Note on non-Abelian two-form gauge fields

Motivated by application to multiple M5-branes, we study some properties of non-Abelian two-form gauge theories. We emphasize that the fake curvature condition which is commonly used in the literature would restrict the dynamics to be either a free theory or a topological system. We then propose a modification of transformation law which simplifies the gauge transformation of 3-form field strength and enables us to write down a gauge invariant action. We then argue that a generalization of Stueckelberg mechanism naturally gives mass to the two-form gauge field. For the application to multiple M5-branes, it should be identified with the KK modes.