A Theory of Non-Abelian Tensor Gauge Field with Non-Abelian Gauge Symmetry G x G

TL;DR

This work proposes a $G×G$ tensor gauge symmetry as the underlying structure for the worldvolume theory of multiple M5-branes, introducing a non-Abelian 2-form $B_{mu nu}$ whose gauge transformations close only when a tensor gauge sector is included. By defining a covariant 3-form $H_{mu nu lambda}$ using ${f A}_er = A_er + A'_er$ and a tensor gauge transformation, the authors construct a consistent non-Abelian tensor gauge theory in arbitrary dimensions and show how matter can couple and how the theory can reproduce a dual 5D Yang-Mills description. The framework naturally accommodates $U(N)$ and suggests a manifest $(1,0)$ supersymmetric organization of the field content, offering a potential route toward a non-perturbative formulation of the 6D $(2,0)$ theory on M5-branes. These insights connect boundary Kac-Moody structures from ABJM to spacetime gauge structure and open avenues for self-dual tensor dynamics and higher-dimensional dualities in M-brane systems.

Abstract

The Chern-Simon action of the ABJM theory is not gauge invariant in the presence of a boundary. In the paper arXiv:0909.2333, this was shown to imply the existence of a Kac-Moody symmetry on the theory of multiple self-dual strings. In this paper we conjecture that the Kac-Moody symmetry induces a U(N)x U(N) gauge symmetry in the theory of N coincident M5-branes. As a start, we construct this G x G gauge symmetry algebra structure which naturally includes the tensor gauge transformation for a non-abelian 2-form tensor gauge field. This new G x G gauge structure allows us to write down a theory of a non-abelian tensor gauge field readily. For application to multiple M5-branes, we note that the field content of the G x G non-abelian tensor gauge theory can be fitted nicely as (1,0) supermultiplets; and we suggest a construction of the theory of multiple M5-branes with manifest (1,0) supersymmetry.