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

TL;DR

This paper establishes a theoretical link between the Polyakov loop, thermodynamics, and the speed of sound in strongly-coupled gauge theories using gauge-string duality, supported by a gravity dual model matching lattice results.

Contribution

It derives a universal relation connecting the derivative of the heavy quark free energy to the speed of sound and provides a gravity dual model that reproduces lattice thermodynamics of SU(3) Yang-Mills theory.

Findings

The derivative of heavy quark free energy is proportional to -1/c_s^2(T).

The gravity dual model matches lattice results for Polyakov loop and thermodynamics.

The relation links the softest point in the equation of state to deconfinement.

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 $dF_{Q}(T)/dT \sim -1/c_s^2(T)$, 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 $3T_c$.