A limit on the ABJ model

Understand

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.