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 λ= N/k fixed. The solution exists up to |λ|=1 for a fixed value of chemical potential. We study the system beyond |λ|=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 |λ|=1.
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