Note on non-Abelian two-form gauge fields

TL;DR

This paper investigates non-Abelian two-form gauge theories motivated by M5 branes, proposing a modified gauge transformation law that allows for a gauge-invariant action and mass generation, advancing understanding of their dynamics.

Contribution

It introduces a new gauge transformation law for non-Abelian two-form fields, enabling a gauge-invariant action and mass generation, addressing limitations of previous approaches.

Findings

Fake curvature condition restricts dynamics to free or topological theories

Proposed a modified transformation law for gauge invariance

Generalized Stueckelberg mechanism gives mass to two-form fields

Abstract

Motivated by application to multiple M5 branes, we study some properties of non-Abelian two-form gauge theories. We note that the fake curvature condition which is commonly used in the literature would restrict the dynamics to be either a free theory or a topological system. We then propose a modification of transformation law which simplifies the gauge transformation of 3-form field strength and enables us to write down a gauge invariant action. We then argue that a generalization of Stueckelberg mechanism naturally gives mass to the two-form gauge field. For the application to multiple M5-branes, it should be identified with the KK modes.