Membranes on an Orbifold

TL;DR

This paper explores the interpretation of a recently discovered N=8 supersymmetric Chern-Simons theory with SO(4) gauge symmetry, relating it to membranes in an orbifold and analyzing its moduli space and spectrum.

Contribution

It provides a new interpretation of the N=8 supersymmetric Chern-Simons theory as describing membranes in an orbifold and analyzes the moduli space structure at various levels.

Findings

At levels k=1 and k=2, the moduli space matches super Yang-Mills theory.

For higher levels, the moduli space is a quotient of the classical space.

The massive spectrum relates to the geometry of membranes and the orbifold.

Abstract

We harvest clues to aid with the interpretation of the recently discovered N=8 supersymmetric Chern-Simons theory with SO(4) gauge symmetry. The theory is argued to describe two membranes moving in the orbifold R8/Z2. At level k=1 and k=2, the classical moduli space M coincides with the infra-red moduli space of SO(4) and SO(5) super Yang-Mills theory respectively. For higher Chern-Simons level, the moduli space is a quotient of M. At a generic point in the moduli space, the massive spectrum is proportional to the area of the triangle formed by the two membranes and the orbifold fixed point.