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

Thermodynamics of large N SYM theories with chemical potentials associated with R-symmetry charges must be interesting, since they will be duals of rotating/charged black holes, which have rich phase structures, e.g. black hole/black ring transitions and/or black hole/hairy black hole transitions. However these gauge theories usually involve perturbatively massless adjoint scalars and it is difficult to consider the chemical potentials, since they cause perturbative instabilities. In order to investigate this problem, 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.) I will demonstrate that we can overcome the chemical potential problem by using a 1/D expansion and show the phase structure of this model. I will also mention the application to higher dimensional gauge theories.