M5-brane in three-form flux and multiple M2-branes

TL;DR

This paper explores a gauge theory model based on the Nambu-Poisson algebra that describes an M5-brane in a large C-field background, deriving its properties and connections to D-brane theories.

Contribution

It introduces a gauge theory framework for the M5-brane using the Nambu-Poisson algebra and demonstrates its relation to D4-brane gauge theories through dimensional reduction.

Findings

The model reproduces non-commutative U(1) gauge theory on D4-branes.

The equations of motion exhibit manifest self-dual tensor structure.

Relations between BLG model parameters and M-theory parameters are established.

Abstract

We investigate the Bagger-Lambert-Gustavsson model associated with the Nambu-Poisson algebra as a theory describing a single M5-brane. We argue that the model is a gauge theory associated with the volume-preserving diffeomorphism in the three-dimenisonal internal space. We derive gauge transformations, actions, supersymmetry transformations, and equations of motions in terms of six-dimensional fields. The equations of motions are written in gauge-covariant form, and the equations for tensor fields have manifest self-dual structure. We demonstrate that the double dimensional reduction of the model reproduces the non-commutative U(1) gauge theory on a D4-brane with a small non-commutativity parameter. We establish relations between parameters in the BLG model and those in M-theory. This shows that the model describes an M5-brane in a large C-field background.