# The large $N$ phase diagram of ${\cal N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multiplet

## TL;DR

This paper analyzes the phase diagram of large N ${
m extbf{N=2}}$ supersymmetric Chern-Simons theories with fundamental matter, revealing multiple topological phases and conformal points through exact effective potential calculations.

## Contribution

It provides the first detailed large N phase diagram of ${
m extbf{N=2}}$ supersymmetric Chern-Simons theories with fundamental matter, including exact potential and phase transition analysis.

## Key findings

- Four topological phases separated by first and second order transitions
- Identification of conformal points with specific IR dynamics
- Exact effective potential at finite temperature

## Abstract

We study the theory of a single fundamental fermion and boson coupled to Chern-Simons theory at leading order in the large $N$ limit. Utilizing recent progress in understanding the Higgsed phase in Chern-Simons-Matter theories, we compute the quantum effective potential that is exact to all orders in the 't Hooft coupling for the lightest scalar operator of this theory at finite temperature. Specializing to the zero temperature limit we use this potential to determine the phase diagram of the large $N$ ${\cal N}=2$ supersymmetric theory with this field content. This intricate two dimensional phase diagram has four topological phases that are separated by lines of first and second order phase transitions and includes special conformal points at which the infrared dynamics is governed by Chern-Simons theory coupled respectively to free bosons, Gross-Neveu fermions, and to a theory of Wilson-Fisher bosons plus free fermions. We also describe the vacuum structure of the most general ${\cal N} = 1$ supersymmetric theory with one fundamental boson and one fundamental fermion coupled to an $SU(N)$ Chern-Simons gauge field, at arbitrary values of the 't Hooft coupling.