of the gauge potentials are discussed and the interesting feature that comes out is a sort of chirality for one of the gauge potentials whenever light-cone coordinates are chosen. (author)
Let's Twist Again: N=2 Super Yang Mills Theory Coupled To Matter
Maggiore, Nicola
2010-01-01
We give the twisted version of N=2 Super Yang Mills theory coupled to matter, including quantum fields, supersymmetry transformations, action and algebraic structure. We show that the whole action, coupled to matter, can be written as the variation of a nilpotent operator, modulo field equations. An extended Slavnov-Taylor identity, collecting gauge symmetry and supersymmetry, is written, which allows to define the web of algebraic constraints, in view of the algebraic renormalization and of the extension of the non-renormalization theorems holding for N=2 SYM theory without matter.
Wilson punctured network defects in 2D q-deformed Yang-Mills theory
Watanabe, Noriaki [Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa, Chiba 277-8583 (Japan)
2016-12-14
In the context of class S theories and 4D/2D duality relations there, we discuss the skein relations of general topological defects on the 2D side which are expected to be counterparts of composite surface-line operators in 4D class S theory. Such defects are geometrically interpreted as networks in a three dimensional space. We also propose a conjectural computational procedure for such defects in two dimensional SU(N) topological q-deformed Yang-Mills theory by interpreting it as a statistical mechanical system associated with ideal triangulations.
Towards the large N limit of pure Nu = 1 super Yang-Mills theory.
Maldacena, J; Nuñez, C
2001-01-22
We find the gravity solution corresponding to a large number of Neveu-Schwarz or D5-branes wrapped on a two sphere so that we have pure Nu = 1 super Yang-Mills in the IR. The supergravity solution is smooth, it shows confinement, and it breaks the U(1)(R) chiral symmetry in the appropriate way. When the gravity approximation is valid the masses of glueballs are comparable to the masses of Kaluza-Klein (KK) states on the 5-brane, but if we could quantize strings on this background it looks like we should be able to decouple the KK states.
Quantum fields in the non-perturbative regime. Yang-Mills theory and gravity
Eichhorn, Astrid
2011-09-06
In this thesis we study candidates for fundamental quantum field theories, namely non-Abelian gauge theories and asymptotically safe quantum gravity. Whereas the first ones have a stronglyinteracting low-energy limit, the second one enters a non-perturbative regime at high energies. Thus, we apply a tool suited to the study of quantum field theories beyond the perturbative regime, namely the Functional Renormalisation Group. In a first part, we concentrate on the physical properties of non-Abelian gauge theories at low energies. Focussing on the vacuum properties of the theory, we present an evaluation of the full effective potential for the field strength invariant F{sub {mu}}{sub {nu}}F{sup {mu}}{sup {nu}} from non-perturbative gauge correlation functions and find a non-trivial minimum corresponding to the existence of a dimension four gluon condensate in the vacuum. We also relate the infrared asymptotic form of the {beta} function of the running background-gauge coupling to the asymptotic behavior of Landau-gauge gluon and ghost propagators and derive an upper bound on their scaling exponents. We then consider the theory at finite temperature and study the nature of the confinement phase transition in d = 3+1 dimensions in various non-Abelian gauge theories. For SU(N) with N= 3,..,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. Our studies shed light on the question which property of a gauge group determines the order of the phase transition. In a second part we consider asymptotically safe quantum gravity. Here, we focus on the Faddeev-Popov ghost sector of the theory, to study its properties in the context of an interacting UV regime. We investigate several truncations, which all lend support to the conjecture that gravity may be asymptotically safe. In a first truncation, we study the ghost anomalous dimension
N=4 Supersymmetric Yang-Mills on S^3 in Plane Wave Matrix Model at Finite Temperature
Kitazawa, Yoshihisa
2008-01-01
We investigate the large N reduced model of gauge theory on a curved spacetime through the plane wave matrix model. We formally derive the action of the N=4 supersymmetric Yang-Mills theory on R \\times S^3 from the plane wave matrix model in the large N limit. Furthermore, we evaluate the effective action of the plane wave matrix model up to the two-loop level at finite temperature. We find that the effective action is consistent with the free energy of the N=4 supersymmetric Yang-Mills theory on S^3 at high temperature limit where the planar contributions dominate. We conclude that the plane wave matrix model can be used as a large N reduced model to investigate nonperturbative aspects of the N=4 supersymmetric Yang-Mills theory on R \\times S^3.
Twisted Superspace for N=D=2 Super BF and Yang-Mills with Dirac-K\\"ahler Fermion Mechanism
Kato, J; Uchida, Y; Kato, Junji; Kawamoto, Noboru; Uchida, Yukiya
2003-01-01
We propose a twisted D=N=2 superspace formalism. The relation between the twisted super charges including the BRST charge, vector and pseudo scalar super charges and the N=2 spinor super charges is established. We claim that this relation is essentially related with the Dirac-K\\"ahler fermion mechanism. We show that a fermionic bilinear form of twisted N=2 chiral and anti-chiral superfields is equivalent to the quantized version of BF theory with the Landau type gauge fixing while a bosonic bilinear form leads to the N=2 Wess-Zumino action. We then construct a Yang-Mills action described by the twisted N=2 chiral and vector superfields, and show that the action is equivalent to the twisted version of the D=N=2 super Yang-Mills action, previously obtained from the quantized generalized topological Yang-Mills action with instanton gauge fixing.
Mass Deformations of Super Yang-Mills Theories in D= 2+1, and Super-Membranes: A Note
Agarwal, Abhishek
2008-01-01
Mass deformations of supersymmetric Yang-Mills theories in three spacetime dimensions are considered. The gluons of the theories are made massive by the inclusion of a non-local gauge and Poincare invariant mass term due to Alexanian and Nair, while the matter fields are given standard Gaussian mass-terms. It is shown that the dimensional reduction of such mass deformed gauge theories defined on $R^3$ or $R\\times T^2$ produces matrix quantum mechanics with massive spectra. In particular, all known massive matrix quantum mechanical models obtained by the deformations of dimensional reductions of minimal super Yang-Mills theories in diverse dimensions are shown also to arise from the dimensional reductions of appropriate massive Yang-Mills theories in three spacetime dimensions. Explicit formulae for the gauge theory actions are provided.
Dark-bright ring solitons in Bose-Einstein condensates
Stockhofe, J; Schmelcher, P [Zentrum fuer Optische Quantentechnologien, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany); Kevrekidis, P G [Department of Mathematics and Statistics, University of Massachusetts, Amherst MA 01003-4515 (United States); Frantzeskakis, D J, E-mail: jstockho@physnet.uni-hamburg.de, E-mail: kevrekid@math.umass.edu [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84 (Greece)
2011-10-14
We study dark-bright (DB) ring solitons in two-component Bose-Einstein condensates. In the limit of large densities of the dark component, we describe the soliton dynamics by means of an equation of motion for the ring radius. The presence of the bright, 'filling' species is demonstrated to have a stabilizing effect on the ring dark soliton. Near the linear limit, we discuss the symmetry-breaking bifurcations of DB soliton stripes and vortex-bright soliton clusters from the DB ring and relate the stabilizing effect of filling to changes in the bifurcation diagram. Finally, we show that the stabilization by means of a second component is not limited to the radially symmetric structures, but can also be observed in a cross-like DB soliton configuration. (fast track communication)
Instanton Calculus, Topological Field Theories and N = 2 Super Yang-Mills Theories
Bellisai, D; Tanzini, A; Travaglini, G; Bellisai, Diego; Fucito, Francesco; Tanzini, Alessandro; Travaglini, Gabriele
2000-01-01
The results obtained by Seiberg and Witten for the low-energy Wilsonian effective actions of N=2 supersymmetric theories with gauge group SU(2) are in agreement with instanton computations carried out for winding numbers one and two. This suggests that the instanton saddle point saturates the non-perturbative contribution to the functional integral. A natural framework in which corrections to this approximation are absent is given by the topological field theory built out of the N=2 Super Yang-Mills theory. After extending the standard construction of the Topological Yang-Mills theory to encompass the case of a non-vanishing vacuum expectation value for the scalar field, a BRST transformation is defined (as a supersymmetry plus a gauge variation), which on the instanton moduli space is the exterior derivative. The topological field theory approach makes the so-called "constrained instanton" configurations and the instanton measure arise in a natural way. As a consequence, instanton-dominated Green's functions...
Aspects Of Yang-mills Theory: Solitons, Dualities And Spin Chains
Freyhult, L K
2004-01-01
One of the still big problems in the Standard Model of particle physics is the problem of confinement. Quarks or other coloured particles have never been observed in isolation. Quarks are only observed in colour neutral bound states. The strong interactions are described using a Yang-Mills theory. These type of theories exhibits asymptotic freedom, i.e. the coupling is weak at high energies. This means that the theory is perturbative at high energies only. Understanding quark confinement requires knowledge of the non perturbative regime. One attempt has been to identify the proper order parameters for describing the low energy limit and then to write down effective actions in terms of these order parameters. We discuss one possible scenario for confinement and the effective models constructed with this as inspiration. Further we discuss solitons in these models and their properties. Yang-Mills theory has also become important in the context of string theory. According to the AdS/CFT correspondence string theo...
Analytical approach to the D3-brane gravity dual for 3d Yang-Mills theory
Forkel, Hilmar
2015-01-01
The complexity of "top-down" string-dual candidates for strongly-coupled Yang-Mills theories and in particular for QCD almost always prohibits their exact analytical or even comprehensive numerical treatment. This impedes both a thorough quantitative analysis and the development of more realistic gravity duals. To mitigate these impediments, we devise an analytical approach to top-down duals on the basis of controlled, uniformly converging high-accuracy approximations for the normalizable string modes corresponding to gauge-theory states. We demonstrate the potential of this approach in Witten's dual for $3d$ Yang-Mills theory, i.e. in the near-horizon limit of non-extremal $D\\text{3}$-branes, compactified on $S^{1}$. We obtain accurate analytical approximations to the bulk modes which satisfy the boundary conditions exactly. On their basis, analytical results for masses, sizes, pole residues and correlation functions of glueball excitations are derived by spectral methods. These approximations can be systema...
Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
Cé, Marco; Engel, Georg P; Giusti, Leonardo
2015-01-01
We study the topological charge distribution of the SU(3) Yang--Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo simulations by implementing a naive discretization of the topological charge evolved with the Yang--Mills gradient flow. This definition is far less demanding than the one suggested from Neuberger's fermions and, as shown in this paper, in the continuum limit its cumulants coincide with those of the universal definition appearing in the chiral Ward identities. Thanks to the range of lattice volumes and spacings considered, we can extrapolate the results for the second and fourth cumulant of the topological charge distribution to the continuum limit with confidence by keeping finite volume effects negligible with respect to the statistical errors. Our best results for the topological susceptibility is t_0^2*chi=6.67(7)*10^-4, where t_0 is a standard reference scale, while for the...
Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory
Koekenyesi, Zoltan; Sinkovics, Annamaria [Institute of Theoretical Physics, MTA-ELTE Theoretical Research Group, Eoetvoes Lorand University, 1117, Budapest, Pazmany, s. 1/A (Hungary); Szabo, Richard J. [Heriot-Watt Univ., Edinburgh (United Kingdom). Dept. of Mathematics; Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom); The Higgs Centre for Theoretical Physics, Edinburgh (United Kingdom)
2016-11-15
We derive the analog of the large N Gross-Taylor holomorphic string expansion for the refinement of q-deformed U(N) Yang-Mills theory on a compact oriented Riemann surface. The derivation combines Schur-Weyl duality for quantum groups with the Etingof-Kirillov theory of generalized quantum characters which are related to Macdonald polynomials. In the unrefined limit we reproduce the chiral expansion of q-deformed Yang-Mills theory derived by de Haro, Ramgoolam and Torrielli. In the classical limit q = 1, the expansion defines a new β-deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit β = 1 to the orbifold Euler characteristics of Hurwitz spaces of holomorphic maps. We discuss the geometrical meaning of our expansions in relation to quantum spectral curves and β-ensembles of matrix models arising in refined topological string theory. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
Bern, Zvi; Dixon, Lance J.; Douglas, Michael R.; von Hippel, Matt; Johansson, Henrik
2013-01-01
The connection of maximally supersymmetric Yang-Mills theory to the (2,0) theory in six dimensions has raised the possibility that it might be perturbatively ultraviolet finite in five dimensions. We test this hypothesis by computing the coefficient of the first potential ultraviolet divergence of planar (large $N_c$) maximally supersymmetric Yang-Mills theory in D = 5, which occurs at six loops. We show that the coefficient is nonvanishing. Furthermore, the numerical value of the divergence falls very close to an approximate exponential formula based on the coefficients of the divergences through five loops. This formula predicts the approximate values of the ultraviolet divergence at loop orders L > 6 in the critical dimension D = 4 + 6/L. To obtain the six-loop divergence we first construct the planar six-loop four-point amplitude integrand using generalized unitarity. The ultraviolet divergence follows from a set of vacuum integrals, which are obtained by expanding the integrand in the external momenta. T...
Gravity duals for the Coulomb branch of marginally deformed N=4 Yang-Mills
Hernández, R; Zoakos, D; Hernandez, Rafael; Sfetsos, Konstadinos; Zoakos, Dimitrios
2006-01-01
Supergravity backgrounds dual to a class of exactly marginal deformations of N supersymmetric Yang-Mills can be constructed through an SL(2,R) sequence of T-dualities and coordinate shifts. We apply this transformation to multicenter solutions and derive supergravity backgrounds describing the Coulomb branch of N=1 theories at strong 't Hooft coupling as marginal deformations of N=4 Yang-Mills. For concreteness we concentrate to cases with an SO(4)xSO(2) symmetry preserved by continuous distributions of D3-branes on a disc and on a three-dimensional spherical shell. We compute the expectation value of the Wilson loop operator and confirm the Coulombic behaviour of the heavy quark-antiquark potential in the conformal case. When the vev is turned on we find situations where a complete screening of the potential arises, as well as a confining regime where a linear or a logarithmic potential prevails depending on the ratio of the quark-antiquark separation to the typical vev scale. The spectra of massless excitat...
Gravitating vortices, cosmic strings, and the K\\"ahler--Yang--Mills equations
Álvarez-Cónsul, Luis; García-Prada, Oscar
2015-01-01
In this work we study equations describing Abelian vortices on a Riemann surface with back reaction of the metric. The gravitating vortex equations are derived by dimensional reduction of the K\\"ahler--Yang--Mills equations on the product of the complex projective line with a Riemann surface, and inherit their moment map interpretation. Applying the general theory for the K\\"ahler--Yang--Mills equations, we give evidence of an analogue of the Donaldson--Uhlembeck--Yau Theorem for gravitating vortices --- commonly referred to as a Hitchin--Kobayashi correspondence. As a particular case of the gravitating vortex equations on $\\mathbb{P}^1$ we find the Einstein--Bogomol'nyi equations, whose solutions correspond to Nielsen--Olesen cosmic strings in the Bogomol'nyi phase. Using an existence theorem by Yisong Yang, our main result implies a Hitchin--Kobayashi correspondence for the Einstein--Bogomol'nyi equations. In particular, we prove a conjecture by Yang about the non-existence of cosmic strings on $\\mathbb{P}^...
Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
Anber, Mohamed M; Teeple, Brett
2014-01-01
We study the phase structure of N=1 supersymmetric Yang-Mills theory on R^3XS^1, with massive gauginos, periodic around the S^1, with Sp(2N) (N>=2), Spin(N) (N>=5), G_2, F_4, E_6, E_7, E_8 gauge groups. As the gaugino mass m is increased, with S^1 size and strong coupling scale fixed, we find a first-order phase transition both for theories with and without a center. This semiclassically calculable transition is driven, as in SU(N) and G_2, arxiv.org/abs/1205.0290 and arxiv.org/abs/1212.1238, by a competition between monopole-instantons and exotic topological "molecules"---"neutral" or "magnetic" bions. We compute the trace of the Polyakov loop and its two-point correlator near the transition. We find a behavior similar to the one observed near the thermal deconfinement transition in the corresponding pure Yang-Mills (YM) theory in lattice studies (whenever available). Our results lend further support to the conjectured continuity, as a function of m, between the quantum phase transition studied here and the ...
Thermodynamics of SU(2) quantum Yang-Mills theory and CMB anomalies
Hofmann, Ralf
2013-01-01
A brief review of effective SU(2) Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field $\\phi$, based on non-propagating (anti)selfdual field configurations of topological charge unity. We explain why the screening physics of an SU(2) photon is subject to an electric-magnetically dual interpretation. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB) determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2) Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2) photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planc...
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.
Brihaye, Yves; Hartmann, Betti
2005-01-01
We construct solutions of an Einstein Yang Mills system including a cosmological constant in 4 + n spacetime dimensions, where the n-dimensional manifold associated with the extra dimensions is taken to be Ricci flat. Assuming the matter and metric fields to be independent of the n extra coordinates, a spherical symmetric ansatz for the fields leads to a set of coupled ordinary differential equations. We find that for n > 1 only solutions with either one non-zero Higgs field or with all Higgs fields constant and zero gauge field function (corresponding to a Wu Yang-type ansatz) exist. We give the analytic solutions available in this model. These are 'embedded' Abelian solutions with a diverging size of the manifold associated with the extra n dimensions. Depending on the choice of parameters, these latter solutions either represent naked singularities or they possess a single horizon. We also present solutions of the effective four-dimensional Einstein Yang Mills Higgs-dilaton model, where the higher-dimensional cosmological constant induces a Liouville-type potential. The solutions are non-Abelian solutions with diverging Higgs fields, which exist only up to a maximal value of the cosmological constant.
Static Spherically Symmetric Solutions of the SO(5) Einstein Yang-Mills Equations
Bartnik, Robert A; Oliynyk, Todd A
2009-01-01
Globally regular (ie. asymptotically flat and regular interior), spherically symmetric and localised ("particle-like") solutions of the coupled Einstein Yang-Mills (EYM) equations with gauge group SU(2) have been known for more than 20 years, yet their properties are still not well understood. Spherically symmetric Yang--Mills fields are classified by a choice of isotropy generator and SO(5) is distinguished as the simplest model with a \\emph{non-Abelian} residual (little) group, $SU(2)\\times U(1)$, and which admits globally regular particle-like solutions. We exhibit an algebraic gauge condition which normalises the residual gauge freedom to a finite number of discrete symmetries. This generalises the well-known reduction to the real magnetic potential $w(r,t)$ in the original SU(2) YM model. Reformulating using gauge invariant polynomials dramatically simplifies the system and makes numerical search techniques feasible. We find three families of embedded SU(2) EYM equations within the SO(5) system, one of w...
Three-dimensional super Yang-Mills with compressible quark matter
Faedo, Antón F; Mateos, David; Pantelidou, Christiana; Tarrío, Javier
2015-01-01
We construct the gravity dual of three-dimensional, $SU(N_{\\textrm{c}})$ super Yang-Mills theory with $N_{\\textrm{f}}$ flavors of dynamical quarks in the presence of a non-zero quark density $N_{\\textrm{q}}$. The supergravity solutions include the backreaction of $N_{\\textrm{c}}$ color D2-branes and $N_{\\textrm{f}}$ flavor D6-branes with $N_{\\textrm{q}}$ units of electric flux on their worldvolume. For massless quarks, the solutions depend non-trivially only on the dimensionless combination $\\rho=N_{\\textrm{c}}^2 N_{\\textrm{q}} / \\lambda^2 N_{\\textrm{f}}^4$, with $\\lambda=g_{\\textrm{YM}}^2 N_{\\textrm{c}}$ the 't Hooft coupling, and describe renormalization group flows between the super Yang-Mills theory in the ultraviolet and a non-relativistic theory in the infrared. The latter is dual to a hyperscaling-violating, Lifshitz-like geometry with dynamical and hyperscaling-violating exponents $z=5$ and $\\theta=1$, respectively. If $\\rho \\ll 1$ then at intermediate energies there is also an approximate AdS$_4$ reg...
Solving the Ghost-Gluon System of Yang-Mills Theory on GPUs
Hopfer, Markus; Haase, Gundolf
2012-01-01
We solve the ghost-gluon system of Yang-Mills theory using Graphics Processing Units (GPUs). Working in Landau gauge, we use the Dyson-Schwinger formalism for the mathematical description as this approach is well-suited to directly benefit from the computing power of the GPUs. With the help of a Chebyshev expansion for the dressing functions and a subsequent appliance of a Newton-Raphson method, the non-linear system of coupled integral equations is linearized. The resulting Newton matrix is generated in parallel using OpenMPI and CUDA(TM). Our results show, that it is possible to cut down the run time by two orders of magnitude as compared to a sequential version of the code. This makes the proposed techniques well-suited for Dyson-Schwinger calculations on more complicated systems where the Yang-Mills sector of QCD serves as a starting point. In addition, the computation of Schwinger functions using GPU devices is studied.
From d logs to dilogs; the super Yang-Mills MHV amplitude revisited
Lipstein, Arthur E.; Mason, Lionel [The Mathematical Institute, University of Oxford,24-29 St Giles’, Oxford, OX1 3LB (United Kingdom)
2014-01-30
Recently, loop integrands for certain Yang-Mills scattering amplitudes and correlation functions have been shown to be systematically expressible in d log form, raising the possibility that these loop integrals can be performed directly without Feynman parameters. We do so here to give a new description of the planar 1-loop MHV amplitude in N=4 super Yang-Mills theory. We explicitly incorporate the standard Feynman iϵ prescription into the integrands. We find that the generic MHV diagram contributing to the 1-loop MHV amplitude, known as Kermit, is dual conformal invariant up to the choice of reference twistor explicit in our axial gauge (the generic MHV diagram was already known to be finite). The new formulae for the amplitude are nontrivially related to previous ones in the literature. The divergent diagrams are evaluated using mass regularization. Our techniques extend directly to higher loop diagrams, and we illustrate this by sketching the evaluation of a non-trivial 2-loop example. We expect this to lead to a simple and efficient method for computing amplitudes and correlation functions with less supersymmetry and without the assumption of planarity.
A unified field theory II: Gravity interacting with a Yang-Mills and Higgs field
Gerhardt, Claus
2016-01-01
We quantize the interaction of gravity with a Yang-Mills and Higgs field using canonical quantization. Similar to the approach in a previous paper we discard the Wheeler-DeWitt equation and express the Hamilton constraint by the evolution equation of the mean curvature of the hypersurfaces in the foliation defined by the Hamiltonian setting. Expressing the time derivative of the mean curvature with the help of the Poisson brackets the canonical quantization of this equation leads to a wave equation in $Q=(0,\\infty)\\times \\cal{S}_o$, where $\\cal{S}_o$ is one of the Cauchy hypersurfaces in the Hamiltonian setting. The wave equation describes the interaction of an arbitrary Riemannian metric in $\\cal{S}_o$ and a given Yang-Mills and Higgs field. If the metric is complete $Q$ is globally hyperbolic. In case $\\cal{S}_o$ is compact we also prove a spectral resolution of the wave equation and establish sufficient conditions guaranteeing a mass gap.
Transport properties of N = 4 supersymmetric Yang-Mills theory at finite coupling
Benincasa, Paolo [Department of Applied Mathematics, University of Western Ontario, Middlesex College, London, ON, N6A 5B7 (Canada); Buchel, Alex [Department of Applied Mathematics, University of Western Ontario, Middlesex College, London, ON, N6A 5B7 (Canada); Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada)
2006-01-15
Gauge theory-string theory duality describes strongly coupled N = 4 supersymmetric SU(n{sub c}) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in the inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-n{sub c} N = 4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation of the shear and the sound wave lowest quasinormal modes in the leading order {alpha}'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the {alpha}'-corrected nonextremal black branes in string theory.
Transport properties of Script N = 4 supersymmetric Yang-Mills theory at finite coupling
Benincasa, Paolo; Buchel, Alex
2006-01-01
Gauge theory-string theory duality describes strongly coupled Script N = 4 supersymmetric SU(nc) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in the inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-nc Script N = 4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation of the shear and the sound wave lowest quasinormal modes in the leading order α'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the α'-corrected nonextremal black branes in string theory.
Does the Gursey-Tze solution represent a monopole condensate?
Nergiz, S; Nergiz, Serdar; Saclioglu, Cihan
1995-01-01
We recast the quaternionic Gursey-Tze solution, which is a fourfold quasi-periodic self-dual Yang-Mills field with a unit instanton number per Euclidean spacetime cell, into an ordinary coordinate formulation. After performing the sum in the Euclidean time direction, we use an observation by Rossi which suggests the solution represents an arrangement with a BPS monopole per space lattice cell. This may provide a concrete realization of a monopole condensate in pure Yang-Mills theory.
Kajantie, K; Vepsalainen, M; Vuorinen, Aleksi
2011-01-01
We use AdS/QCD duality to compute the finite temperature Green's function G(omega,k;T) of the shear operator T_12 for all omega,k in hot Yang-Mills theory. The goal is to assess how the existence of scales like the transition temperature and glueball masses affects the correlator computed in the scalefree conformal N=4 supersymmetric Yang-Mills theory. We observe sizeable effects for T close to T_c which rapidly disappear with increasing T. Quantitative agreement of these predictions with future lattice Monte Carlo data would suggest that QCD matter in this temperature range is strongly interacting.
Tadmon, Calvin
2012-01-01
We show how to assign initial data for the characteristic Einstein-Yang-Mills-Higgs system on two intersecting smooth null hypersurfaces. We successfully adapt the hierarchical method set up by A. D. Rendall to solve the same problem for the Einstein equations in vacuum and with perfect fluid source. Unlike the work of Rendall, many delicate calculations and expressions are given in details so as to address, in a forthcoming work, the issue of global resolution of the characteristic initial value problem for the Einstein-Yang-Mills-Higgs system. The method obviously applies to the Einstein-Maxwell and the Einstein-scalar field models.
U(1) decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relations in N=4 super Yang-Mills
Jia, Yin; Huang, Rijun; Liu, Chang-Yong
2010-09-01
By using the Britto-Cachazo-Feng-Witten recursion relation of N=4 super Yang-Mills theory, we proved the color reflection, U(1) decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relations for color-ordered amplitudes of N=4 super Yang-Mills theory. This proof verified the conjectured Bern-Carrasco-Johansson relations of matter fields. The proof depended only on general properties of superamplitudes. We showed also that the color reflection relation and U(1)-decoupling relation are special cases of Kleiss-Kuijf relations.
High energy behavior of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory
Bartels, Jochen; Hentschinski, Martin; Mischler, Anna-Maria [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Ewerz, Carlo [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; GSI Helmholtzzentrum fuer Schwerionenforschung, Darmstadt (Germany). ExtreMe Matter Institute EMMI; Bielefeld Univ. (Germany). Fakultaet fuer Physik; European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT), Villazzano (Italy)
2009-12-15
We study the high energy limit of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory for finite N{sub c}. We make use of the framework of perturbative resummation of large logarithms of the energy. More specifically, we apply the (extended) generalized leading logarithmic approximation. We find that the same conformally invariant two-to-four gluon vertex occurs as in non-supersymmetric Yang-Mills theory. As a new feature we find a direct coupling of the four-gluon t-channel state to the R-current impact factor. (orig.)
Continuum strong-coupling expansion of Yang-Mills theory: quark confinement and infra-red slavery
Mansfield, P. (Dept. of Mathematical Sciences, Univ. of Durham (United Kingdom))
1994-04-25
We solve Schroedinger's equation for the ground-state of four-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading-order approximation are reduced to a calculation in two-dimensional Yang-Mills theory which is known to confine. Consequently the Wilson loop in the four-dimensional theory obeys an area law to leading order and the coupling becomes infinite as the mass scale goes to zero. (orig.)
Zhu, Yan
2013-01-01
In this PhD thesis, I will review recent progress in perturbative studies of energy momentum tensor correlators in high-temperature Yang-Mills theory. After briefly introducing the necessary tools and physical motivation, I proceed to discuss the machinery developed for the extraction of next-to-leading order Operator Product Expansions and thermal spectral functions and to introduce the results obtained in the bulk and shear channels of Yang-Mills theory. Particular emphasis is placed on the comparison of the results with recent lattice and gauge/gravity calculations, as well as on discussing their use in extracting the corresponding transport coefficients from Euclidean lattice data.
Kleihaus, B
1999-01-01
We point out that the statements in [hep-th/9903063] concerning the regularity of static axially symmetric solutions in Yang-Mills-dilaton (YMD) [1] and Einstein-Yang-Mills(-dilaton) (EYMD) theory [2,3] are incorrect, and that the non-singular local gauge potential of the YMD solutions [4] is twice differentiable.
Dark Matter Halos as Bose-Einstein Condensates
Mielke, E W; Schunck, F E; Mielke, Eckehard W.; Fuchs, Burkhard; Schunck, Franz E.
2006-01-01
Galactic dark matter is modelled by a scalar field in order to effectively modify Kepler's law without changing standard Newtonian gravity. In particular, a solvable toy model with a self-interaction U(Phi) borrowed from non-topological solitons produces already qualitatively correct rotation curves and scaling relations. Although relativistic effects in the halo are very small, we indicate corrections arising from the general relativistic formulation. Thereby, we can also probe the weak gravitational lensing of our soliton type halo. For cold scalar fields, it corresponds to a gravitationally confined Boson-Einstein condensate, but of galactic dimensions.
Kleihaus, B; Kunz, Jutta
1999-01-01
In [hep-th/9907222] Hannibal claims to exclude the existence of particle-like static axially symmetric non-abelian solutions in SU(2) Einstein-Yang-Mills-dilaton theory. His argument is based on the asymptotic behaviour of such solutions. Here we disprove his claim by giving explicitly the asymptotic form of non-abelian solutions with winding number n=2.
All Next-to-Maximally-Helicity-Violating One-Loop Gluon Amplitudes in N=4 Super-Yang-Mills Theory
Bern, Z; Kosower, D A; Bern, Zvi; Dixon, Lance J.; Kosower, David A.
2004-01-01
We compute the next-to-MHV one-loop n-gluon amplitudes in N=4 super-Yang-Mills theory. These amplitudes contain three negative-helicity gluons and an arbitrary number of positive-helicity gluons, and are the first infinite series of amplitudes beyond the simplest, MHV, amplitudes. We also discuss some aspects of their twistor-space structure.
Krishnaswami, G.S.
2008-01-01
We consider large-N multi-matrix models whose action closely mimics that of Yang-Mills theory, including gauge-fixing and ghost terms. We show that the factorized Schwinger-Dyson loop equations, expressed in terms of the generating series of gluon and ghost correlations G( ), are quadratic equations
Fargnoli, H.G.; Sampaio, Marcos; Nemes, M.C. [Federal University of Minas Gerais, ICEx, Physics Department, P.O. Box 702, Belo Horizonte, MG (Brazil); Hiller, B. [Coimbra University, Faculty of Science and Technology, Physics Department, Center of Computational Physics, Coimbra (Portugal); Baeta Scarpelli, A.P. [Setor Tecnico-Cientifico, Departamento de Policia Federal, Lapa, Sao Paulo (Brazil)
2011-05-15
We present both an ultraviolet and an infrared regularization independent analysis in a symmetry preserving framework for the N=1 Super Yang-Mills beta function to two loop order. We show explicitly that off-shell infrared divergences as well as the overall two loop ultraviolet divergence cancel out, whilst the beta function receives contributions of infrared modes. (orig.)
Itoh, K; Sawanaka, H; So, H; Ukita, N
2003-01-01
We present a lattice theory with an exact fermionic symmetry, which mixes the link and the fermionic variables. The staggered fermionic variables may be reconstructed into a Majorana fermion in the continuum limit. The gauge action has a novel structure. Though it is the ordinary plaquette action, two different couplings are assigned in the ``Ichimatsu pattern'' or the checkered pattern. In the naive continuum limit, the fermionic symmetry survives as a continuum (or an $O(a^0)$) symmetry. The transformation of the fermion is proportional to the field strength multiplied by the difference of the two gauge couplings in this limit. This work is an extension of our recently proposed cell model toward the realization of supersymmetric Yang-Mills theory on lattice.
Charge-density waves in deconfining SU(2) Yang-Mills thermodynamics
Falquez, Carlos; Baumbach, Tilo
2011-01-01
At one-loop accuracy we compute, characterize, and discuss the dispersion laws for the three low-momentum branches of propagating longitudinal, electric U(1) fields in the effective theory for the deconfining phase of pure SU(2) Yang-Mills thermodynamics. With an electric-magnetically dual interpretation of SU(2)$_{\\tiny CMB}$ we argue that upon a breaking of plasma isotropy and homogeneity, introduced e.g. by a temperature gradient, the longitudinal modes could conspire to provide magnetic seed fields for magneto-hydrodynamical dynamos inside structures of galaxy, galaxy-cluster, and cosmological scales. Such a scenario ultimately links structure with seed-field formation. As judged from the present cosmological epoch, the maximally available coherent field strength of 10$^{-8}$\\,Gauss from SU(2)$_{\\tiny CMB}$ matches with the upper bound for cosmological present-day field strength derived from small-angle anisotropies of the cosmic microwave background.
Geometrodynamics of gauge fields on the geometry of Yang-Mills and gravitational gauge theories
Mielke, Eckehard W
2016-01-01
This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter t...
Phase transitions of an anisotropic N=4 super Yang-Mills plasma via holography
Banks, Elliot
2016-01-01
Black hole solutions of type IIB supergravity were previously found that are dual to N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. In the zero temperature limit, these black holes approach a Liftshitz like scaling solution in the IR. It was recently shown that these black holes are unstable, and at low temperatures there is a new class of black hole solutions that are thermodynamically preferred. We extend this analysis, by considering consistent truncations of the Kaluza-Klein reduction of IIB supergravity on a five-sphere that preserves multiple scalar and $U(1)$ gauge fields. We show that the previously constructed black holes become unstable at low temperatures, and construct new classes of exotic black hole solutions. We study the DC thermo-electric conductivity of these $U(1)$ charged black holes, and find a diverging DC conductivity at zero temperature due to the divergence of the gauge field coupling.
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.
Equal-time two-point correlation functions in Coulomb gauge Yang-Mills theory
Campagnari, D; Reinhardt, H; Astorga, F; Schleifenbaum, W
2009-01-01
We apply a new functional perturbative approach to the calculation of the equal-time two-point correlation functions and the potential between static color charges to one-loop order in Coulomb gauge Yang-Mills theory. The functional approach proceeds through a solution of the Schroedinger equation for the vacuum wave functional to order g^2 and derives the equal-time correlation functions from a functional integral representation via new diagrammatic rules. We show that the results coincide with those obtained from the usual Lagrangian functional integral approach, extract the beta function and determine the anomalous dimensions of the equal-time gluon and ghost two-point functions and the static potential under the assumption of multiplicative renormalizability to all orders.
Stochastic Feynman Rules for Yang-Mills Theory on the Plane
Nguyen, Timothy
2016-01-01
We analyze quantum Yang-Mills theory on $\\mathbb{R}^2$ using a novel discretization method based on an algebraic analogue of stochastic calculus. Such an analogue involves working with "Gaussian" free fields whose covariance matrix is indefinite rather than positive definite. Specifically, we work with Lie-algebra valued fields on a lattice and exploit an approximate gauge-invariance that is restored when taking the continuum limit. This analysis is applied to show the equivalence between Wilson loop expectations computed using partial axial-gauge, complete axial-gauge, and the Migdal-Witten lattice formulation. As a consequence, we obtain intriguing Lie-theoretic identities involving heat kernels and iterated integrals.
Gravitating Vortices, Cosmic Strings, and the Kähler-Yang-Mills Equations
Álvarez-Cónsul, Luis; Garcia-Fernandez, Mario; García-Prada, Oscar
2017-04-01
In this paper we construct new solutions of the Kähler-Yang-Mills equations, by applying dimensional reduction methods to the product of the complex projective line with a compact Riemann surface. The resulting equations, which we call gravitating vortex equations, describe abelian vortices on the Riemann surface with back reaction of the metric. As a particular case of these gravitating vortices on the Riemann sphere we find solutions of the Einstein-Bogomol'nyi equations, which physically correspond to Nielsen-Olesen cosmic strings in the Bogomol'nyi phase. We use this to provide a Geometric Invariant Theory interpretation of an existence result by Y. Yang for the Einstein-Bogomol'nyi equations, applying a criterion due to G. Székelyhidi.
The large $N$ limit of the topological susceptibility of Yang-Mills gauge theory
Cè, Marco; Giusti, Leonardo; Schaefer, Stefan
2016-01-01
We present a precise computation of the topological susceptibility $\\chi_{_\\mathrm{YM}}$ of SU$(N)$ Yang-Mills theory in the large $N$ limit. The computation is done on the lattice, using high-statistics Monte Carlo simulations with $N=3, 4, 5, 6$ and three different lattice spacings. Two major improvements make it possible to go to finer lattice spacing and larger $N$ compared to previous works. First, the topological charge is implemented through the gradient flow definition; and second, open boundary conditions in the time direction are employed in order to avoid the freezing of the topological charge. The results allow us to extrapolate the dimensionless quantity $t_0^2\\chi_{_\\mathrm{YM}}$ to the continuum and large $N$ limits with confidence. The accuracy of the final result represents a new quality in the verification of large $N$ scaling.
The Stringy Representation of the D>=3 Yang-Mills Theory
Dubin, A Yu
2001-01-01
I put forward the stringy representation of the 1/N strong coupling (SC) expansion for the regularized Wilson's loop-averages in the continuous D>=3 Yang-Mills theory (YM_{D}) with a sufficiently large bare coupling constant \\lambda>\\lambda_{cr} and a fixed ultraviolet cut off \\Lambda. The proposed representation is proved to provide with the confining solution of the Dyson-Schwinger chain of the judiciously regularized U(N) Loop equations. Building on the results obtained, we suggest the stringy pattern of the low-energy theory associated to the D=4 U(\\infty)=SU(\\infty) gauge theory in the standard \\lambda=>0 phase with the asymptotic freedom in the UV domain. A nontrivial test, to clarify whether the AdS/CFT correspondence conjecture may be indeed applicable to the large N pure YM_{4} theory in the \\lambda=>\\infty limit, is also discussed.
Einstein-Yang-Mills Black Hole Interiors Serious Problems But Simple Solution
Zotov, M Yu
1997-01-01
Recently, E. E. Donets, D. V. Galtsov, and the author have reported about the results of numerical and analytical investigation of the SU(2) Einstein-Yang-Mills (EYM) black hole interior solutions (gr-qc/9612067). It was shown that a generic interior solution develops a new type of an infinitely oscillating behavior with exponentially growing amplitude. Numerical data for three sequential oscillations were presented. The numerical integration technique was not discussed. Later P. Breitenlohner, G. Lavrelashvili, and D. Maison confirmed our main results (gr-qc/9703047). But they made some misleading statements, in particular, they claimed, discussing the oscillations, that ``as one performs the numerical integration one quickly runs into serious problems...'' so that ``it is practically impossible to follow more than one or two of them numerically'' because ``the numerical integration procedure breaks down''. It is shown here that trivial logarithmic substitutions and integration along the integral curve solve...
Towards the spectrum of low-lying particles in supersymmetric Yang-Mills theory
Bergner, Georg; Münster, Gernot; Özugurel, Umut D; Sandbrink, Dirk
2013-01-01
We present the current results of our simulations of N=1 supersymmetric Yang-Mills theory on a lattice. The masses of the gluino-glue particle, the a-eta-prime, the a-f0 meson, and the scalar glueball are obtained at finer lattice spacing than before, and extrapolations towards vanishing gluino mass are made. The calculations employ different levels of stout smearing. The statistical accuracy as well as the control of finite size effects and lattice artefacts are better than in previous investigations. Taking the statistical and systematic uncertainties into account, the extrapolations towards vanishing gluino mass of the masses of the fermionic and bosonic states in our present calculations are consistent with the formation of degenerate supermultiplets.
A local and BRST-invariant Yang-Mills theory within the Gribov horizon
Capri, M A L; Fiorentini, D; Guimaraes, M S; Justo, I F; Pereira, A D; Mintz, B W; Palhares, L F; Sobreiro, R F; Sorella, S P
2016-01-01
We present a local setup for the recently introduced BRST-invariant formulation of Yang-Mills theories for linear covariant gauges that takes into account the existence of gauge copies \\`a la Gribov and Zwanziger. Through the convenient use of auxiliary fields, including one of the Stueckelberg type, it is shown that both the action and the associated nilpotent BRST operator can be put in local form. Direct consequences of this fully local and BRST-symmetric framework are drawn from its Ward identities: (i) an exact prediction for the longitudinal part of the gluon propagator in linear covariant gauges that is compatible with recent lattice results and (ii) a proof of the gauge-parameter independence of all correlation functions of local BRST-invariant operators.
On super form factors of half-BPS operators in N=4 super Yang-Mills
Penante, Brenda; Travaglini, Gabriele; Wen, Congkao
2014-01-01
We compute form factors of half-BPS operators in N=4 super Yang-Mills dual to massive Kaluza-Klein modes in supergravity. These are appropriate supersymmetrisations T_k of the scalar operators Tr(\\phi^k) for any k, which for k=2 give the chiral part of the stress-tensor multiplet operator. Using harmonic superspace, we derive simple Ward identities for these form factors, which we then compute perturbatively at tree level and one loop. We propose a novel on-shell recursion relation which links form factors with different numbers of fields. Using this, we conjecture a general formula for the n-point MHV form factors of T_k for arbitrary k and n. Finally, we use supersymmetric generalised unitarity to derive compact expressions for all one-loop MHV form factors of T_k in terms of one-loop triangles and finite two-mass easy box functions.
Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N
Morita, Takeshi; Wiseman, Toby; Withers, Benjamin
2014-01-01
Maximally supersymmetric (p+1)-dimensional Yang-Mills theory at large N and finite temperature, with possibly compact spatial directions, has a rich phase structure. Strongly coupled phases may have holographic descriptions as black branes in various string duality frames, or there may be no gravity dual. In this paper we provide tools in the gauge theory which give a simple and unified picture of the various strongly coupled phases, and transitions between them. Building on our previous work we consider the effective theory describing the moduli of the gauge theory, which can be computed precisely when it is weakly coupled far out on the Coulomb branch. Whilst for perturbation theory naive extrapolation from weak coupling to strong gives little information, for this moduli theory naive extrapolation from its weakly to its strongly coupled regime appears to encode a surprising amount of information about the various strongly coupled phases. We argue it encodes not only the parametric form of thermodynamic qua...
Towards a Spin-foam unification of gravity, Yang-Mills interactions and matter fields
Alexander, Stephon; Tacchi, Ruggero Altair
2011-01-01
We propose a new method of unifying gravity and the Standard Model by introducing a spin-foam model. We realize a unification between an SU(2) Yang-Mills interaction and 3D general relativity by considering a Spin(4) Plebanski action. The theory is quantized a la spin-foam by implementing the analogue of the simplicial constraints for the broken phase of the Spin(4) symmetry. A natural 4D extension of the theory is shown. We also present a way to recover 2-point correlation functions between the connections as a first way to implement scattering amplitudes between particle states, aiming to connect Loop Quantum Gravity to new physical predictions.
Bassetto, A.; Nardelli, G.; Torrielli, A.
2002-10-01
Commutative Yang-Mills theories in 1+1 dimensions exhibit an interesting interplay between geometrical properties and U(N) gauge structures: in the exact expression of a Wilson loop with n windings a nontrivial scaling intertwines n and N. In the noncommutative case the interplay becomes tighter owing to the merging of space-time and ``internal'' symmetries in a larger gauge group U(∞). We perform an explicit perturbative calculation of such a loop up to O(g6) rather surprisingly, we find that in the contribution from the crossed graphs (the genuine noncommutative terms) the scaling we mentioned occurs for large n and N in the limit of maximal noncommutativity θ=∞. We present arguments in favor of the persistence of such a scaling at any perturbative order and succeed in summing the related perturbative series.
Wilson Loop Area Law for 2D Yang-Mills in Generalized Axial Gauge
Nguyen, Timothy
2016-01-01
We prove that Wilson loop expectation values for arbitrary simple closed contours obey an area law up to second order in perturbative two-dimensional Yang-Mills theory. Our analysis occurs within a general family of axial-like gauges, which include and interpolate between holomorphic gauge and the Wu-Mandelstam-Liebrandt light cone gauge. Our methods make use of the homotopy invariance properties of iterated integrals of closed one-forms, which allows us to evaluate the nontrivial integrals occurring at second order. We close with a discussion on complex gauge-fixing and deformation of integration cycles for holomorphic path integrals to shed light on some of the quantum field-theoretic underpinnings of our results.
Unconstrained Hamiltonian formulation of low energy SU(3) Yang-Mills quantum theory
Pavel, Hans-Peter
2012-01-01
An unconstrained Hamiltonian formulation of the SU(3) Yang-Mills quantum mechanics of spatially constant fields is given using the method of minimal embedding of SU(2) into SU(3) by Kihlberg and Marnelius. Using a canonical transformation of the gluon fields to a new set of adapted coordinates (a non-standard type polar decomposition), which Abelianizes the Non-Abelian Gauss law constraints to be implemented, the corresponding unconstrained Hamiltonian and total angular momentum are derived. This reduces the colored spin-1 gluons to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields. The obtained unconstrained Hamiltonian is then rewritten into a form, which separates the rotational from the scalar degrees of freedom. It is shown that the chromomagnetic potential has classical zero-energy valleys for two arbitrarily large classical glueball fields, which are the unconstrained analogs of the well-known "constant Abelian fields". On the quantum level, practically all glueball excitation e...
The Hilbert series of 3d N=2 Yang-Mills theories with vectorlike matter
Cremonesi, Stefano
2015-01-01
This paper presents a formula for the Hilbert series that counts gauge invariant chiral operators in 3d N=2 Yang-Mills theories with vectorlike matter and no Chern-Simons interactions. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background, which is determined by the Higgs mechanism. The sum over magnetic charges is restricted due to instanton effects that partially lift the classical Coulomb branch. The formalism is applied to unitary and symplectic gauge theories with fundamental matter, reproducing old results for the moduli space of vacua and the chiral ring, without resorting to any further effective superpotential on the moduli space.
Towards the spectrum of low-lying particles in supersymmetric Yang-Mills theory
Bergner, G. [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Montvay, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Muenster, G.; Oezugurel, U.D.; Sandbrink, D. [Muenster Univ. (Germany). Inst. fuer Theoretische Physik 1
2013-04-15
We present the current results of our simulations of N=1 supersymmetric Yang-Mills theory on a lattice. The masses of the gluino-glue particle, the a-{eta}', the a-f{sub 0} meson, and the scalar glueball are obtained at finer lattice spacing than before, and extrapolations towards vanishing gluino mass are made. The calculations employ different levels of stout smearing. The statistical accuracy as well as the control of finite size effects and lattice artefacts are better than in previous investigations. Taking the statistical and systematic uncertainties into account, the extrapolations towards vanishing gluino mass of the masses of the fermionic and bosonic states in our present calculations are consistent with the formation of degenerate supermultiplets.
Gravitating Vortices, Cosmic Strings, and the Kähler-Yang-Mills Equations
Álvarez-Cónsul, Luis; Garcia-Fernandez, Mario; García-Prada, Oscar
2016-09-01
In this paper we construct new solutions of the Kähler-Yang-Mills equations, by applying dimensional reduction methods to the product of the complex projective line with a compact Riemann surface. The resulting equations, which we call gravitating vortex equations, describe abelian vortices on the Riemann surface with back reaction of the metric. As a particular case of these gravitating vortices on the Riemann sphere we find solutions of the Einstein-Bogomol'nyi equations, which physically correspond to Nielsen-Olesen cosmic strings in the Bogomol'nyi phase. We use this to provide a Geometric Invariant Theory interpretation of an existence result by Y. Yang for the Einstein-Bogomol'nyi equations, applying a criterion due to G. Székelyhidi.
Hydrodynamics of the Polyakov Line in SU$(N_c)$ Yang-Mills
Liu, Yizhuang; Zahed, Ismail
2015-01-01
We discuss a hydrodynamical description of the eigenvalues of the Polyakov line at large but finite $N_c$ for Yang-Mills theory in even and odd space-time dimensions. The hydro-static solutions for the eigenvalue densities are shown to interpolate between a uniform distribution in the confined phase and a localized distribution in the de-confined phase. The resulting critical temperatures are in overall agreement with those measured on the lattice over a broad range of $N_c$, and are consistent with the string model results at $N_c=\\infty$. The stochastic relaxation of the eigenvalues of the Polyakov line out of equilibrium is captured by a hydrodynamical instanton. An estimate of the probability of formation of a Z(N$_c)$ bubble using a piece-wise sound wave is suggested.
Effective lattice Polyakov loop theory vs. full SU(3) Yang-Mills at finite temperature
Bergner, Georg; Philipsen, Owe
2013-01-01
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 b...
Phase transitions of an anisotropic N=4 super Yang-Mills plasma via holography
Banks, Elliot
2016-07-01
Black hole solutions of type IIB supergravity were previously found that are dual to N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. In the zero temperature limit, these black holes approach a Liftshitz like scaling solution in the IR. It was recently shown that these black holes are unstable, and at low temperatures there is a new class of black hole solutions that are thermodynamically preferred. We extend this analysis, by considering consistent truncations of the Kaluza-Klein reduction of IIB supergravity on a five-sphere that preserves multiple scalar and U(1) gauge fields. We show that the previously constructed black holes become unstable at low temperatures, and construct new classes of exotic black hole solutions. We study the DC thermo-electric conductivity of these U(1) charged black holes, and find a diverging DC conductivity at zero temperature due to the divergence of the gauge field coupling.
Confinement interpretation in a Yang-Mills + Higgs theory when considering Gribov's ambiguity
Justo, I F; Dudal, D; Gómez, A J; Guimaraes, M S; Sorella, S P; Vercauteren, D
2015-01-01
This work presents concisely the results obtained from the analysis of the two-point function of the gauge field in the $SU(2)$ and $SU(2)\\times U(1)$ gauge theories, in the Landau gauge, coupled to a scalar Higgs field in the fundamental or adjoint representation. Non-perturbative effects are considered by taking into account the Gribov ambiguity. In general, in both Yang-Mills models the gluon propagator has non-trivial contributions of physical and non-physical modes, which clearly depends on the group representation of the Higgs field. These results were presented during the Fourth Winter Workshop on Non-perturbative Quantum Field Theory, which took place in Sophia-Antipolis - France.
Finite temperature and the Polyakov loop in the covariant variational approach to Yang-Mills Theory
Quandt, Markus; Reinhardt, Hugo
2017-03-01
We extend the covariant variational approach for Yang-Mills theory in Landau gauge to non-zero temperatures. Numerical solutions for the thermal propagators are presented and compared to high-precision lattice data. To study the deconfinement phase transition, we adapt the formalism to background gauge and compute the effective action of the Polyakov loop for the colour groups SU(2) and SU(3). Using the zero-temperature propagators as input, all parameters are fixed at T = 0 and we find a clear signal for a deconfinement phase transition at finite temperatures, which is second order for SU(2) and first order for SU(3). The critical temperatures obtained are in reasonable agreement with lattice data.
Covariant variational approach to Yang-Mills theory: Effective potential of the Polyakov loop
Quandt, M.; Reinhardt, H.
2016-09-01
We compute the effective action of the Polyakov loop in S U (2 ) and S U (3 ) Yang-Mills theory using a previously developed covariant variational approach. The formalism is extended to background gauge and it is shown how to relate the low-order Green's functions to the ones in Landau gauge studied earlier. The renormalization procedure is discussed. The self-consistent effective action is derived and evaluated using the numerical solution of the gap equation. We find a clear signal for a deconfinement phase transition at finite temperatures, which is second order for S U (2 ) and first order for S U (3 ). The critical temperatures obtained are in reasonable agreement with high-precision lattice data.
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.
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.
Parametric Instability of Classical Yang-Mills Fields in an Expanding Geometry
Tsutsui, Shoichiro; Ohnishi, Akira
2015-01-01
We investigate the instability of classical Yang-Mills field in an expanding geometry under a color magnetic background field within the linear regime. We consider homogeneous, boost-invariant and time-dependent color magnetic fields simulating the glasma configuration. We introduce the conformal coordinates which enable us to map an expanding problem approximately into a nonexpanding problem. We find that the fluctuations with finite longitudinal momenta can grow exponentially due to parametric instability. Fluctuations with finite transverse momenta can also show parametric instability, but their momenta are restricted to be small. The most unstable modes start to grow exponentially in the early stage of the dynamics and they may affect the thermalization in heavy-ion collisions.
Parametric instability of classical Yang-Mills fields in an expanding geometry
Tsutsui, Shoichiro; Kunihiro, Teiji; Ohnishi, Akira
2016-07-01
We investigate the instability of a classical Yang-Mills field in an expanding geometry under a color magnetic background field within the linear regime. We consider homogeneous, boost-invariant, and time-dependent color magnetic fields simulating the glasma configuration. We introduce the conformal coordinates which enable us to map an expanding problem approximately into a nonexpanding problem. We find that the fluctuations with finite longitudinal momenta can grow exponentially due to parametric instability. Fluctuations with finite transverse momenta can also show parametric instability, but their momenta are restricted to be small. The most unstable modes start to grow exponentially in the early stage of the dynamics, and they may affect the thermalization in heavy-ion collisions.
Noncommutative Yang-Mills-Higgs actions from derivation-based differential calculus
Cagnache, Eric; Wallet, Jean-Christophe
2008-01-01
Derivations of a (noncommutative) algebra can be used to construct various consistent differential calculi, the so-called derivation-based differential calculi. We apply this framework to the noncommutative Moyal algebras for which all the derivations are inner and analyse in detail the case where the derivation algebras generating the differential calculus are related to area preserving diffeomorphisms. The ordinary derivations corresponding to spatial dimensions are supplemented by additional derivations necessarely related to additional covariant coordinates. It is shown that these latter have a natural interpretation as Higgs fields when involved in gauge invariant actions built from the noncommutative curvature. The UV/IR mixing problem for (some of) the resulting Yang-Mills-Higgs models is discussed. A comparition to other noncommutative geometries already considered in the litterature is given.
Yang-Mills Field from Quaternion Space Geometry, and its Klein-Gordon Representation
Yefremov A.
2007-07-01
Full Text Available Analysis of covariant derivatives of vectors in quaternion (Q- spaces performed using Q-unit spinor-splitting technique and use of SL(2C-invariance of quaternion multiplication reveals close connexion of Q-geometry objects and Yang-Mills (YM field principle characteristics. In particular, it is shown that Q-connexion (with quaternion non-metricity and related curvature of 4 dimensional (4D space-times with 3D Q-space sections are formally equivalent to respectively YM-field potential and strength, traditionally emerging from the minimal action assumption. Plausible links between YM field equation and Klein-Gordon equation, in particular via its known isomorphism with Duffin-Kemmer equation, are also discussed.
Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence
Kassandrov, Vladimir V.; Rizcallah, Joseph A.
We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, SL(2, ℂ) Yang-Mills and complex Maxwell fields, the latter produced by integer-valued electric charges (“elementary” for the Kerr-like congruences), can all be explicitly associated with any shear-free null geodesic congruence. Using twistor variables, we derive the general solution of the equations of the shear-free null geodesic congruence (as a modification of the Kerr theorem) and analyze the corresponding “particle-like” field distributions, with bounded singularities of the associated physical fields. These can be obtained in a straightforward algebraic way and exhibit nontrivial collective dynamics simulating physical interactions.
Realization of Center Symmetry in Two Adjoint Flavor Large-N Yang-Mills
Catterall, Simon; /Syracuse U.; Galvez, Richard; /Syracuse U.; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept.
2010-08-26
We report on the results of numerical simulations of SU(N) lattice Yang Mills with two flavors of (light) Wilson fermion in the adjoint representation. We analytically and numerically address the question of center symmetry realization on lattices with {Lambda} sites in each direction in the large-N limit. We show, by a weak coupling calculation that, for massless fermions, center symmetry realization is independent of {Lambda}, and is unbroken. Then, we extend our result by conducting simulations at non zero mass and finite gauge coupling. Our results indicate that center symmetry is intact for a range of fermion mass in the vicinity of the critical line on lattices of volume 2{sup 4}. This observation makes it possible to compute infinite volume physical observables using small volume simulations in the limit N {yields} {infinity}, with possible applications to the determination of the conformal window in gauge theories with adjoint fermions.
Regge meets collinear in strongly-coupled $\\mathcal{N} = 4$ super Yang-Mills
Sprenger, Martin
2016-01-01
We revisit the calculation of the six-gluon remainder function in planar $\\mathcal{N} = 4$ super Yang-Mills theory from the strong coupling TBA in the multi-Regge limit and identify an infinite set of kinematically subleading terms. These new terms can be compared to the strong coupling limit of the finite-coupling expressions for the impact factor and the BFKL eigenvalue proposed by Basso et al. in arXiv:1407.3766, which were obtained from an analytic continuation of the Wilson loop OPE. After comparing the results order by order in those subleading terms, we show that it is possible to precisely map both formalisms onto each other. A similar calculation can be carried out for the seven-gluon amplitude, the result of which shows that the central emission vertex does not become trivial at strong coupling.
Perturbative quantization of Yang-Mills theory with classical double as gauge algebra
Ruiz, F Ruiz
2015-01-01
Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary.
Integrable Open Spin Chain in Super Yang-Mills and the Plane-wave/SYM duality
Chen, B; Wu, Y S; Chen, Bin; Wang, Xiao-Jun; Wu, Yong-Shi
2004-01-01
We investigate the integrable structures in an N=2 superconfomal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the closed string sector, an integrable structure is inherited from its parent theory, N=4 SYM. For the open string sector, the planar one-loop mixing matrix for gauge invariant holomorphic operators is identified with the Hamiltonian of an integrable SU(3) open spin chain. Using the K-matrix formalism we identify the integrable open-chain boundary conditions that correspond to string boundary conditions. The solutions to the algebraic Bethe ansatz equations (ABAE) with a few impurities are shown to recover the anomalous dimensions that exactly match the spectrum of free open string in the plane-wave background. We also discuss the properties of the solutions of ABAE beyond the BMN regime.
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.)
The five-loop beta function of Yang-Mills theory with fermions
Herzog, F.; Ruijl, B.; Ueda, T.; Vermaseren, J. A. M.; Vogt, A.
2017-02-01
We have computed the five-loop corrections to the scale dependence of the renormalized coupling constant for Quantum Chromodynamics (QCD), its generalization to non-Abelian gauge theories with a simple compact Lie group, and for Quantum Electrodynamics (QED). Our analytical result, obtained using the background field method, infrared rearrangement via a new diagram-by-diagram implementation of the R* operation and the Forcer program for massless four-loop propagators, confirms the QCD and QED results obtained by only one group before. The numerical size of the five-loop corrections is briefly discussed in the standard overline{MS} scheme for QCD with n f flavours and for pure SU( N) Yang-Mills theory. Their effect in QCD is much smaller than the four-loop contributions, even at rather low scales.
Anti-self-dual Yang-Mills equations on noncommutative spacetime
Takasaki, K
2001-01-01
By replacing the ordinary product with the so called $\\star$-product, one can construct an analogue of the anti-self-dual Yang-Mills (ASDYM) equations on the noncommutative $\\bbR^4$. Many properties of the ordinary ASDYM equations turn out to be inherited by the $\\star$-product ASDYM equation. In particular, the twistorial interpretation of the ordinary ASDYM equations can be extended to the noncommutative $\\bbR^4$, from which one can also derive the fundamental strutures for integrability such as a zero-curvature representation, an associated linear system, the Riemann-Hilbert problem, etc. These properties are further preserved under dimensional reduction to the principal chiral field model and Hitchin's Higgs pair equations. However, some structures relying on finite dimensional linear algebra break down in the $\\star$-product analogues.
Integrable open spin chain in super Yang-Mills and the plane-wave/SYM duality
Chen, Bin; Wang, Xiao-Jun; Wu, Yong-Shi
2004-02-01
We investigate the integrable structures in an Script N = 2 superconformal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the closed string sector, an integrable structure is inherited from its parent theory, Script N = 4 SYM. For the open string sector, the planar one-loop mixing matrix for gauge invariant holomorphic scalar operators is identified with the hamiltonian of an integrable SU(3) open spin chain. Using the K-matrix formalism we identify the integrable open-chain boundary conditions that correspond to string boundary conditions. The solutions to the algebraic Bethe ansatz equations (ABAE) with a few impurities are shown to recover the anomalous dimensions that exactly match the spectrum of free open string in the plane-wave background. We also discuss the properties of the solutions of ABAE beyond the BMN regime.
Lattice simulation of a center symmetric three dimensional effective theory for SU(2) Yang-Mills
Smith, Dominik
2010-11-17
We present lattice simulations of a center symmetric dimensionally reduced effective field theory for SU(2) Yang Mills which employ thermal Wilson lines and three-dimensional magnetic fields as fundamental degrees of freedom. The action is composed of a gauge invariant kinetic term, spatial gauge fields and a potential for theWilson line which includes a ''fuzzy'' bag term to generate non-perturbative fluctuations between Z(2) degenerate ground states. The model is studied in the limit where the gauge fields are set to zero as well as the full model with gauge fields. We confirm that, at moderately weak coupling, the ''fuzzy'' bag term leads to eigenvalue repulsion in a finite region above the deconfining phase transition which shrinks in the extreme weak-coupling limit. A non-trivial Z(N) symmetric vacuum arises in the confined phase. The effective potential for the Polyakov loop in the theory with gauge fields is extracted from the simulations including all modes of the loop as well as for cooled configurations where the hard modes have been averaged out. The former is found to exhibit a non-analytic contribution while the latter can be described by a mean-field like ansatz with quadratic and quartic terms, plus a Vandermonde potential which depends upon the location within the phase diagram. Other results include the exact location of the phase boundary in the plane spanned by the coupling parameters, correlation lengths of several operators in the magnetic and electric sectors and the spatial string tension. We also present results from simulations of the full 4D Yang-Mills theory and attempt to make a qualitative comparison to the 3D effective theory. (orig.)
`Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories
Raptis, Ioannis
2007-05-01
Certain pivotal results from various applications of Abstract Differential Geometry (ADG) to gravity and gauge theories are presently collected and used to argue that we already possess a geometrically (pre)quantized, second quantized and manifestly background spacetime manifold independent vacuum Einstein gravitational field dynamics. The arguments carry also mutatis mutandis to the case of free Yang-Mills theories, since from the ADG-theoretic perspective gravity is regarded as another gauge field theory. The powerful algebraico-categorical, sheaf cohomological conceptual and technical machinery of ADG is then employed, based on the fundamental ADG-theoretic conception of a field as a pair ({mathcal{E}},{mathcal{D}}) consisting of a vector sheaf {mathcal{E}} and an algebraic connection {mathcal{D}} acting categorically as a sheaf morphism on {mathcal{E}}'s local sections, to introduce a ‘universal’, because expressly functorial, field quantization scenario coined third quantization. Although third quantization is fully covariant, on intuitive and heuristic grounds alone it formally appears to follow a canonical route; albeit, in a purely algebraic and, in contradistinction to geometric (pre)quantization and (canonical) second quantization, manifestly background geometrical spacetime manifold independent fashion, as befits ADG. All in all, from the ADG-theoretic vantage, vacuum Einstein gravity and free Yang-Mills theories are regarded as external spacetime manifold unconstrained, third quantized, pure gauge field theories. The paper abounds with philosophical smatterings and speculative remarks about the potential import and significance of our results to current and future Quantum Gravity research. A postscript gives a brief account of this author's personal encounters with Rafael Sorkin and his work.
Three-dimensional super Yang-Mills with compressible quark matter
Faedo, Antón F. [Departament de Física Fonamental and Institut de Ciències del Cosmos, Universitat de Barcelona,Martí i Franquès 1, ES-08028, Barcelona (Spain); Kundu, Arnab [Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064 (India); Mateos, David [Departament de Física Fonamental and Institut de Ciències del Cosmos, Universitat de Barcelona,Martí i Franquès 1, ES-08028, Barcelona (Spain); Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluís Companys 23, ES-08010, Barcelona (Spain); Pantelidou, Christiana [Departament de Física Fonamental and Institut de Ciències del Cosmos, Universitat de Barcelona,Martí i Franquès 1, ES-08028, Barcelona (Spain); Tarrío, Javier [Departament de Física Fonamental and Institut de Ciències del Cosmos, Universitat de Barcelona,Martí i Franquès 1, ES-08028, Barcelona (Spain); Université Libre de Bruxelles (ULB) and International Solvay Institutes,Service de Physique Théorique et Mathématique, Campus de la Plaine, CP 231, B-1050, Brussels (Belgium)
2016-03-22
We construct the gravity dual of three-dimensional, SU(N{sub /tiny} {sub c}) super Yang-Mills theory with N{sub /tiny} {sub f} flavors of dynamical quarks in the presence of a non-zero quark density N{sub /tiny} {sub q}. The supergravity solutions include the backreaction of N{sub /tiny} {sub c} color D2-branes and N{sub /tiny} {sub f} flavor D6-branes with N{sub /tiny} {sub q} units of electric flux on their worldvolume. For massless quarks, the solutions depend non-trivially only on the dimensionless combination ρ=N{sub /tiny} {sub c}{sup 2}N{sub /tiny} {sub q}/λ{sup 2}N{sub /tiny} {sub f}{sup 4}, with λ=g{sub /tiny} {sub YM}{sup 2}N{sub /tiny} {sub c} the ’t Hooft coupling, and describe renormalization group flows between the super Yang-Mills theory in the ultraviolet and a non-relativistic theory in the infrared. The latter is dual to a hyperscaling-violating, Lifshitz-like geometry with dynamical and hyperscaling-violating exponents z=5 and θ=1, respectively. If ρ≪1 then at intermediate energies there is also an approximate AdS{sub 4} region, dual to a conformal Chern-Simons-Matter theory, in which the flow exhibits quasi-conformal dynamics. At zero temperature we compute the chemical potential and the equation of state and extract the speed of sound. At low temperature we compute the entropy density and extract the number of low-energy degrees of freedom. For quarks of non-zero mass M{sub /tiny} {sub q} the physics depends non-trivially on ρ and M{sub /tiny} {sub q}N{sub /tiny} {sub c}/λN{sub /tiny} {sub f}.
Gravitational, lensing, and stability properties of Bose-Einstein condensate dark matter halos
Harko, Tiberiu
2015-01-01
The possibility that dark matter, whose existence is inferred from the study of the galactic rotation curves and from the mass deficit in galaxy clusters, can be in a form of a Bose-Einstein condensate has recently been extensively investigated. In the present work, we consider a detailed analysis of the astrophysical properties of the Bose-Einstein condensate dark matter halos that could provide clear observational signatures and help discriminate between different dark matter models. In the Bose-Einstein condensation model dark matter can be described as a non-relativistic, gravitationally confined Newtonian gas, whose density and pressure are related by a polytropic equation of state with index $n=1$. The mass and the gravitational properties of the condensate halos are obtained in a systematic form, including the mean logarithmic slopes of the density and of the tangential velocity. Furthermore, the lensing properties of the condensate dark matter are also investigated in detail. In particular, a general ...
Dark matter as the Bose-Einstein condensation in loop quantum cosmology
Atazadeh, K.; Mousavi, M. [Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of); Darabi, F. [Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of)
2016-06-15
We consider the FLRW universe in a loop quantum cosmological model filled with radiation, baryonic matter (with negligible pressure), dark energy, and dark matter. The dark matter sector is supposed to be of Bose-Einstein condensate type. The Bose-Einstein condensation process in a cosmological context by supposing it as an approximate first-order phase transition, has already been studied in the literature. Here, we study the evolution of the physical quantities related to the early universe description such as the energy density, temperature, and scale factor of the universe, before, during, and after the condensation process. We also consider in detail the evolution era of the universe in a mixed normal-condensate dark matter phase. The behavior and time evolution of the condensate dark matter fraction is also analyzed. (orig.)
On the irrelevance of the Gribov issue in N=4 Super Yang-Mills in the Landau gauge
Capri, M A L; Justo, I F; Palhares, L F; Sorella, S P
2014-01-01
The issue of the Gribov copies is discussed in Euclidean N=4 Super Yang-Mills theory quantized in the Landau gauge. As a consequence of the absence of a renormalization group invariant scale, it turns out that it is not possible to attach a dynamical meaning to the Gribov parameter. This implies that, in N=4 Super Yang-Mills, there is no need for the restriction of the domain of integration in the functional integral to the Gribov region, and no non-perturbative dynamical scale is generated. This result is in agreement with the absence of a confining phase observed from the Coulomb behaviour of the Wilson loop evaluated through the AdS/CFT correspondence. The non-renormalization theorem of the gluon-ghost-antighost vertex of the Landau gauge is also explicitly checked till three loops.
Leble, Sergey
2011-01-01
One-dimensional Yang-Mills-Nahm models are considered from algebrogeometric points of view. A quasiclassical quantization of the models based on path integral and its zeta function representation in terms of a Green function diagonal for a heat equation with an elliptic potential is considered. The Green function diagonal and, hence, zeta function and its derivative are expressed via solutions of Hermit equation and, alternatively, by means of Its-Matveev formalism in terms of Riemann teta-functions. For the Nahm model, which field is represented via elliptic (lemniscate) integral by construction, one-loop quantum corrections to action are evaluated as the zeta function derivative in zero point in terms of a hyperelliptic integral. The alternative expression should help to link the representations and continue investigation of the Yang-Mills-Nahm models. Keywords: Nahm model, one-loop quantum corrections, zeta function, elliptic potential, hyperelliptic integral, Its-Matveev formula. MSC numbers: 81Q30, 35J10...
Dyon of a non-Abelian Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions
Navarro-Lerida, Francisco
2013-01-01
Dyons of an SO(5) Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions are presented. These solitons carry both magnetic and electric global charges. The SO(3)xSO(2) solutions are constructed numerically. These are Chern-Simons dyons, differing radically from Julia-Zee dyons. The Chern-Simons densities employed are defined in 3+1 dimensions, and they are the first two of the 'new' Chern-Simons densities introduced recently. They are defined in terms of both Yang-Mills fields and a 5-component isomultiplet Higgs. When two or more of these Chern-Simons densities are present in the Lagrangian, solutions with vanishing electric charge but nonvanishing electrostatic potential may exist.
Balakin, Alexander B; Zayats, Alexei E
2016-01-01
Alternative theories of gravity and their solutions are of considerable importance as at some fundamental level the world can reveal new features. Indeed, it is suspected that the gravitational field might be nonminimally coupled to the other fields at scales not yet probed, bringing into the forefront nonminimally coupled theories. In this mode, we consider a nonminimal Einstein-Yang-Mills theory with a cosmological constant. Imposing spherical symmetry and staticity for the spacetime and a magnetic Wu-Yang ansatz for the Yang-Mills field, we find expressions for the solutions of the theory. Further imposing constraints on the nonminimal parameters we find a family of exact solutions of the theory depending on five parameters, namely, two nonminimal parameters, the cosmological constant, the magnetic charge, and the mass. These solutions represent magnetic monopoles and black holes in magnetic monopoles with de Sitter, Minkowskian, and anti-de Sitter asymptotics, depending on the sign and value of the cosmol...
Genesis of electroweak and dark matter scales from a bilinear scalar condensate
Kubo, Jisuke
2015-01-01
The condensation of scalar bilinear in a classically scale invariant strongly interacting hidden sector is used to generate electroweak scale, where the excitation of the condensate is identified as dark matter. We formulate an effective theory for the condensation of scalar bilinear and find in the self-consistent mean field approximation that the dark matter mass is of $O(1)$ TeV with the spin-independent elastic cross section off the nucleon slightly below the LUX upper bound.
${\\cal N}=4$ Supersymmetric Yang-Mills Theory on Orbifold-$T^4\\/{\\bf Z}_$2 Higher Rank Case
Jinzenji, M; Jinzenji, Masao; Sasaki, Toru
2001-01-01
We derive the partition function of ${\\cal N}=4$ supersymmetric Yang-Mills theory on orbifold-$T^4/{\\bf Z}_2$ for SU(N). We generalize our previous work for SU(2) to the SU(N) case. These partition functions can be factorized into product of bulk contribution of quotient space $T^4/{\\bf Z}_2$ and of blow-up formula including $A_{N-1}$ theta functions with level N.
Non-perturbative renormalization of the energy-momentum tensor in SU(3) Yang-Mills theory
Giusti, Leonardo
2014-01-01
We present a strategy for a non-perturbative determination of the finite renormalization constants of the energy-momentum tensor in the SU(3) Yang-Mills theory. The computation is performed by imposing on the lattice suitable Ward Identites at finite temperature in presence of shifted boundary conditions. We show accurate preliminary numerical data for values of the bare coupling g_0^2 ranging for 0 to 1.
Narita, Makoto [Department of Mathematics, National Taiwan University, 1, Sec. 4, Roosevelt Rd., Taipei 106, Taiwan (China)
2006-12-21
We discuss the strong cosmic censorship conjecture for cosmological spacetimes in the Einstein-Yang-Mills-dilaton system. Locally rotational symmetric Bianchi I spacetimes are considered. We show local and global existence theorems for the system. Asymptotic behaviour for the spacetimes is also investigated. The curvature invariant is blowup at the initial singularities and the spacetimes are future geodesic complete. Thus, the strong cosmic censorship conjecture for the spacetimes holds.
Saleem, U; Hassan, M; Siddiq, M [Department of Physics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590 (Pakistan)
2007-05-11
We present an infinite number of non-local continuity equations of noncommutative (anti) self-dual Yang-Mills (nc-(A)SDYM) equations using the induction method of Brezin et al (1979 Phys. Lett. B 82 442) and relate it to the Lax pair and the parametric Baecklund transformation of the system. From the Lax pair, we derive a binary Darboux transformation to generate solutions of the nc-(A)SDYM equations.
Effect of Self-Interaction on Vacuum Energy for Yang-Mills System in Kaluza-Klein Theory
Shiraishi, Kiyoshi
2015-01-01
We calculate the vacuum energy for Yang--Mills (YM) system in the background space-time $M^4 \\times S^3$, taking the effect of self-interaction of the YM fields into account. The compactification scale obtained by Candelas--Weinberg mechanism becomes large if the YM coupling is large. The case with an extra space $S^3/Z_2$ is also considered, and it is shown that the vacuum associated with broken gauge symmetry is unstable.
Meng, K.; Li, J.
2016-10-01
We construct a new static black hole solution of Gauss-Bonnet massive gravity coupled to Maxwell and Yang-Mills fields in five dimensions. We calculate the thermodynamical quantities of the black hole and check the first law of black hole thermodynamics. Thermal stability of the black hole is explored in the context of both canonical and grand canonical ensembles. By identifying the cosmological constant as the pressure of the gravitational system, we study the phase transitions of the black hole.
Lattice Study of the Extent of the Conformal Window in Two-Color Yang-Mills Theory
Voronov, Gennady
2013-01-01
We perform a lattice calculation of the Schr\\"odinger functional running coupling in SU(2) Yang-Mills theory with six massless Wilson fermions in the fundamental representation. The aim of this work is to determine whether the above theory has an infrared fixed point. Due to sensitivity of the $SF$ renormalized coupling to the tuning of the fermion bare mass we were unable to reliably extract the running coupling for stronger bare couplings.
String theory and the dark glueball problem
Halverson, James; Nelson, Brent D.; Ruehle, Fabian
2017-02-01
We study cosmological constraints on dark pure Yang-Mills sectors. Dark glueballs are overproduced for large regions of ultraviolet parameter space. The problem may be alleviated in two ways: via a large preferential reheating into the visible sector, motivating certain inflation or modulus decay models, or via decays into axions or moduli, which are strongly constrained by nucleosynthesis and Δ Neff bounds. String models frequently have multiple hidden Yang-Mills sectors, which are subject to even stronger constraints due to the existence of multiple dark glueballs.
String Theory and the Dark Glueball Problem
Halverson, James; Ruehle, Fabian
2016-01-01
We study cosmological constraints on dark pure Yang-Mills sectors. Dark glueballs are overproduced for large regions of ultraviolet parameter space. The problem may be alleviated in two ways: via a large preferential reheating into the visible sector, motivating certain inflation or modulus decay models, or via decays into axions or moduli, which are strongly constrained by nucleosynthesis and $\\Delta N_{\\text{eff}}$ bounds. String models frequently have multiple hidden Yang-Mills sectors, which are subject to even stronger constraints due to the existence of multiple dark glueballs.
Suhendro I.
2008-01-01
Full Text Available In this work, we attempt at constructing a comprehensive four-dimensional unified field theory of gravity, electromagnetism, and the non-Abelian Yang-Mills gauge field in which the gravitational, electromagnetic, and material spin fields are unified as intrinsic geometric objects of the space-time manifold $S_4$ via the connection, with the generalized non-Abelian Yang-Mills gauge field appearing in particular as a sub-field of the geometrized electromagnetic interaction.
Schabinger, Robert M
2011-01-01
In this paper we discuss in detail computational methods and new results for one-loop virtual corrections to N = 4 super Yang-Mills scattering amplitudes calculated to all orders in epsilon, the dimensional regularization parameter. It is often the case that one-loop gauge theory computations are carried out to order epsilon^0, since higher order in epsilon contributions vanish in the small epsilon limit. We will show, however, that the higher order contributions are actually quite useful. In the context of maximally supersymmetric Yang-Mills, we consider two examples in detail to illustrate our point. First we will concentrate on computations with gluonic external states and argue that N = 4 supersymmetry implies a simple relation between all-orders-in-epsilon one-loop N = 4 super Yang-Mills amplitudes and the first and second stringy corrections to analogous tree-level superstring amplitudes. For our second example we will derive a new result for the all-orders-in-epsilon one-loop superamplitude for planar ...
SU(3) Yang-Mills Hamiltonian in the flux-tube gauge: Strong coupling expansion and glueball dynamics
Pavel, Hans-Peter
2016-01-01
It is shown that the formulation of the SU(3) Yang-Mills quantum Hamiltonian in the "flux-tube gauge" A_{a1}=0 for all a=1,2,4,5,6,7 and A_{a2}=0 for all a=5,7 allows for a systematic and practical strong coupling expansion of the Hamiltonian in \\lambda\\equiv g^{-2/3}, equivalent to an expansion in the number of spatial derivatives. Introducing an infinite spatial lattice with box length a, the "free part" is the sum of Hamiltonians of Yang-Mills quantum mechanics of constant fields for each box, and the "interaction terms" contain higher and higher number of spatial derivatives connecting different boxes. The Faddeev-Popov operator, its determinant and inverse, are rather simple, but show a highly non-trivial periodic structure of six Gribov-horizons separating six Weyl-chambers. The energy eigensystem of the gauge reduced Hamiltonian of SU(3) Yang-Mills mechanics of spatially constant fields can be calculated in principle with arbitrary high precision using the orthonormal basis of all solutions of the corr...
Non-Gaussianity of the topological charge distribution in $\\mathrm{SU}(3)$ Yang-Mills theory
Cè, Marco
2015-01-01
In Yang-Mills theory, the cumulants of the na\\"ive lattice discretization of the topological charge evolved with the Yang-Mills gradient flow coincide, in the continuum limit, with those of the universal definition. We sketch in these proceedings the main points of the proof. By implementing the gradient-flow definition in numerical simulations, we report the results of a precise computation of the second and the fourth cumulant of the $\\mathrm{SU}(3)$ Yang-Mills theory topological charge distribution, in order to measure the deviation from Gaussianity. A range of high-statistics Monte Carlo simulations with different lattice volumes and spacings is used to extrapolate the results to the continuum limit with confidence by keeping finite-volume effects negligible with respect to the statistical errors. Our best result for the topological susceptibility is $t_0^2\\chi=6.67(7)\\times 10^{-4}$, while for the ratio between the fourth and the second cumulant we obtain $R=0.233(45)$.
Drechsler, Wolfgang; Havas, Peter; Rosenblum, Arnold
1984-02-01
In two recent papers, the general form of the laws of motion for point particles which are multipole sources of the classical coupled Yang-Mills-Higgs fields was determined by Havas, and for the special case of monopole singularities of a Yang-Mills field an iteration procedure was developed by Drechsler and Rosenblum to obtain the equations of motion of mass points, i.e., the laws of motion including the explicit form of the fields of all interacting particles. In this paper we give a detailed derivation of the laws of motion of monopole-dipole singularities of the coupled Yang-Mills-Higgs fields for point particles with mass and spin, following a procedure first applied by Mathisson and developed by Havas. To obtain the equations of motion, a systematic approximation method is developed in the following paper for the solution of the nonlinear field equations and determination of the fields entering the laws of motion found here to any given order in the coupling constant g.
Bergner, G. [Universität Bern, Institut für Theoretische Physik,Länggasse, 3012 Bern (Switzerland); Langelage, J.; Philipsen, O. [Institut für Theoretische Physik, Goethe-Universität Frankfurt,Max-von-Laue-Str. 1, 60438 Frankfurt am Main (Germany)
2015-11-04
We consider a three-dimensional effective theory of Polyakov lines derived previously from lattice Yang-Mills theory and QCD by means of a resummed strong coupling expansion. The effective theory is useful for investigations of the phase structure, with a sign problem mild enough to allow simulations also at finite density. In this work we present a numerical method to determine improved values for the effective couplings directly from correlators of 4d Yang-Mills theory. For values of the gauge coupling up to the vicinity of the phase transition, the dominant short range effective coupling are well described by their corresponding strong coupling series. We provide numerical results also for the longer range interactions, Polyakov lines in higher representations as well as four-point interactions, and discuss the growing significance of non-local contributions as the lattice gets finer. Within this approach the critical Yang-Mills coupling β{sub c} is reproduced to better than one percent from a one-coupling effective theory on N{sub τ}=4 lattices while up to five couplings are needed on N{sub τ}=8 for the same accuracy.
Plane-wave matrix theory from N=4 super-Yang-Mills on RxS{sup 3}
Kim, Nakwoo E-mail: kim@aei.mpg.de; Klose, Thomas E-mail: thklose@aei.mpg.de; Plefka, Jan E-mail: plefka@aei.mpg.de
2003-11-03
Recently a mass deformation of the maximally supersymmetric Yang-Mills quantum mechanics has been constructed from the supermembrane action in eleven-dimensional plane-wave backgrounds. However, the origin of this plane-wave matrix theory in terms of a compactification of a higher-dimensional super-Yang-Mills model has remained obscure. In this paper we study the Kaluza-Klein reduction of D=4, N=4 super-Yang-Mills theory on a round three-sphere, and demonstrate that the plane-wave matrix theory arises through a consistent truncation to the lowest lying modes. We further explore the relation between the dilatation operator of the conformal field theory and the Hamiltonian of the quantum mechanics through perturbative calculations up to two-loop order. In particular, we find that the one-loop anomalous dimensions of pure scalar operators are completely captured by the plane-wave matrix theory. At two-loop level this property ceases to exist.
Keller, Jochen
2008-01-01
The thesis is considering aspects of SU(2) Yang-Mills thermodynamics in its deconfining high-temperature phase. We calculate the two-point correlation function of the energy density of the photon in a thermalized gas, at first in the conventional U(1) gauge theory, followed by a calculation, where the photon is identified with the massless gauge mode in deconfining SU(2) Yang-Mills thermodynamics. Apart from the fact, that this calculation is interesting from a technical point of view, we can consider several aspects of phenomenological relevance. Since we interpret the two-point correlator of energy density as a measure for the energy transfer, and thus for the electromagnetic interaction of microscopic objects, such as atoms immersed into a photon gas, we are able to give an explanation for the unexpected stability of cold, innergalactic clouds consisting of atomic hydrogen. Subsequently, we evaluate the spatial string tension in deconfining SU(2) Yang-Mills thermodynamics, which can be regarded as measure ...
N=4 super-Yang-Mills in LHC superspace. Part I: Classical and quantum theory
Chicherin, Dmitry
2017-02-10
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.
The Yang-Mills Vacuum Wave Functional in 2+1 Dimensions
Krug, Sebastian
2014-01-01
We investigate Yang-Mills theory in 2+1 dimensions in the Schroedinger representation. The Schroedinger picture is interesting because it is well suited to explore properties of the vacuum state in the non-perturbative regime. Yet, not much analytical work has been done on this subject, and even the topic of perturbation theory in the Schroedinger representation is not well developed, especially in the case of gauge theories. In a paper by Hatfield [Phys.Lett.B 147, 435 (1984)] the vacuum wave functional for SU(2) theory was computed to O(e). In the non-perturbative regime, the most sophisticated analytical approach has been developed by Karabali et al. in a series of papers (see [Nucl.Phys.B 824, 387 (2010)] and references therein). This thesis aims to put perturbation theory in the Schroedinger representation on more solid ground by computing the vacuum wave functional for a general gauge group SU$(N_c)$ up to O$(e^2)$, utilizing modifications of these two methods. This is important since it provides us wit...
Running couplings in equivariantly gauge-fixed SU(N) Yang--Mills theories
Golterman, M F L; Golterman, Maarten; Shamir, Yigal
2006-01-01
In equivariantly gauge-fixed SU(N) Yang--Mills theories, the gauge symmetry is only partially fixed, leaving a subgroup $H\\subset SU(N)$ unfixed. Such theories avoid Neuberger's nogo theorem if the subgroup $H$ contains at least the Cartan subgroup $U(1)^{N-1}$, and they are thus non-perturbatively well defined if regulated on a finite lattice. We calculate the one-loop beta function for the coupling $\\tilde{g}^2=\\xi g^2$, where $g$ is the gauge coupling and $\\xi$ is the gauge parameter, for a class of subgroups including the cases that $H=U(1)^{N-1}$ or $H=SU(M)\\times SU(N-M)\\times U(1)$. The coupling $\\tilde{g}$ represents the strength of the interaction of the gauge degrees of freedom associated with the coset $SU(N)/H$. We find that $\\tilde{g}$, like $g$, is asymptotically free. We solve the renormalization-group equations for the running of the couplings $g$ and $\\tilde{g}$, and find that dimensional transmutation takes place also for the coupling $\\tilde{g}$, generating a scale $\\tilde{\\Lambda}$ which c...
The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
Bern, Z; Kosower, D A; Roiban, R; Spradlin, M; Vergu, C; Volovich, A
2008-01-01
We give a representation of the parity-even part of the planar two-loop six-gluon MHV amplitude of N=4 super-Yang-Mills theory, in terms of loop-momentum integrals with simple dual conformal properties. We evaluate the integrals numerically in order to test directly the ABDK/BDS all-loop ansatz for planar MHV amplitudes. We find that the ansatz requires an additive remainder function, in accord with previous indications from strong-coupling and Regge limits. The planar six-gluon amplitude can also be compared with the hexagonal Wilson loop computed by Drummond, Henn, Korchemsky and Sokatchev in arXiv:0803.1466 [hep-th]. After accounting for differing singularities and other constants independent of the kinematics, we find that the Wilson loop and MHV-amplitude remainders are identical, to within our numerical precision. This result provides non-trivial confirmation of a proposed n-point equivalence between Wilson loops and planar MHV amplitudes, and suggests that an additional mechanism besides dual conformal...
Three-Loop Yang-Mills $\\beta$-Function via the Covariant Background Field Method
Boernsen, J P; Ven, Anton E. M. van de
2003-01-01
We demonstrate the effectivity of the covariant background field method by means of an explicit calculation of the 3-loop beta-function for a pure Yang-Mills theory. To maintain manifest background invariance throughout our calculation, we stay in coordinate space and treat the background field non-perturbatively. In this way the presence of a background field does not increase the number of vertices and leads to a relatively small number of vacuum graphs in the effective action. Restricting to a covariantly constant background field in Fock-Schwinger gauge permits explicit expansion of all quantum field propagators in powers of the field strength only. Hence, Feynman graphs are at most logarithmically divergent. At 2-loop order only a single Feynman graph without subdivergences needs to be calculated. At 3-loop order 24 graphs remain. Insisting on manifest background gauge invariance at all stages of a calculation is thus shown to be a major labor saving device. All calculations were performed with Mathemati...
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 ...
The Gauge String Solution of the D>=3 Yang-Mills Loop Equations
Dubin, A Yu
2001-01-01
I adapt the Gauge String, representing the strong coupling (SC) expansion in the continuous D>=3 Yang-Mills theory (YM_{D}) with a sufficiently large bare coupling constant \\lambda>\\lambda_{cr} and a fixed ultraviolet cut off \\Lambda, to the analysis of the regularized Wilson's loop-averages. When generalized to describe the fat (rather than infinitely thin) flux-tubes, the pattern of thus modified U(N) Gauge String is proved to be consistent with the chain of the judiciously regularized U(N) Loop equations. In particular, we reveal the dimensional reduction YM_{D}=>YM_{2}, taking place in the extreme SC limit \\lambda=>\\infty, and compare it with the implications of the AdS/CFT correspondence conjecture. On the other hand, for the loop-averages associated to the sufficiently large minimal areas, the proposed stringy pattern is supposed to be in the one infrared universality class (provided the loops are without zig-zag backtrackings) with the novel implementation of the noncritical D-dimensional Nambu-Goto st...
Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
Kamata, Norihiko
2016-01-01
We study several types of tree-level improvement in the Yang-Mills gradient flow method in order to reduce the lattice discretization errors in line with a reference [Fodor et al., arXiv:1406.0827]. The tree-level $\\mathcal{O}(a^2)$ improvement can be achieved in a simple manner, where an appropriate weighted average is computed between two definitions of the action density $\\langle E(t)\\rangle$ measured at every flow time $t$. We further develop the idea of achieving the tree-level $\\mathcal{O}(a^4)$ improvement. For testing our proposal, we present numerical results of $\\langle E(t)\\rangle$ obtained on gauge configurations generated with the Wilson and Iwasaki gauge actions at three lattice spacings ($a\\approx 0.1, 0.07$ and 0.05 fm). Our results show that tree-level improved flows significantly eliminate the discretization corrections in the relatively small-$t$ regime. To demonstrate the feasibility of our proposal, we also study the scaling behavior of the dimensionless combinations of the $\\Lambda_{\\ove...
A Tree-level Unitary Noncompact Weyl-Einstein-Yang-Mills Model
Dengiz, Suat
2016-01-01
We construct and study perturbative unitarity (i.e., ghost and tachyon analysis) of a $3+1$-dimensional noncompact Weyl-Einstein-Yang-Mills model. The model describes a local noncompact Weyl's scale plus $SU(N)$ phase invariant Higgs-like field, conformally coupled to a generic Weyl-invariant dynamical background. Here, the Higgs-like sector generates the Weyl's conformal invariance of system. The action does not admit any dimensionful parameter and genuine presence of de Sitter vacuum spontaneously breaks the noncompact gauge symmetry in an analogous manner to the Standard Model Higgs mechanism. As to flat spacetime, the dimensionful parameter is generated within the dimensional transmutation in quantum field theories, and thus the symmetry is radiatively broken through the one-loop Effective Coleman-Weinberg potential. We show that the mere expectation of reducing to Einstein's gravity in the broken phases forbids anti-de Sitter space to be its stable constant curvature vacuum. The model is unitary in de Si...
N = 4 super-Yang-Mills in LHC superspace part I: classical and quantum theory
Chicherin, Dmitry; Sokatchev, Emery
2017-02-01
We present a formulation of the maximally supersymmetric N = 4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N =4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the N = 4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the N = 2 gauge and hypermultiplet matter theories. In the twin paper arXiv:1601.06804 we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the N = 4 stress-tensor supermultiplet.
Deconfinement transition in SU(2) Yang-Mills theory: a two-loop study
Reinosa, U; Tissier, M; Wschebor, N
2014-01-01
In a recent work we have proposed a perturbative approach for the study of the phase transition of pure Yang-Mills theories at finite temperature. This is based on a simple massive extension of background field methods in the Landau-DeWitt gauge, where the gluon mass term is related to the existence of Gribov ambiguities. We have shown that a one-loop calculation of the background field effective potential describes well the phase structure of the SU(2) and SU(3) theories. Here, we present the calculation of the next-to-leading order contribution in perturbation theory for the SU(2) case. In particular, we compute the background field effective potential at two-loop order and the corresponding Polyakov loop, a gauge invariant order parameter of the transition, at one-loop order. We show that the two-loop correction brings the critical temperature closer to its actual value as compared to the previous one-loop result. We also compute the thermodynamic pressure as a function of the temperature and show that two...
Doubled Lattice Chern-Simons-Yang-Mills Theories with Discrete Gauge Group
Caspar, Stephan; Olesen, Therkel Z; Vlasii, Nadiia D; Wiese, Uwe-Jens
2016-01-01
We construct doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group $G$ in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov-Bohm pha...
The decay of unstable strings in SU(2) Yang-Mills theory
Pepé, M
2009-01-01
We investigate the stability of strings connecting charges Q in the representation {2Q+1} of SU(2) Yang-Mills theory in (2+1) dimensions. While the fundamental {2}-string between two charges Q=1/2 is unbreakable and stable, the string connecting static charges transforming under any other representation Q>1/2 is unstable and decays. A charge Q=1 can be completely screened by gluons and so the adjoint {3}-string ultimately breaks. A charge Q=3/2 can be only partially screened to a fundamental charge Q=1/2. Thus, stretching a {4}-string beyond a critical length, it decays into the stable {2}-string by gluon pair creation. The complete breaking of a {5}-string happens in two steps, it first decays into a {3}-string and then breaks completely. A phenomenological constituent gluon model provides a good quantitative description of the energy of the screened charges at the ends of an unstable string.
Picard-Fuchs Ordinary Differential Systems in $N = 2$ Supersymmetric Yang-Mills Theories
Ohta, Y
1999-01-01
In general, Picard-Fuchs systems in N=2 supersymmetric Yang-Mills theories are realized as a set of simultaneous partial differential equations. However, if the QCD scale parameter is used as unique independent variable instead of moduli, the resulting Picard-Fuchs systems are represented by a single ordinary differential equation (ODE) whose order coincides with the total number of independent periods. This paper discusses some properties of these Picard-Fuchs ODEs. In contrast with the usual Picard-Fuchs systems written in terms of moduli derivatives, there exists a Wronskian for this ordinary differential system and this Wronskian produces a new relation among periods, moduli and QCD scale parameter, which in the case of SU(2) is reminiscent of scaling relation of prepotential. On the other hand, in the case of the SU(3) theory, there are two kinds of ordinary differential equations, one of which is the equation directly constructed from periods and the other is derived from the SU(3) Picard-Fuchs equation...