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

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 μ-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.

37 pages, 4 figures; v2: minor corrections, references added; v3: minor corrections, to appear in JHEP

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Cited by in corpus (8)

• Gregory-Laflamme as the confinement/deconfinement transition in holographic QCD
• More on the New Large $D$ Limit of Matrix Models
• Phases of a two dimensional large N gauge theory on a torus
• Nuclear states and spectra in holographic QCD
• A Scaling Relation, $Z_m$-type Deconfinement Phases and Imaginary Chemical Potentials in Finite Temperature Large-$N$ Gauge Theories
• Complex Langevin Method on Rotating Matrix Quantum Mechanics at Thermal Equilibrium
• D-dependence of gap between critical temperatures in one-dimensional gauge theories
• Randomized Wilson loops, reduced models and the large D expansion