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

TL;DR

This paper develops a Yang-Mills theory in loop space with an affine Lie gauge group, systematically deriving generalized Chapline-Manton couplings among various tensor and gauge fields, including BF-like terms.

Contribution

It introduces a novel framework for Yang-Mills theory in loop space and derives new generalized couplings involving non-abelian and abelian tensor fields.

Findings

Derived the standard Chapline-Manton coupling via Chern-Simons term.

Extended to generalized couplings among non-abelian and abelian tensor fields.

Identified BF-like terms accompanying the generalized couplings.

Abstract

We consider a Yang-Mills theory in loop space with an affine Lie gauge group. The Chapline-Manton coupling, the coupling between Yang-Mills fields and an abelian antisymmetric tensor field of second rank via the Chern-Simons term, is systematically derived within the framework of the Yang-Mills theory. The generalized Chapline-Manton couplings, the couplings among non-abelian tensor fields of second rank, Yang-Mills fields, and an abelian tensor field of third rank, are also derived by applying the non-linear realization method to the Yang-Mills theory. These couplings are accompanied by {\it BF}-like terms.