Anomalous dimensions in non-supersymmetric bifundamental Chern-Simons theories

Abstract

Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points [1]. 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 × 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 (formula presented), it is possible to calculate physical quantities to all orders in λ in a (formula presented) theory, in the limit M ≪ N, in an M/N expansion. To illustrate this, we calculate the anomalous dimension of the primary operator tr to first order in M/N, to all orders in (formula presented) but with (formula presented). We also comment on possible bosonization dualities for bifundamental Chern-Simons theories.