BLG-motivated Lagrangian formulation for the chiral two-form gauge field in D=6 and M5-branes

TL;DR

This paper develops a covariant Lagrangian formulation for the chiral two-form gauge field in six dimensions, inspired by M5-branes, revealing hidden symmetries and coupling to gravity and supersymmetry.

Contribution

It introduces a new covariant Lagrangian for the chiral two-form field using auxiliary scalars, addressing gauge and Lorentz symmetry issues in M5-brane models.

Findings

Covariant Lagrangian formulation with auxiliary scalars.

Self-duality of non-linear gauge field strength proven.

Discussion of relations to existing M5-brane theories.

Abstract

We reveal non-manifest gauge and SO(1,5) Lorentz symmetries in the Lagrangian description of a six-dimensional free chiral field derived from the Bagger-Lambert-Gustavsson model in arXiv:0804.3629 and make this formulation covariant with the use of a triplet of auxiliary scalar fields. We consider the coupling of this self-dual construction to gravity and its supersymmetrization. In the case of the non-linear model of arXiv:0805.2898 we solve the equations of motion of the gauge field, prove that its non-linear field strength is self-dual and find a gauge-covariant form of the non-linear action. Issues of the relation of this model to the known formulations of the M5-brane worldvolume theory are discussed.