The Bethe ansatz for superconformal Chern-Simons

TL;DR

This paper demonstrates the integrability of a three-dimensional superconformal Chern-Simons theory by deriving Bethe equations that determine anomalous dimensions of scalar operators, revealing deep algebraic structures.

Contribution

It introduces a set of Bethe equations for the full superconformal group OSp(2,2|6) in this theory, extending integrability methods to a new class of models.

Findings

Two-loop mixing matrix matches an integrable SU(4) spin chain

Derived Bethe equations for anomalous dimensions

Proposed Bethe equations for the full superconformal symmetry

Abstract

We study the anomalous dimensions for scalar operators for a three-dimensional Chern-Simons theory recently proposed in arXiv:0806.1218. We show that the mixing matrix at two-loop order is that for an integrable Hamiltonian of an SU(4) spin chain with sites alternating between the fundamental and the anti-fundamental representations. We find a set of Bethe equations from which the anomalous dimensions can be determined and give a proposal for the Bethe equations to the full superconformal group of OSp(2,2|6).