The Free Energy of N=4 Super-Yang-Mills and the AdS/CFT Correspondence

TL;DR

This paper compares weak and strong coupling calculations of the free energy in N=4 super-Yang-Mills theory, highlighting curvature effects and testing the AdS/CFT correspondence at high temperature.

Contribution

It provides the first detailed comparison of weak and strong coupling free energy expressions for N=4 SYM on curved backgrounds, including curvature corrections.

Findings

Weak coupling results valid for general ultrastatic backgrounds.

Strong coupling results obtained via AdS/CFT for constant curvature spaces.

Curvature corrections significantly affect free energy calculations.

Abstract

We compute the high-temperature limit of the free energy for four-dimensional N=4 supersymmetric SU(N_c) Yang-Mills theory. At weak coupling we do so for a general ultrastatic background spacetime, and in the presence of slowly-varying background gauge fields. Using Maldacena's conjectured duality, we calculate the strong-coupling large-N_c expression for the special case that the three-space has constant curvature. We compare the two results paying particular attention to curvature corrections to the leading order expressions.