Classification of linearly compact simple N=6 3-algebras

TL;DR

This paper classifies linearly compact simple N=6 3-algebras, which are relevant in supersymmetric gauge theories, by relating them to specific Lie superalgebras with certain gradings and symmetries.

Contribution

It provides the first classification of linearly compact simple N=6 3-algebras, extending previous work on N=8 cases, using a novel correspondence with Lie superalgebras.

Findings

Classified linearly compact simple N=6 3-algebras.

Established correspondence with Lie superalgebras with Z-grading.

Brief discussion on N=5 3-algebras.

Abstract

$N\leq 8$ 3-algebras have recently appeared in N-supersymmetric 3-dimensional Chern-Simons gauge theories. In our previous paper we classified linearly compact simple N = 8 n-algebras for any $n \geq 3$. In the present paper we classify linearly compact simple N = 6 3-algebras, using their correspondence with simple linearly compact Lie superalgebras with a consistent short Z-grading, endowed with a graded conjugation. We also briefly discuss N = 5 3-algebras.