Three-algebras inN=5, 6 superconformal Chern-Simons theories: Representations and relations

Abstract

In this work we present 3-algebraic constructions and representations for three-dimensional $\mathcal{N}=5$ supersymmetric Chern-Simons theories, and show how they relate to theories with additional supersymmetries. The $\mathcal{N}=5$ structure constants give theories with $\mathrm{Sp}(2N)\ifmmode\times\else\texttimes\fi{}\mathrm{SO}(M)$ gauge symmetry, as well as more exotic symmetries known from gauged supergravity. We find explicit lifts from $\mathcal{N}=6$ to 8, and $\mathcal{N}=5$ to 6 and 8, for appropriate gauge groups.