Gerbes, M5-Brane Anomalies and E8Gauge Theory

Abelian gerbes and twisted bundles describe the topology of the NS-NS 3-formgauge field strength H. We review how they have been usefully applied to studyand resolve global anomalies in open string theory. Abelian 2-gerbes andtwisted nonabelian gerbes describe the topology of the 4-form field strength Gof M-theory. We show that twisted nonabelian gerbes are relevant in the studyand resolution of global anomalies of multiple coinciding M5-branes. Globalanomalies for one M5-brane have been studied by Witten and by Diaconescu, Freedand Moore. The structure and the differential geometry of twisted nonabeliangerbes (i.e. modules for 2-gerbes) is defined and studied. The nonabelian2-form gauge potential living on multiple coinciding M5-branes arises ascurving (curvature) of twisted nonabelian gerbes. The nonabelian group is ingeneral $\tilde\Omega E_8$, the central extension of the E_8 loop group. Thetwist is in general necessary to cancel global anomalies due to thenontriviality of the 11-dimensional 4-form G field strength and due to thepossible torsion present in the cycles the M5-branes wrap. Our description ofM5-branes global anomalies leads to the D4-branes one upon compactification ofM-theory to Type IIA theory.Comment: 19 page