The Morphology of N=6 Chern-Simons Theory

TL;DR

This paper systematically analyzes the representation theory of N=6 Chern-Simons (ABJM) theory, providing detailed character formulas, tensor product decompositions, and applying these to compute corrections to the Hagedorn temperature.

Contribution

It introduces a comprehensive enumeration of irreducible representations and tensor products for ABJM theory, and applies these to calculate physical temperature corrections.

Findings

Character formulas for all irreducible representations up to four letters.

Tensor product decompositions for up to four singletons.

Leading correction to the Hagedorn temperature in weakly-coupled ABJM.

Abstract

We tabulate various properties of the language of N=6 Chern-Simons Theory, in the sense of Polyakov. Specifically we enumerate and compute character formulas for all syllables of up to four letters, i.e. all irreducible representations of OSp(6|4) built from up to four fundamental fields of the ABJM theory. We also present all tensor product decompositions for up to four singletons and list the (cyclically invariant) four-letter words, which correspond to single-trace operators of length four. As an application of these results we use the two-loop dilatation operator to compute the leading correction to the Hagedorn temperature of the weakly-coupled planar ABJM theory on R \times S^2.