Bagger-Lambert theory on an orbifold and its relation to Chern-Simons-matter theories

TL;DR

This paper explores how orbifold reductions of the Bagger-Lambert M2-brane theory relate to Chern-Simons-matter theories, showing a pathway to N=6 supersymmetric models with specific gauge groups and levels.

Contribution

It introduces an orbifolding procedure for the Bagger-Lambert theory and demonstrates its connection to known Chern-Simons-matter theories with supersymmetry.

Findings

Derived a reduction from M2-brane theory to Chern-Simons theories

Connected orbifolded Bagger-Lambert theory to ABJM models

Showed how to obtain N=6 supersymmetric theories with specific gauge groups

Abstract

We consider how to take an orbifold reduction for the multiple M2-brane theory recently proposed by Bagger and Lambert, and discuss its relation to Chern-Simons theories. Starting from the infinite dimensional 3-algebra realized as the Nambu bracket on a 3-torus, we first suggest an orbifolding prescription for various fields. Then we introduce a second truncation, which effectively reduces the internal space to a 2-torus. Eventually one obtains a large-N limit of Chern-Simons gauge theories coupled to matter fields. We consider an abelian orbifold C^4/Z_n, and illustrate how one can arrive at the N=6 supersymmetric theories with gauge groups U(N) x U(N) and Chern-Simons levels (k,-k), as recently constructed by Aharony, Bergman, Jafferis and Maldacena.