The Polyakov loop of an operator in the anti-symmetric representation in N=4 SYM theory on spacial R^3 is calculated, to leading order in 1/N and at large 't Hooft coupling, by solving the saddle point equations of the corresponding quantum impurity model. Agreement is found with previous results from the supergravity dual, which is given by a D5-brane in an asymptotically AdS_5 x S^5 black brane background. It is shown that the azimuth angle, at which the dual D5-brane wraps the S^5, is related to the spectral asymmetry angle in the spectral density associated with the Green's function of the impurity fermions. Much of the calculation also applies to the Polyakov loop on spacial S^3 or H^3.
Aspects of d=4, N=4 superconformal U(N) gauge theory are studied at finite temperature. Utilizing dual description of large $N$ and strong coupling limit via Type IIB string theory compactification on Schwarzschild anti-de Sitter spacetime, we study correlations of Wilson-Polyakov loops and heavy quark potential thereof. We find that the heavy quark potential is Coulomb-like and has a finite range, as expected for gauge theory in high temperature, deconfinement phase. The potential exhibits finite temperature scaling consistent with underlying conformal invariance. We also study isolated heavy…
Closed string field theory is constructed by stochastically quantizing a matrix model for Polyakov loops that describes phases of a large N gauge theory at finite temperature. Coherent states in this string field theory describes winding string condensation which has been expected to cause a topology change from thermal AdS geometry to AdS-Schwarzschild black hole geometry. D-branes in this closed string field theory is also discussed. Slightly extended version of a talk given at CosPA 2007, Nov.13-15, Taipei, Taiwan.
We study holographic probes dual to heavy quark impurities interpolating between fundamental and symmetric/antisymmetric tensor representations in strongly coupled N=4 supersymmetric gauge theory. These correspond to non-conformal D3- and D5-brane probe embeddings in AdS_5 x S^5 exhibiting flows on their world-volumes. By examining the asymptotic regimes of the embeddings and the one-point function of static fields sourced by the boundary impurity, we conclude that the D5-brane embedding describes the screening of fundamental quarks in the UV into an antisymmetric source in the IR, whilst the …
We study effective lattice actions describing the Polyakov loop dynamics originating from finite-temperature Yang-Mills theory. Starting with a strong-coupling expansion the effective action is obtained as a series of Z(3)-invariant operators involving higher and higher powers of the Polyakov loop, each with its own coupling. Truncating to a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved. To this end we employ a modified mean field approximation and Monte Carlo simulations based on a novel cluster algorithm. We find excellent agreement of both …
We present a new formulation of the theory of an arbitrary quantum impurity in an antiferromagnet, using the O(3) non-linear sigma model. We obtain the low temperature expansion for the impurity spin susceptibilities of antiferromagnets with magnetic long-range order in the ground state. We also consider the bulk quantum phase transition in d=2 to the gapped paramagnet (d is the spatial dimension): the impurity is described solely by a topological Berry phase term which is an exactly marginal perturbation to the critical theory. The physical properties of the quantum impurity near criticality …
It has recently been shown that the low energy dynamics of the large $N$ gauge theory on $S^3$ at finite temperature reduces to a one-matrix model, where the matrix is given by the holonomy of the gauge field around the Euclidean time direction compactified on a circle. On the other hand, there is a prescription for constructing a closed string field theory in the temporal gauge from a given one-matrix model via loop equations. I identify the closed string field theory in the temporal gauge constructed from the above matrix model as effective closed string field theory that describes the propa…
We study two Polyakov loop correlators in large $N$ limit of ${\cal{N}}=4$ super Yang-Mills theory at finite temperature using the AdS-Schwarzschild black hole. In the case that one of the two loops is of the anti-symmetric representation, we use D5-branes to evaluate them. The phase structure of these correlators is also examined. A previous result, derived in hep-th/9803135 and hep-th/9803137, is realized as a limiting case.}
A large-n approximation to the S=1 antiferromagnetic chain, using the symmetric tensor representation and its conjugate, is developed to order 1/n in order to calculate the magnon wave-function and to study the effect of modifying the exchange coupling from J to J' on a single link. It is shown that a magnon boundstate exists below the Haldane gap for arbitrarily small negative J'-J but only above a certain critical value of J'-J for positive values. In the former case the binding energy vanishes as the square of (J-J').
A study of the center symmetric phase of SU(2) Yang Mills theory is presented. Realization of the center symmetry is shown to result from non-perturbative gauge fixing. Dictated by the center symmetry, this phase exhibits already at the perturbative level confinement like properties. The analysis is performed by investigating the dynamics of the Polyakov loops. The ultralocality of these degrees of freedom implies significant changes in the vacuum structure of the theory. General properties of the confined phase and of the transition to the deconfined phase are discussed. Perturbation theory b…
Based on the strong coupling expansion we obtain effective 3-dimensional models for the Polyakov loop in finite-temperature G_2 gluodynamics. The Svetitsky-Jaffe conjecture relates the resulting continuous spin models with G_2 gluodynamics near phase transition points. In the present work we analyse the effective theory in leading order with the help of a generalised mean field approximation and with detailed Monte-Carlo simulations. In addition we derive a Potts-type discrete spin model by restricting the characters of the Polyakov loops to the three extremal points of the fundamental domain …
We study the Polyakov loop correlator in the weak coupling expansion and show how the perturbative series re-exponentiates into singlet and adjoint contributions. We calculate the order $g^7$ correction to the Polyakov loop correlator in the short distance limit. We show how the singlet and adjoint free energies arising from the re-exponentiation formula of the Polyakov loop correlator are related to the gauge invariant singlet and octet free energies that can be defined in pNRQCD, namely we find that the two definitions agree at leading order in the multipole expansion, but differ at first or…
In this paper we explore some of the features of a heavy quark-antiquark pair at finite temperature using a five-dimensional framework nowadays known as AdS/QCD. We shall show that the resulting behavior is consistent with our qualitative expectations of thermal gauge theory. Some of the results are in good agreement with the lattice data that provides additional evidence for the validity of the proposed model.
We consider pure Yang Mills theory on the four torus. A set of non-Abelian transition functions is presented which encompass all instanton sectors. It is argued that these transition functions are a convenient starting point for gauge fixing. In particular, we give an extended Abelian projection with respect to the Polyakov loop, where $A_0$ is independent of time and in the Cartan subalgebra. In the non-perturbative sectors such gauge fixings are necessarily singular. These singularities can be restricted to Dirac strings joining monopole and anti-monopole like ``defects''.
We study effective Polyakov loop models for SU(N) Yang-Mills theories at finite temperature. In particular effective models for SU(3) YM with an additional adjoint Polyakov loop potential are considered. The rich phase structure including a center and anti-center directed phase is reproduced with an effective model utilizing the inverse Monte-Carlo method. The demon method as a possibility to obtain the effective models' couplings is compared to the method of Schwinger-Dyson equations. Thermalization effects of microcanonical and canonical demon method are analyzed. Finally the elaborate canon…
Recently the Schur index of ${\cal N}=4$ SYM was evaluated in closed form to all orders including exponential corrections in the large $N$ expansion and for fixed finite $N$. This was achieved by identifying the matrix model which calculates the index with the partition function of a system of free fermions on a circle. The index can be enriched by the inclusion of loop operators and the case of Wilson loops is particularly easy, as it amounts to inserting extra characters into the matrix model. The Fermi-gas approach is applied here to this problem, the formalism is explored and explicit resu…
We compute the vacuum polarization energies (VPE) of solitons in a self-dual impurity model in which the soliton profiles take the shape of a separated kink-antikink pair. Classically the soliton energies are invariant under the change of a continuous parameter that can be interpreted as the kink-antikink separation. This is not the case for the VPE so that quantum effects decide on the energetically most favorable separation. The considered configurations are classically stable so that its quantum fluctuations have only real frequency eigenvalues. Hence, in contrast to the kink-antikink confi…
We find a family of (half) self-dual impurity models such that the self-dual (BPS) sector is exactly solvable, for any spatial distribution of the impurity, both in the topologically trivial case and for kink (or antikink) configurations. This allows us to derive the metric on the corresponding one-dimensional moduli space in an analytical form. Also the generalized translational symmetry is found in an exact form. This symmetry provides a motion on moduli space which transforms one BPS solution into another. Finally, we analyse exactly how vibrational properties (spectral modes) of the BPS so…
A self-dual generalization of the lump-impurity system is introduced. This model possesses lump-antilump-like pairs as static solutions of the pertinent Bogomolny equations. This allows for a moduli space approximation analysis of the BPS solutions which are identified as lump-antilump configurations. Some geometrical properties of the resulting moduli are analyzed. In addition, it is argued that, this type of impurity models can be interpreted as a limit of certain non-impurity theories.
Confinement in SU($N$) gauge theory is due to the linear potential between colored objects. At short distances, the linear contribution could be considered as the quadratic correction to the leading Coulomb term. Recent lattice data show that such quadratic corrections also appear in the deconfined phase, in both the thermal quantities and the Polyakov loop. These contributions are studied systematically employing the gauge/string duality. "Confinement" in ${\mathcal N}=4$ SU($N$) Super Yang-Mills (SYM) theory could be achieved kinematically when the theory is defined on a compact space manifo…
We construct exact t Hooft-Polyakov monopole solutions in a non-Hermitian field theory with local non-Abelian SU(2) gauge symmetry and a modified antilinear CPT symmetry. The solutions are obtained in a fourfold Bogomolny-Prasad-Sommerfield scaling limit giving rise to two different types of monopole masses that saturate the lower energy bound. These two masses only coincide in the Hermitian limit and in the limit in which the symmetry breaking vacuum tends to the trivial symmetry preserving vacuum. In the two theories corresponding to the two known Dyson maps these two masses are exchanged, u…
We discuss how to extract renormalized from bare Polyakov loops in SU(N) lattice gauge theories at nonzero temperature in four spacetime dimensions. Single loops in an irreducible representation are multiplicatively renormalized without mixing, through a renormalization constant which depends upon both representation and temperature. The values of renormalized loops in the four lowest representations of SU(3) were measured numerically on small, coarse lattices. We find that in magnitude, condensates for the sextet and octet loops are approximately the square of the triplet loop. This agrees wi…
We show the existence of strong (anti)correlations between the topological hot spots and the local values of the trace of the Polyakov loop in $2+1$ flavor QCD with physical quark mass, in the vicinity of the crossover transition corresponding to the simultaneous restoration of chiral symmetry and deconfinement. Using sophisticated lattice techniques, we have carefully identified the topological hot spots using quark zero modes and measured the short-distance fluctuations of the Polyakov loop about them, showing how the latter is repelled quite strongly around the peak of the zero modes. Thoug…
Spectral sums of the Dirac-Wilson operator and their relation to the Polyakov loop are thoroughly investigated. The approach by Gattringer is generalized to mode sums which reconstruct the Polyakov loop locally. This opens the possibility to study the mode sum approximation to the Polyakov loop correlator. The approach is re-derived for the ab initio continuum formulation of Yang-Mills theories, and the convergence of the mode sum is studied in detail. The mode sums are then explicitly calculated for the Schwinger model and SU(2) gauge theory in a homogeneous background field. Using SU(2) latt…
Dual representations are constructed for non-abelian lattice spin models with U(N) and SU(N) symmetry groups, for all N and in any dimension. These models are usually related to the effective models describing the interaction between Polyakov loops in the strong coupled QCD. The original spin degrees of freedom are explicitly integrated out and a dual theory appears to be a local theory for the dual integer-valued variables. The construction is performed for the partition function and for the most general correlation function. The latter include the two-point function corresponding to quark-an…
