Octonions, G_2 and generalized Lie 3-algebras

TL;DR

This paper constructs a generalized Lie 3-algebra using octonions, leading to a novel three-dimensional N=2 Chern-Simons-matter theory with G_2 gauge symmetry, relevant for multiple M2-branes.

Contribution

It explicitly constructs a generalized Lie 3-algebra from octonions and links it to a new M2-brane theory with exceptional G_2 gauge symmetry.

Findings

Constructed a generalized Lie 3-algebra from octonions.

Derived a 3D N=2 Chern-Simons-matter theory with G_2 gauge group.

Proposed a candidate theory for multiple M2-branes with G_2 symmetry.

Abstract

We construct an explicit example of a generalized Lie 3-algebra from the octonions. In combination with the result of arXiv:0807.0808, this gives rise to a three-dimensional N=2 Chern-Simons-matter theory with exceptional gauge group G_2 and with global symmetry SU(4)\times U(1). This gives a possible candidate for the theory on multiple M2-branes with G_2 gauge symmetry.