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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 whichattachs a closed loop to each point of the spacetime. It is argued that thisset-up is consistent with the surface ordering ambiguity which is the mainproblem to construct the Wilson surface operator for non-Abelian groups. Withthe aim of the Wilson surface operator, we achieve a non-Abelian gaugetransformation for two-forms. We interpret the Dirac operator as a vector fieldand define a covariant derivative and rederive the gauge transformation of thetwo-form. At the end, we construct an Abelian interacting gauge theory in sixdimensions.

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