Connecting Polyakov Loops to the Thermodynamics of $SU(N_c)$ Gauge Theories Using the Gauge-String Duality

Abstract

We show that in four-dimensional gauge theories dual to five-dimensional Einstein gravity coupled to a single scalar field in the bulk the derivative of the single heavy quark free energy in the deconfined phase is $d{F}_Q(T)/dT\sim -1/c_s^2(T)$, where $c_s(T)$ is the speed of sound. This general result provides a direct link between the softest point in the equation of state of strongly-coupled plasmas and the deconfinement phase transition described by the expectation value of the Polyakov loop. We give an explicit example of a gravity dual with black hole solutions that can reproduce the lattice results for the expectation value of the Polyakov loop and the thermodynamics of SU(3) Yang-Mills theory in the (non-perturbative) temperature range between $T_c$ and $3T_c$.

13 pages, 2 figures, minor corrections, version published in PRD

References in corpus (37)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Linear Confinement and AdS/QCD
• Equation of state and QCD transition at finite temperature
• Viscosity Bound and Causality Violation
• Exploring improved holographic theories for QCD: Part II
• Hadronic Spectra and Light-Front Wavefunctions in Holographic QCD
• Light-Front Dynamics and AdS/QCD Correspondence: The Pion Form Factor in the Space- and Time-Like Regions
• On the Strongly-Interacting Low-Viscosity Matter Created in Relativistic Nuclear Collisions
• Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory
• Light-Front Holography: A First Approximation to QCD
• Thermodynamics of the QCD plasma and the large-N limit
• Beyond eta/s = 1/4pi
• Mimicking the QCD equation of state with a dual black hole
• Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics
• Deconfinement and Gluon Plasma Dynamics in Improved Holographic QCD
• Quantum corrections to eta/s
• Toward a Systematic Holographic QCD: A Braneless Approach
• Renormalized Polyakov loops in many representations
• The Spatial String Tension, Thermal Phase Transition, and AdS/QCD
• Shear Viscosity from Gauss-Bonnet Gravity with a Dilaton Coupling
• Effective Theory of Wilson Lines and Deconfinement
• Debye screening in strongly coupled N=4 supersymmetric Yang-Mills plasma
• A bound on the speed of sound from holography
• Fuzzy Bags and Wilson Lines
• The pressure of the SU(N) lattice gauge theory at large-N
• Thermal Width of the ${\rm Y}$ at Large t' Hooft Coupling
• Some Thermodynamic Aspects of Pure Glue, Fuzzy Bags and Gauge/String Duality
• Holography and the speed of sound at high temperatures
• Renormalized Polyakov Loop in the Deconfined Phase of SU(N) Gauge Theory and Gauge/String Duality
• Gluon Condensate, Wilson Loops and Gauge/String Duality
• Trace Anomaly, Thermal Power Corrections and Dimension Two condensates in the deconfined phase
• The Heavy Quark Potential as a Function of Shear Viscosity at Strong Coupling
• Zero Point Energy of Renormalized Wilson Loops
• Spatial string tension of finite temperature QCD matter in gauge/gravity duality
• The Spatial String Tension in the Deconfined Phase of SU(N) Gauge Theory and Gauge/String Duality
• Universal relations of transport coefficients from holography
• The Powers of Deconfinement

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