Gerbes, M5-Brane Anomalies and E_8 Gauge Theory

TL;DR

This paper explores the role of twisted nonabelian gerbes in describing the topology of 4-form fields in M-theory, addressing global anomalies of M5-branes and their relation to E_8 gauge theory.

Contribution

It introduces the structure of twisted nonabelian gerbes and their application to M5-brane anomalies, extending previous work on single branes to multiple coincident branes.

Findings

Twisted nonabelian gerbes describe M5-brane gauge potentials.

The framework resolves global anomalies in M-theory.

Connection established between M5-brane anomalies and D4-branes via compactification.

Abstract

Abelian gerbes and twisted bundles describe the topology of the NS-NS 3-form gauge field strength H. We review how they have been usefully applied to study and resolve global anomalies in open string theory. Abelian 2-gerbes and twisted nonabelian gerbes describe the topology of the 4-form field strength G of M-theory. We show that twisted nonabelian gerbes are relevant in the study and resolution of global anomalies of multiple coinciding M5-branes. Global anomalies for one M5-brane have been studied by Witten and by Diaconescu, Freed and Moore. The structure and the differential geometry of twisted nonabelian gerbes (i.e. modules for 2-gerbes) is defined and studied. The nonabelian 2-form gauge potential living on multiple coinciding M5-branes arises as curving (curvature) of twisted nonabelian gerbes. The nonabelian group is in general $\tilde\Omega E_8$, the central extension of the E_8 loop group. The twist is in general necessary to cancel global anomalies due to the nontriviality of the 11-dimensional 4-form G field strength and due to the possible torsion present in the cycles the M5-branes wrap. Our description of M5-branes global anomalies leads to the D4-branes one upon compactification of M-theory to Type IIA theory.