  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.

High Energy Physics - Theory