  Non-abelian Chern-Simons theories coupled to fermions are known to provide an
interesting class of non-supersymmetric conformal fixed points
\cite{Giombi:2011kc}. These theories, particularly those based on bifundamental
matter, are important because they may provide simple non-supersymmetric
examples of the AdS/CFT correspondence. For instance, it seems natural to
conjecture that $O(N)_{-k}\times O(N)_k$ Chern-Simons theory coupled to
Majorana fermions transforming in a bi-vector representation may be dual to
pure Einstein gravity with a small negative cosmological constant in the
"M-theory" limit where $k=1$ and $N$ is large. While it is extremely difficult
to directly study such bifundamental theories when $k=1$ or even at strong 't
Hooft coupling $\lambda=\frac{N}{k}$, it is possible to calculate physical
quantities to all orders in $\lambda$ in a $U(M)_{k_M} \times U(N)_{k_N}$
theory, in the limit $M \ll N$, in an $M/N$ expansion. To illustrate this, we
calculate the anomalous dimension of the primary operator $\bar{\psi}{\psi}$,
to first order in $M/N$, to all orders in $\lambda_M=\frac{N}{k_M}$, but with
$\lambda_N=\frac{N}{k_N}=0$. We also comment on possible bosonization dualities
for bifundamental Chern-Simons theories.
