Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion

TL;DR

This paper investigates the thermodynamics of large N gauge theories with chemical potentials using a 1/D expansion, revealing phase structures, scalar condensation, and stability properties across different dimensions.

Contribution

It introduces a 1/D expansion approach to study phase structures and scalar condensation in large N gauge theories with chemical potentials, extending understanding to higher dimensions.

Findings

Identifies three phases in the - plane.

Demonstrates scalar condensation and dynamical mass generation.

Shows stability of the system at large chemical potentials in the D  limit.

Abstract

In order to understand thermodynamical properties of N D-branes with chemical potentials associated with R-symmetry charges, we study a one dimensional large N gauge theory (bosonic BFSS type model) as a first step. This model is obtained through a dimensional reduction of a 1+D dimensional SU(N) Yang-Mills theory and we use a 1/D expansion to investigate the phase structure. We find three phases in the \mu-T plane. We also show that all the adjoint scalars condense at large D and obtain a mass dynamically. This dynamical mass protects our model from the usual perturbative instability of massless scalars in a non-zero chemical potential. We find that the system is at least meta-stable for arbitrary large values of the chemical potentials in D \to \infty limit. We also explore the existence of similar condensation in higher dimensional gauge theories in a high temperature limit. In 2 and 3 dimensions, the condensation always happens as in one dimensional case. On the other hand, if the dimension is higher than 4, there is a critical chemical potential and the condensation happens only if the chemical potentials are below it.