The Coulomb Branch of Gauge Theory from Rotating Branes

TL;DR

This paper explores the supergravity description of the Coulomb branch of ${ m extbf{N}}=4$ super Yang-Mills theory using rotating black D3-branes, revealing thermodynamic properties and effective string dynamics at finite temperature.

Contribution

It introduces a supergravity framework for rotating black D3-branes to analyze the Coulomb branch at finite temperature and chemical potential, highlighting new geometric and thermodynamic insights.

Findings

Rotating black D3-branes describe the lifted vacuum degeneracy.

Preferred brane distributions correspond to minima of free energy.

Low energy excitations relate to an effective string theory.

Abstract

At zero temperature the Coulomb Branch of ${\cal N}=4$ super Yang-Mills theory is described in supergravity by multi-center solutions with D3-brane charge. At finite temperature and chemical potential the vacuum degeneracy is lifted, and minima of the free energy are shown to have a supergravity description as rotating black D3-branes. In the extreme limit these solutions single out preferred points on the moduli space that can be interpreted as simple distributions of branes --- for instance, a uniformly charged planar disc. We exploit this geometrical representation to study the thermodynamics of rotating black D3-branes. The low energy excitations of the system appear to be governed by an effective string theory which is related to the singularity in spacetime.