Multiple M5-branes, String 2-connections, and 7d nonabelian Chern-Simons theory

Domenico Fiorenza, Hisham Sati, Urs Schreiber

Research output: Contribution to journalArticlepeer-review


The worldvolume theory of coincident M5-branes is expected to contain a nonabelian 2-form/nonabelian gerbe gauge theory that is a higher analog of self-dual Yang-Mills theory. But the precise details - in particular the global moduli/instanton/magnetic charge structure - have remained elusive. Here we deduce from anomaly cancellation a natural candidate for the holographic dual of this nonabelian 2-form field, under AdS7/CFT6 duality. We find this way a 7-dimensional nonabelian Chern-Simons theory of String 2-connection fields, which, in a certain higher gauge, are given locally by non-abelian 2-forms with values in an affine Kac-Moody Lie algebra. We construct the corresponding action functional on the entire smooth moduli 2-stack of field configurations, thereby defining the theory globally, at all levels and with the full instanton structure, which is nontrivial due to the twists imposed by the quantum corrections. Along the way we explain some general phenomena of higher nonabelian gauge theory that we need.

Original languageEnglish (US)
Pages (from-to)229-321
Number of pages93
JournalAdvances in Theoretical and Mathematical Physics
Issue number2
StatePublished - 2014

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy


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