Classification of N=6 superconformal theories of ABJM type

TL;DR

This paper classifies all gauge groups and matter representations that yield N=6 superconformal theories of ABJM type, extending the understanding of supersymmetry enhancement in these models.

Contribution

It provides a comprehensive classification of gauge groups and matter representations compatible with N=6 supersymmetry in ABJM-like theories, including a proof of algebra classification.

Findings

Allowed gauge groups are SU(n) x U(1), Sp(n) x U(1), SU(n) x SU(n), and SU(n) x SU(m) x U(1).

Matter fields are restricted to (bi)fundamentals.

Complete classification of three algebras by Bagger and Lambert is reaffirmed.

Abstract

Studying the supersymmetry enhancement mechanism of Aharony, Bergman, Jafferis and Maldacena, we find a simple condition on the gauge group generators for the matter fields. We analyze all possible compact Lie groups and their representations. The only allowed gauge groups leading to the manifest N=6 supersymmetry are, up to discrete quotients, SU(n) x U(1), Sp(n) x U(1), SU(n) x SU(n), and SU(n) x SU(m) x U(1) with possibly additional U(1)'s. Matter representations are restricted to be the (bi)fundamentals. As a byproduct we obtain another proof of the complete classification of the three algebras considered by Bagger and Lambert.