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

TL;DR

This paper develops a Yang--Mills theory in loop space with a Kac--Moody gauge group, deriving a local field theory that includes the Chapline--Manton coupling between Yang--Mills and tensor fields.

Contribution

It introduces a novel formulation of Yang--Mills theory in loop space with a Kac--Moody gauge group and systematically derives the Chapline--Manton coupling.

Findings

Derivation of a local field theory from loop space Yang--Mills theory.

Systematic construction of the Chapline--Manton coupling.

Inclusion of antisymmetric and symmetric tensor fields of the second rank.

Abstract

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.