Non-Abelian two-form gauge transformation and gauge theories in six dimensions

TL;DR

This paper introduces a novel non-Abelian gauge transformation for two-forms in six dimensions, addressing the surface ordering ambiguity and constructing a Wilson surface operator, with an application to Abelian gauge theory.

Contribution

It proposes a new non-Abelian gauge transformation for two-forms based on a loop space map, resolving key issues in defining Wilson surface operators.

Findings

Consistent non-Abelian gauge transformation for two-forms.

Construction of a Wilson surface operator for non-Abelian groups.

Development of an Abelian gauge theory in six dimensions.

Abstract

A new non-Abelian gauge transformation for two-forms is introduced. Construction is based on a fixed map from the spacetime to the loop space which attachs a closed loop to each point of the spacetime. It is argued that this set-up is consistent with the surface ordering ambiguity which is the main problem to construct the Wilson surface operator for non-Abelian groups. With the aim of the Wilson surface operator, we achieve a non-Abelian gauge transformation for two-forms. We interpret the Dirac operator as a vector field and define a covariant derivative and rederive the gauge transformation of the two-form. At the end, we construct an Abelian interacting gauge theory in six dimensions.