Non-Abelian two-form gauge transformation and gauge theories 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.