  It has been conjectured that Chern-Simons (CS) gauged `regular' bosons in the
fundamental representation are `level-rank' dual to CS gauged critical fermions
also in the fundamental representation. Generic relevant deformations of these
conformal field theories lead to one of two distinct massive phases. In
previous work, the large $N$ thermal free energy for the bosonic theory in the
unHiggsed phase has been demonstrated to match the corresponding fermionic
results under duality. In this note we evaluate the large $N$ thermal free
energy of the bosonic theory in the Higgsed phase and demonstrate that our
results, again, perfectly match the predictions of duality. Our computation is
performed in a unitary gauge by integrating out the physical excitations of the
theory - i.e. W bosons - at all orders in the 't Hooft coupling. Our results
allow us to construct an exact quantum effective potential for ${\bar \phi}
\phi$, the lightest gauge invariant scalar operator in the theory. In the zero
temperature limit this exact Landau-Ginzburg potential is non-analytic at
${\bar \phi \phi}=0$. The extrema of this effective potential at positive
${\bar \phi}\phi$ solve the gap equations in the Higgsed phase while the
extrema at negative ${\bar \phi} \phi$ solve the gap equations in the unHiggsed
phase. Our effective potential is bounded from below only for a certain range
of $x_6$ (the parameter that governs sextic interactions of $\phi$). This
observation suggests that the regular boson theory has a stable vacuum only
when $x_6$ lies in this range.
