scholarly journals $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills thermodynamics to order λ2

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Qianqian Du ◽  
Michael Strickland ◽  
Ubaid Tantary
Keyword(s):  
Strong Coupling ◽  
Finite Temperature ◽  
Weak Coupling ◽  
Chemical Potential ◽  
Entropy Density ◽  
Thermal Mass ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Debye Mass ◽  
Infrared Divergences

Abstract We calculate the resummed perturbative free energy of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills in four spacetime dimensions (SYM4,4) through second order in the ’t Hooft coupling λ at finite temperature and zero chemical potential. Our final result is ultraviolet finite and all infrared divergences generated at three-loop level are canceled by summing over SYM4,4 ring diagrams. Non-analytic terms at $$ \mathcal{O} $$ O (λ3/2) and $$ \mathcal{O} $$ O (λ2 log λ) are generated by dressing the A0 and scalar propagators. The gauge-field Debye mass mD and the scalar thermal mass MD are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of SYM4,4 to $$ \mathcal{O} $$ O (λ2). We compare our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Padé approximant that interpolates between the weak-coupling result and the large-Nc strong-coupling result. Our results suggest that the $$ \mathcal{O} $$ O (λ2) weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2.

scholarly journals Scrambling in Yang-Mills

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Robert de Mello Koch ◽  
Eunice Gandote ◽  
Augustine Larweh Mahu
Keyword(s):  
Relaxation Time ◽  
Weak Coupling ◽  
Degrees Of Freedom ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Dilatation Operator ◽  
Super Yang Mills Theory

Abstract Acting on operators with a bare dimension ∆ ∼ N2 the dilatation operator of U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory defines a 2-local Hamiltonian acting on a graph. Degrees of freedom are associated with the vertices of the graph while edges correspond to terms in the Hamiltonian. The graph has p ∼ N vertices. Using this Hamiltonian, we study scrambling and equilibration in the large N Yang-Mills theory. We characterize the typical graph and thus the typical Hamiltonian. For the typical graph, the dynamics leads to scrambling in a time consistent with the fast scrambling conjecture. Further, the system exhibits a notion of equilibration with a relaxation time, at weak coupling, given by t ∼ $$ \frac{\rho }{\lambda } $$ ρ λ with λ the ’t Hooft coupling.

scholarly journals Classical integrability for three-point functions: cognate structure at weak and strong couplings

2016 ◽  
Vol 2016 (10) ◽  
Author(s):  
Yoichi Kazama ◽  
Shota Komatsu ◽  
Takuya Nishimura
Keyword(s):  
Strong Coupling ◽  
Functional Equations ◽  
Weak Coupling ◽  
Sigma Model ◽  
Monodromy Matrix ◽  
Integration Contour ◽  
Universal Logic ◽  
Coupling Analysis ◽  
Yang Mills ◽  
Bootstrap Approach

Abstract In this paper, we develop a new method of computing three-point functions in the SU(2) sector of the $$ \mathcal{N}=4 $$ N = 4 super Yang-Mills theory in the semi-classical regime at weak coupling, which closely parallels the strong coupling analysis. The structure threading two disparate regimes is the so-called monodromy relation, an identity connecting the three-point functions with and without the insertion of the monodromy matrix. We shall show that this relation can be put to use directly for the semi-classical regime, where the dynamics is governed by the classical Landau-Lifshitz sigma model. Specifically, it reduces the problem to a set of functional equations, which can be solved once the analyticity in the spectral parameter space is specified. To determine the analyticity, we develop a new universal logic applicable at both weak and strong couplings. As a result, compact semi-classical formulas are obtained for a general class of three-point functions at weak coupling including the ones whose semi-classical behaviors were not known before. In addition, the new analyticity argument applied to the strong coupling analysis leads to a modification of the integration contour, producing the results consistent with the recent hexagon bootstrap approach. This modification also makes the Frolov-Tseytlin limit perfectly agree with the weak coupling form.

scholarly journals Phase Structures of Strong Coupling Lattice QCD with Overlap Fermions at Finite Temperature and Chemical Potential

2007 ◽  
Vol 22 (07n10) ◽  
pp. 537-546 ◽  
Author(s):  
XIAO-LU YU ◽  
XIANG-QIAN LUO
Keyword(s):  
Lattice Qcd ◽  
Strong Coupling ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Order Approximation ◽  
Tricritical Point ◽  
Chiral Condensate ◽  
Mean Field Approximation ◽  
Lattice Action ◽  
Chiral Phase

Lattice QCD at finite temperature T and chemical potential μ is studied analytically in the strong coupling limit with overlap fermions. We start from the first order approximation of lattice action with generalized overlap (GO) fermions to derive an effective free energy written in terms of chiral condensate as a function of T and μ with the use of mean field approximation. We elucidate the phase structure on the (μ, T) plane and discover the tricritical point separating the first and the second order chiral phase transition. Discussion of the doubling problem and higher order terms are given.

scholarly journals Strong coupling methods in QCD thermodynamics

2021 ◽  
Author(s):  
Owe Philipsen
Keyword(s):  
Monte Carlo ◽  
Strong Coupling ◽  
Chemical Potential ◽  
Yang Mills ◽  
Coupling Methods ◽  
Sign Problem ◽  
Monte Carlo Studies ◽  
Long Time ◽  
Scaling Region ◽  
Strong Coupling Expansions

AbstractFor a long time, strong coupling expansions have not been applied systematically in lattice QCD thermodynamics, in view of the success of numerical Monte Carlo studies. The persistent sign problem at finite baryo-chemical potential, however, has motivated investigations using these methods, either by themselves or combined with numerical evaluations, as a route to finite density physics. This article reviews the strategies, by which a number of qualitative insights have been attained, notably the emergence of the hadron resonance gas or the identification of the onset transition to baryon matter in specific regions of the QCD parameter space. For the simpler case of Yang–Mills theory, the deconfinement transition can be determined quantitatively even in the scaling region, showing possible prospects for continuum physics.

scholarly journals BROWN-RHO SCALING IN THE STRONG COUPLING LATTICE QCD

2008 ◽  
Vol 23 (27n30) ◽  
pp. 2459-2464 ◽  
Author(s):  
A. OHNISHI ◽  
N. KAWAMOTO ◽  
K. MIURA
Keyword(s):  
Lattice Qcd ◽  
Strong Coupling ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Chiral Condensate ◽  
Strong Coupling Limit ◽  
Analytical Expression

We examine the Brown-Rho scaling for meson masses in the strong coupling limit of lattice QCD with one species of staggered fermion. Analytical expression of meson masses is derived at finite temperature and chemical potential. We find that meson masses are approximately proportional to the equilibrium value of the chiral condensate, which evolves as a function of temperature and chemical potential.

scholarly journals Lattice $$ \mathcal{N} $$ = 4 super Yang-Mills at strong coupling

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Simon Catterall ◽  
Joel Giedt ◽  
Goksu Can Toga
Keyword(s):  
Strong Coupling ◽  
Lattice Theory ◽  
Numerical Study ◽  
Lattice Action ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Sign Problem ◽  
Wide Range ◽  
Phase Out ◽  
Sign Problems

Abstract In this paper we present results from numerical simulations of $$ \mathcal{N} $$ N = 4 super Yang-Mills for two color gauge theory over a wide range of ’t Hooft coupling 0 < λ ≤ 30 using a supersymmetric lattice action [1]. Numerical study of this lattice theory has been stymied until recently by both sign problems and the occurrence of lattice artifact phases at strong coupling. We have recently developed a new action that appears capable of solving both problems. The resulting action possesses just SU(2) rather than U(2) gauge symmetry. By explicit computations of the fermion Pfaffian we present evidence that the theory possesses no sign problem and exists in a single phase out to arbitrarily strong coupling. Furthermore, preliminary work shows that the logarithm of the supersymmetric Wilson loop varies as the square root of the ’t Hooft coupling λ for large λ in agreement with holographic predictions.

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