The Coulomb Branch of Gauge Theory from Rotating Branes

TL;DR

This work develops a holographic framework for the Coulomb branch of N=4 SYM by identifying moduli-space vacua with multi-center D3-brane geometries. It extends the AdS/CFT correspondence to finite temperature and chemical potential via rotating D3-branes and analyzes extremal rotation to reveal concrete brane distributions (disks, ellipsoids, shells). The thermodynamics of these rotating branes highlights regimes where low-energy excitations are governed by an effective string theory and links spacetime singularities to RG flows in the boundary theory. Overall, the paper connects bulk geometric distributions to Coulomb-branch physics, providing insights into IR dynamics, phase structure, and the emergence of string-like behavior in the gauge 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.