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

TL;DR

This paper analyzes two-loop anomalous dimensions in N=6 supersymmetric Chern-Simons theories, confirming integrability via Hamiltonian construction and Bethe ansatz consistency for ABJM and ABJ models.

Contribution

It constructs the full two-loop Hamiltonian for the OSp(6|4) spin chain, extending previous results and demonstrating integrability in these models.

Findings

Hamiltonian consistent with Bethe ansatz for ABJM

ABJ and ABJM models indistinguishable at two loops

Constructed Hamiltonian for full OSp(6|4) spin chain

Abstract

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). We show that this Hamiltonian is consistent with the Hamiltonian found for the fermionic operators.