Gerbes, M5-Brane Anomalies and E_8 Gauge Theory

Paolo Aschieri; Branislav Jurco

doi:10.1088/1126-6708/2004/10/068

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arXiv · hep-th/0409200

Gerbes, M5-Brane Anomalies and E_8 Gauge Theory

Paolo Aschieri·Branislav Jurco

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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 $\tildeΩE_8$, 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.

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Paolo Aschieri, Branislav Jurco. 2004-09-20. Gerbes, M5-Brane Anomalies and E_8 Gauge Theory. https://doi.org/10.1088/1126-6708%2F2004%2F10%2F068

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