Free energy of N=4 super Yang-Mills in Higgs phase and non-extremal D3-brane interactions

TL;DR

This paper analyzes the free energy of N=4 super Yang-Mills theory in the Higgs phase at strong coupling, comparing low and high temperature regimes, and incorporates string corrections to supergravity predictions.

Contribution

It provides a detailed comparison of free energy structures at strong and weak coupling in the Higgs phase, including string correction effects.

Findings

Similar free energy structures at strong and weak coupling in low-temperature regime.

Predicted strong coupling terms at high temperature match weak-coupling results.

String corrections introduce (N g^2_{YM})^{-3/2} modifications to free energy.

Abstract

We study the free energy of \N=4 super Yang-Mills theory in the Higgs phase with a mass scale M corresponding to non-zero v.e.v. of the scalar fields. At zero temperature this theory describes a system of parallel separated extremal D3-branes. Non-zero temperature corresponds to non-extremality in supergravity description. We interpret the supergravity interaction potential between a non-extremal D3-brane and a D3-brane probe as contribution of massive states to the free energy of N --> infinity SYM theory at strong 't Hooft coupling (N g^2_{YM} >> 1). Both low (M >> T) and high (T >> M) temperature regimes are considered. For low temperature we find that the structure of terms that appear in the free energy at strong and weak coupling is the same. The analysis of the high-temperature regime depends on a careful identification of the scalar field v.e.v. in terms of the distance between branes in the supergravity description and again predicts strong coupling terms similar to those found in the weak-coupling \N=4 SYM theory. We consider also the corrections to the strong coupling results by taking into account the leading \a'^3 R^4 string contribution to the supergravity effective action. This gives rise to the (N g^2_{YM})^{-3/2} corrections in the coefficient functions of 't Hooft coupling which multiply different terms in free energy.