Local symmetries of the non-Abelian two-form

TL;DR

This paper explores the gauge transformation properties and symmetries of non-Abelian two-forms in BF theories, revealing new inhomogeneous transformations, a semiglobal symmetry, and their implications for invariant actions.

Contribution

It introduces a novel inhomogeneous gauge transformation for non-Abelian two-forms and identifies a new semiglobal symmetry in BF type theories.

Findings

Inhomogeneous gauge transformation for non-Abelian two-forms.

Existence of a semiglobal symmetry depending on local functions.

Gauge equivalences between different theory types via vector gauge transformations.

Abstract

It is proposed that a non-Abelian adjoint two-form in BF type theories transform inhomogeneously under the gauge group. The resulting restrictions on invariant actions are discussed. The auxiliary one-form which is required for maintaining vector gauge symmetry transforms like a second gauge field, and hence cannot be fully absorbed in the two-form. But it can be replaced, via a vector gauge transformation, by the usual gauge field, leading to gauge equivalences between different types of theories. A new type of symmetry also appears, one which depends on local functions but cannot be generated by constraints. It is connected to the identity in the limit of a vanishing global parameter, so it should be called a semiglobal symmetry. The corresponding conserved currents and BRST charges are parametrized by the space of flat connections.