Comments on the topological open membrane

TL;DR

This paper explores the theoretical construction of non-Abelian two-form gauge theories in 3+1 dimensions by quantising open membranes in a large three-form background, emphasizing volume-preserving diffeomorphisms.

Contribution

It introduces a novel approach to formulating non-Abelian two-form gauge theories using volume-preserving diffeomorphisms, expanding the theoretical framework of higher-form gauge theories.

Findings

Constructed consistent non-Abelian interactions of a two-form in 3+1 dimensions.

Linked the quantisation of open membranes to volume-preserving diffeomorphisms.

Provided insights into the relation between membrane quantisation and non-Abelian gauge theories.

Abstract

Just as non-commutative gauge theories arise from quantising open strings in a large magnetic field, non-Abelian two-form gauge theories may conceivably be constructed by quantising open membranes in a large three-form magnetic background. We make some observations that arise in following this strategy, with an emphasis on the relation to the quantisation of volume-preserving diffeomorphisms (vpd). In particular, we construct consistent non-Abelian interactions of a two-form in 3+1 dimensions, based on gauge invariance under vpd.