A Yang--Mills Theory in Loop Space and Chapline--Manton Coupling

We consider a Yang--Mills theory in loop space whose gauge group is a Kac--Moody group with the central extension. From this theory, we derive a local field theory constructed of Yang--Mills fields and abelian antisymmetric and symmetric tensor fields of the second rank. The Chapline--Manton coupling, that is, coupling of Yang--Mills fields and a second-rank antisymmetric tensor field via the Chern--Simons 3-form is obtained in a systematic manner.