ABJ(M) and fractional M2's with fractional M2 charge

Abstract

Recently Aharony, Bergman and Jafferis (ABJ) have argued that a 3d U(N+M) k × U(N) -k Chern-Simons gauge theory may have a vacuum with N= 6 supersymmetry only if M ≤k and if a certain period of the B-field in a IIA background is quantized. We use a braneology argument to argue that N= 3 supersymmetry may be preserved under the weaker condition that 2Nk ≥ M(M-k) with no restriction on the B-field. IIB brane cartoons and 11d supergravity solutions corresponding to N= 3 vacua that do not preserve N= 6 supersymmetry are argued to represent cascading gauge theories, generalizing the N= 2 Seiberg duality conjectured by Giveon and Kutasov. While as usual the M2-brane charge runs as a result of the twisted Bianchi identity for *G 4, the M5-brane charge running relies on the fact that it wraps a torsion homology cycle. © 2009 SISSA.