Two loop integrability for Chern-Simons theories with N=6 supersymmetry

Understand

We consider two-loop anomalous dimensions for fermionic operators in the ABJM model and the ABJ model.

• We find the appropriate Hamiltonian and show that it is consistent with a previously predicted Bethe ansatz for the ABJM model.
• The difference between the ABJ and ABJM models is invisible at the two-loop level by cancelation of parity violating diagrams.
• We then construct a Hamiltonian for the full two-loop OSp(6|4) spin chain by first constructing the Hamiltonian for an SL(2|1) subgroup, and then lifting to OSp(6|4).