Non-abelian Action for Multiple Five-Branes with Self-Dual Tensors

TL;DR

This work presents a non-abelian action for a self-dual 2-form in 6d, extending the Perry–Schwarz construction to the M5-brane context. By introducing an auxiliary field $E_{\mu\nu}$ and a constrained YM sector, the model yields a self-duality equation of motion and a modified, nonlocal realization of 6d Lorentz symmetry, while preserving manifest 5d Lorentz invariance. Dimensional reduction on a circle reproduces 5d Yang–Mills with a gauge coupling $g_{YM}^2=R$ and unveils higher-derivative corrections, supporting the interpretation as the gauge sector of coincident M5-branes in flat space. The paper outlines essential steps toward a full (2,0) supersymmetric completion and discusses covariantization, fermions, and scalars as future directions. Overall, the construction provides a concrete bosonic framework for exploring non-abelian self-dual tensor dynamics and their relation to M5-brane physics.

Abstract

We construct an action for non-abelian 2-form in 6-dimensions. Our action consists of a non-abelian generalization of the abelian action of Perry and Schwarz for a single five-brane. It admits a self-duality equation on the field strength as the equation of motion. It has a modified 6d Lorentz symmetry. On dimensional reduction on a circle, our action gives the standard 5d Yang-Mills action plus higher order corrections. Based on these properties, we propose that our theory describes the gauge sector of multiple M5-branes in flat space.