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

TL;DR

This paper proposes a 7-dimensional nonabelian Chern-Simons theory of String 2-connection fields as a holographic dual to the worldvolume theory of coincident M5-branes, revealing new insights into higher gauge theories and their instanton structures.

Contribution

It introduces a globally defined 7d nonabelian Chern-Simons theory based on String 2-connections, advancing understanding of M5-brane worldvolume theories and higher gauge structures.

Findings

Derived from anomaly cancellation, identified a candidate holographic dual for M5-branes.

Constructed the action functional on the full moduli 2-stack, capturing instanton effects.

Explained phenomena of higher nonabelian gauge theory relevant to the model.

Abstract

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.