The Heavy Quark Free Energy in QCD and in Gauge Theories with Gravity Duals

TL;DR

This paper compares the behavior of the Polyakov loop and heavy quark free energy in strongly-coupled gauge theories with gravity duals and lattice QCD, revealing differences in their approach to high-temperature limits.

Contribution

It demonstrates that in theories with gravity duals, the Polyakov loop approaches its asymptotic value from below, contrasting with lattice results where it approaches from above, and discusses implications for the interpretation of heavy quark free energy.

Findings

Polyakov loop approaches its asymptotic value from below in gravity dual theories.

Lattice results show the Polyakov loop approaches from above.

The renormalized heavy quark free energy does not behave as a true thermodynamic free energy.

Abstract

We show that the Polyakov loop approaches its asymptotic value at high temperatures {\it from below} in any strongly-coupled gauge theory at large $N_c$ with a dual supergravity description. In these theories the Polyakov loop can be used to define a quantity that behaves as a free energy of a heavy quark in the medium. This should be compared to the recent lattice results in pure glue SU(3) theory at high temperatures where the Polyakov loop approaches its non-interacting limit {\it from above}. We show that the "heavy quark free energy" obtained from the renormalized loop computed on the lattice does not behave as a true thermodynamic free energy. We conjecture that this should always be the case in asymptotically free gauge theories.