Obstructions to Gauging WZ Terms: a Symplectic Curiosity

TL;DR

This paper explores the relationship between gauging WZ terms in 1D sigma-models and the existence of equivariant moment maps, revealing that obstructions in both contexts are equivalent, thus clarifying foundational geometric structures.

Contribution

It establishes a direct link between obstructions to gauging WZ terms and the existence of equivariant moment maps in symplectic geometry.

Findings

Obstructions to gauging WZ terms match obstructions to moment map existence.

Provides geometric insight into gauging problems in sigma-models.

Clarifies the role of symplectic group actions in field theory.

Abstract

This is an expository talk about the relation between gauging the WZ term of a one-dimensional sigma-model with a symplectic target and the existence of an equivariant moment mapping for symplectic group actions. The punch line is that the obstructions for gauging coincide with the obstructions for the existence of the moment mapping. This paper can be thought of a "prequel" of hep-th/9407149.