Generalized Higher Gauge Theory and M5-brane dynamics. Proceedings: Higher structures in String and M-theory, Tohoku Forum for Creativity, March 7-11 2016

TL;DR

This paper reviews truncated L$_$ algebras in higher gauge theory, explores their topological invariants, and demonstrates how they can model M5-brane dynamics within a generalized geometric framework.

Contribution

It introduces a formalism connecting higher gauge theories, multisymplectic geometry, and Courant algebroids to better understand M5-brane models.

Findings

Unified higher gauge theory formalism for extended objects

Relation of solutions to multisymplectic geometries

Natural interpretation of M5-brane field content

Abstract

We give a review of truncated L$_\infty$ algebras, as used in the study of higher gauge theory. These structures are believed to hold the correct properties to adequately describe gauge theory of extended objects. We discuss how to construct topological higher-gauge-invariant theories and how their solutions relate to multisymplectic geometries. We also show how Courant algebroids fit into this formalism, so as to be able to study higher gauge theory on generalized geometric bundles, i.e. on $ T\Sigma \oplus T^*\Sigma $, for some space-time $\Sigma $. We will see that via this formalism we can match and explain a recently proposed M5-brane model, arrived at in a more heuristic way, whose field content seemed difficult to interpret but finds a natural motivation in this framework.