Gauge transformations of the non-Abelian two-form

TL;DR

This paper introduces a new gauge transformation law for non-Abelian two-forms in four dimensions, providing invariant actions and exploring the role of auxiliary fields and boundary degrees of freedom.

Contribution

It proposes a novel inhomogeneous gauge transformation for non-Abelian two-forms and analyzes associated symmetries and invariance conditions.

Findings

New gauge transformation law for non-Abelian two-forms.

Construction rules for invariant actions under the new symmetry.

Identification of boundary degrees of freedom affecting quantization.

Abstract

A novel inhomogeneous gauge transformation law is proposed for a non-Abelian adjoint two-form in four dimensions. Rules for constructing actions invariant under this are given. The auxiliary vector field which appears in some of these models transforms like a second connection in the theory. Another local symmetry leaves the compensated three-form field strength invariant, but does not seem to be generated by any combination of local constraints. Both types of symmetries change the action by total divergences, suggesting that boundary degrees of freedom have to be taken into account for local quantization.