Heavy Quark Potential at Finite Temperature Using the Holographic Correspondence

TL;DR

This paper refines the calculation of the heavy quark potential at finite temperature in N=4 SYM using holography, revealing a smooth, non-zero potential with an imaginary part and a power-law decay at large distances.

Contribution

It introduces an analytic continuation and a different renormalization scheme to obtain a smooth, non-zero potential with an imaginary component, improving upon previous results.

Findings

Potential is non-zero and smooth without a kink.

Potential has a non-zero imaginary part for large separations.

Large-distance potential decays as 1/r^4, not exponentially.

Abstract

We revisit the calculation of a heavy quark potential in N =4 supersymmetric Yang-Mills theory at finite temperature using the AdS/CFT correspondence. As is widely known, the potential calculated in the pioneering works of Rey et al. and Brandhuber et al. is zero for separation distances r between the quark and the anti-quark above a certain critical separation, at which the potential has a kink. We point out that by analytically continuing the string configurations into the complex plane, and using a slightly different renormalization subtraction, one obtains a smooth non-zero (negative definite) potential without a kink. The obtained potential also has a non-zero imaginary (absorptive) part for separations r > r_c = 0.870/\pi T . At large separations r the real part of the potential does not exhibit the exponential Debye falloff expected from perturbation theory and instead falls off as a power law, proportional to 1/r^4 for r > r_0 = 2.702 / \pi T.