On the general structure of gauged Wess-Zumino-Witten terms

TL;DR

This paper investigates the conditions under which gauging closed forms in WZW models is possible, providing explicit cocycle constructions and analyzing the geometric structures and obstructions involved.

Contribution

It introduces a general framework for gauging closed forms on Lie groups using relative Lie algebra cohomology, with explicit cocycle formulas and insights into geometric obstructions.

Findings

Gauging is unobstructed if a cocycle exists in the relative Lie algebra cohomology.

Explicit expressions for these cocycles are provided.

The geometric structure of gauged forms and their obstructions are clarified.

Abstract

The problem of gauging a closed form is considered. When the target manifold is a simple Lie group G, it is seen that there is no obstruction to the gauging of a subgroup H\subset G if we may construct from the form a cocycle for the relative Lie algebra cohomology (or for the equivariant cohomology), and an explicit general expression for these cocycles is given. The common geometrical structure of the gauged closed forms and the D'Hoker and Weinberg effective actions of WZW type, as well as the obstructions for their existence, is also exhibited and explained.