Large Gauge Transformations in M-theory

TL;DR

This paper develops a gauge-invariant framework for M-brane interactions in M-theory, revealing the structure of large gauge transformations, charge lattices, and topological terms through higher-dimensional surfaces and relative cohomology.

Contribution

It introduces a manifestly gauge-invariant formulation of M-brane interactions using higher-dimensional Dirac surfaces and clarifies the role of relative cohomology in large gauge transformations.

Findings

Preserves noncommutative gauge symmetry in integer-quantized form

Identifies the lattice structure of M-theory charges

Derives the 7D Hopf-Wess-Zumino term

Abstract

We cast M-brane interactions including intersecting membranes and five-branes in manifestly gauge invariant form using an arrangement of higher dimensional Dirac surfaces. We show that the noncommutative gauge symmetry present in the doubled M-theory formalism involving dual 3-form and 6-form gauge fields is preserved in a form quantised over the integers. The proper context for discussing large noncommutative gauge transformations is relative cohomology, in which the 3-form transformation parameters become exact when restricted to the five-brane worldvolume. We show how this structure yields the lattice of M-theory charges and gives rise to the conjectured 7D Hopf-Wess-Zumino term.