A Brief Introduction to Poisson Sigma-Models

TL;DR

This paper introduces Poisson sigma-models, a class of topological field theories based on Poisson manifolds, illustrating their relevance to Yang-Mills, gravity, and WZW models with pedagogical explanations.

Contribution

It provides a pedagogical overview of Poisson sigma-models, connecting mathematical structures to physical theories and illustrating their applications with examples.

Findings

Links Poisson sigma-models to Yang-Mills and gravity theories

Provides illustrative examples clarifying the theory

Offers a pedagogical introduction to the subject

Abstract

The theory of Poisson-$\sigma$-models employs the mathematical notion of Poisson manifolds to formulate and analyze a large class of topological and almost topological two dimensional field theories. As special examples this class of field theories includes pure Yang-Mills and gravity theories, and, to some extent, the G/G gauged WZW-model. The aim of this contribution is to give a pedagogical introduction, explaining many aspects of the general theory by illustrative examples.