  It has previously been conjectured that the theory of free fundamental
scalars minimally coupled to a Chern Simons gauge field is dual to the theory
of critical fundamental fermions minimally coupled to a level rank dual Chern
Simons gauge field. In this paper we study RG flows away from these two fixed
points by turning on relevant operators. In the t' Hooft large N limit we
compute the thermal partition along each of these flows and find a map of
parameters under which the two partition functions agree exactly with each
other all the way from the UV to the IR. We conjecture that the bosonic and
fermionic RG flows are dual to each other under this map of parameters. Our
flows can be tuned to end at the gauged critical scalar theory and gauged free
fermionic theories respectively. Assuming the validity of our conjecture, this
tuned trajectory may be viewed as RG flow from the gauged theory of free bosons
to the gauged theory of free fermions.
