Chern-Simons-Fermion Vector Model with Chemical Potential

TL;DR

This paper provides an exact solution for SU(N) Chern-Simons-fermion theories with chemical potential in the large N,k limit, revealing a phase transition at a critical coupling value.

Contribution

It offers the first exact large N solution of Chern-Simons-fermion models with chemical potential, including analysis beyond the critical coupling.

Findings

Solution exists up to |7|=1 for fixed chemical potential

System becomes unstable and undergoes a phase transition at |7|=1

Inclusion of U(N) gauge group and holonomy affects stability analysis

Abstract

We study SU(N) level k Chern-Simons theories coupling to a fundamental fermion with chemical potential for U(1) flavor symmetry. We solve this system exactly in the 't Hooft limit, N,k\to\infty with \lambda = N/k fixed. The solution exists up to |\lambda|=1 for a fixed value of chemical potential. We study the system beyond |\lambda|=1 by considering U(N) gauge group and taking the diagonal U(1) holonomy into account. The result suggests the system becomes unstable and a phase transition happens at |\lambda|=1.