Connecting Polyakov loops to the thermodynamics of SU(Nc) gauge theories using the gauge-string duality

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 similar to -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 (nonperturbative) temperature range between T-c and 3T(c).