  We present a conjecture for the leading $1/N$ anomalous dimension of the
scalar primary operator in $U(N)_k$ Chern-Simons theories coupled to a single
fundamental field, to all orders in the t'Hooft coupling $\lambda=\frac{N}{k}$.
Following this we compute the anomalous dimension of the scalar in a Regular
Bosonic theory perturbatively at two-loop order and demonstrate that matches
exactly with the result predicted by our conjecture. We also show that our
proposed expression for the anomalous dimension is consistent with all other
existing two-loop perturbative results, which constrain its form at both weak
and strong coupling thanks to the bosonization duality. Furthermore, our
conjecture passes a novel non-trivial all loop test which provides a strong
evidence for its consistency.
