A theory of non-abelian tensor gauge field with non-abelian gauge symmetry image Original Research Article

The Chern–Simons action of the ABJM theory is not gauge invariant in the presence of a boundary. In Chu and Smith (2010) , this was shown to imply the existence of a Kac–Moody current algebra on the theory of multiple self-dual strings. In this paper we conjecture that the Kac–Moody symmetry induces a image gauge symmetry in the theory of N coincident M5-branes. As a start, we construct a image gauge symmetry algebra structure which naturally includes the tensor gauge transformation for a non-abelian 2-form tensor gauge field. The gauge covariant field strength is constructed. This new image gauge symmetry algebra allows us to write down a theory of a non-abelian tensor gauge field in any dimensions. The image gauge bosons can be either propagating, in which case the 2-form gauge fields would interact with each other through the 1-form gauge field; or they can be auxiliary and carry no local degrees of freedom, in which case the 2-form gauge fields would be self-interacting non-trivially. We finally comment on the possible application to the system of multiple M5-branes. We note that the field content of the image non-abelian tensor gauge theory can be fitted nicely into (image) supermultiplets; and we suggest a construction of the theory of multiple M5-branes with manifest (image) supersymmetry.