Gauge Symmetry and Supersymmetry of Multiple M2-Branes

TL;DR

This paper develops a new maximally supersymmetric three-dimensional gauge theory for multiple M2-branes, incorporating gauge symmetry, conformal invariance, and SO(8) R-symmetry, based on an algebra with a triple product.

Contribution

It introduces a novel gauge theory model for multiple M2-branes utilizing an algebra with a totally antisymmetric triple product, achieving maximal supersymmetry and conformal invariance.

Findings

Constructed a supersymmetric theory with 16 supercharges

Achieved a conformally invariant gauge theory in three dimensions

The gauge field is non-dynamical in the model

Abstract

In previous work we proposed a field theory model for multiple M2-branes based on an algebra with a totally antisymmetric triple product. In this paper we gauge a symmetry that arises from the algebra's triple product. We then construct a supersymmetric theory that is consistent with all the symmetries expected of a multiple M2-brane theory: 16 supersymmetries, conformal invariance, and an SO(8) R-symmetry that acts on the eight transverse scalars. The gauge field is not dynamical. The result is a new type of maximally supersymmetric gauge theory in three dimensions.