Anomalous dimensions in non-supersymmetric bifundamental Chern-Simons theories

作者：Gurucharan V^*; Prakash Shiroman

来源：The Journal of High Energy Physics, 2014, 2014(9): 009.

DOI：10.1007/JHEP09(2014)009

• Field Theories in Lower Dimensions
• Chern-Simons Theories
• 1/N Expansion
• AdS-CFT Correspondence

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) x 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 = N/k, it is possible to calculate physical quantities to all orders in lambda in a U(M)(kM) x U(N)(kN) theory, in the limit M << N, in an M/N expansion. To illustrate this, we calculate the anomalous dimension of the primary operator tr (psi) over bar psi, to first order in M/N, to all orders in lambda(M) = N/k(M), but with lambda(N) = N/k(N) = 0. We also comment on possible bosonization dualities for bifundamental Chern-Simons theories.

• 出版日期2014-9-1