Three-Algebras in N = 5, 6 Superconformal Chern-Simons Theories: Representations and Relations

TL;DR

This paper develops 3-algebraic frameworks for 3D N=5 supersymmetric Chern-Simons theories, revealing their relations to theories with higher supersymmetry and specific gauge groups, including explicit lifts between different N levels.

Contribution

It introduces new 3-algebra constructions for N=5 theories and explores their connections to N=6 and N=8 theories with various gauge symmetries.

Findings

N=5 structure constants lead to Sp(2N) x SO(M) gauge theories.

Explicit lifts from N=6 to 8 and N=5 to 6/8 for certain gauge groups.

Relations to gauged supergravity symmetries.

Abstract

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