Target Space Equivariant Cohomological Structure of the Poisson Sigma Model

TL;DR

This paper explores the Poisson sigma model with a Lie algebra action on the target space, revealing how its structure and observables relate to equivariant cohomology using a superfield formalism.

Contribution

It introduces a framework connecting the Poisson sigma model's gauge invariants to target space equivariant cohomology, utilizing a de Rham superfield approach.

Findings

Link between gauge invariants and equivariant cohomology

Efficient analysis via de Rham superfield formalism

Insights into the structure of the Poisson sigma model

Abstract

We study a formulation of the standard Poisson sigma model in which the target space Poisson manifold carries the Hamilton action of some finite dimensional Lie algebra. We show that the structure of the action and the properties of the gauge invariant observables can be understood in terms of the associated target space equivariant cohomology. We use a de Rham superfield formalism to efficiently explore the implications of the Batalin Vilkoviski master equation.