A limit on the ABJ model

Abstract

There is a large amount of evidence that the ABJM model is integrable in the planar limit. Less clear is whether or not the ABJ model is integrable. Here we investigate a limit of the ABJ model in the weak coupling limit where one 't Hooft parameter is much greater than the other. At the 4 loop level in the SU(2) x SU(2) sector the anomalous dimensions of single trace operators map to two Heisenberg spin chains with nearest neighbor interactions with an overall coefficient that is a function of one of the 't Hooft parameters. We conjecture the form of this function and show that is consistent with observations about the ABJ model concerning unitarity and parity, including strong coupling statements.