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arXiv · 0910.1261

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

Jorge Noronha
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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 $3T_c$.

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BibTeXRIS

Jorge Noronha. 2010-03-04. Connecting Polyakov Loops to the Thermodynamics of $SU(N_c)$ Gauge Theories Using the Gauge-String Duality. https://doi.org/10.1103/physrevd.81.045011

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