N=8 superconformal gauge theories and M2 branes

TL;DR

This paper constructs 2+1 dimensional N=8 superconformal gauge theories using extended 3-algebras, circumventing previous no-go theorems, with properties expected for M2 brane worldvolume theories.

Contribution

It introduces a new class of superconformal gauge theories based on infinite 3-algebras with non-compact gauge groups, expanding the landscape of M2 brane models.

Findings

Theories have scale invariance and N=8 supersymmetry.

Gauge group can be any Lie group with non-compact extension.

Moduli space includes a branch (R^8)^N/S_N, matching M2 brane expectations.

Abstract

Based on recent developments, in this letter we find 2+1 dimensional gauge theories with scale invariance and N=8 supersymmetry. The gauge theories are defined by a Lagrangian and are based on an infinite set of 3-algebras, constructed as an extension of ordinary Lie algebras. Recent no-go theorems on the existence of 3-algebras are circumvented by relaxing the assumption that the invariant metric is positive definite. The gauge group is non compact, and its maximally compact subgroup can be chosen to be any ordinary Lie group, under which the matter fields are adjoints or singlets. The theories are parity invariant and do not admit any tunable coupling constant. In the case of SU(N) the moduli space of vacua contains a branch of the form (R^8)^N/S_N. These properties are expected for the field theory living on a stack of M2 branes.