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.
Categories: hep-th cond-mat.str-el