Periodic Arrays of M2-Branes

TL;DR

This paper explores the formulation of maximally supersymmetric Yang-Mills theories via M2-brane arrays, revealing novel dualities and descriptions of M-theory branes in various dimensions.

Contribution

It introduces a new description of 3D and 5D maximally supersymmetric Yang-Mills theories derived from periodic M2-brane arrays and their dualities.

Findings

Formulation of 3D SYM with fermions, scalars, and a dual gluon

Derivation of 5D SYM via T-duality with non-manifest Lorentz invariance

M-theory interpretation of M5-branes on T^3

Abstract

We consider periodic arrays of M2-branes in the ABJM model in the spirit of a circle compactification to D2-branes in type IIA string theory. The result is a curious formulation of three-dimensional maximally supersymmetric Yang-Mills theory in terms of fermions, seven transverse scalars, a non-dynamical gauge field and an additional scalar `dual gluon'. Upon further T-duality on a transverse torus we obtain a non-manifest-Lorentz-invariant description of five-dimensional maximally supersymmetric Yang-Mills. Here the additional scalar field can be thought of as the components of a two-form along the torus. This action can be viewed as an M-theory description of M5-branes on ${\mathbb T}^3$.