Form-field Gauge Symmetry in M-theory

TL;DR

This paper presents a gauge-invariant formulation of M-theory involving higher-dimensional Dirac surfaces, clarifying the structure of gauge symmetries and brane charge lattice at the quantum level.

Contribution

It introduces a novel approach using Dirac surfaces to preserve gauge symmetries in M-theory and relates gauge transformations to relative cohomology.

Findings

Gauge-invariant formulation of M-theory with Dirac surfaces

Preservation of a subgroup of gauge symmetries at quantum level

Correct lattice of M-theory brane charges derived

Abstract

We show how to cast an interacting system of M--branes into manifestly gauge-invariant form using an arrangement of higher-dimensional Dirac surfaces. Classical M--theory has a cohomologically nontrivial and noncommutative set of gauge symmetries when written using a ``doubled'' formalism containing 3-form and 6-form gauge fields. We show how the arrangement of Dirac surfaces allows an integral subgroup of these symmetries to be preserved at the quantum level. The proper context for discussing these large gauge transformations is relative cohomology, in which the 3-form transformation parameters become exact when restricted to the five-brane worldvolume. This structure yields the correct lattice of M-theory brane charges.