A Brief Introduction to Poisson Sigma-Models

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.

10 pages, LaTex. Based on two talks delivered in Schladming, March 1995

References in corpus (3)

• Poisson Structure Induced (Topological) Field Theories
• The Topological G/G WZW Model in the Generalized Momentum Representation
• On Induced Gravity in 2-d Topological Theories

Cited by in corpus (18)

• WZW-Poisson manifolds
• Exact Physical Black Hole States in Generic 2-D Dilaton Gravity
• Gravity in Two Spacetime Dimensions
• Abelian p-Form (p = 1, 2, 3) Gauge Theories as the Field Theoretic Models for the Hodge Theory
• Abelian 2-form gauge theory: special features
• Cyclicity of non-associative products on D-branes
• Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
• Target-Superspace in 2d Dilatonic Supergravity
• Supergravity in Two Spacetime Dimensions
• Wilson surface observables from equivariant cohomology
• Jacobi sigma models
• Lie algebroids, non-associative structures and non-geometric fluxes
• Target Space Equivariant Cohomological Structure of the Poisson Sigma Model
• Topological and dynamical aspects of Jacobi sigma models
• From BFV to BV and spacetime covariance
• Gravity from AKSZ-Manin theories in two, three, and four dimensions
• Geometric quantization and non-perturbative Poisson sigma model
• Homotopy Manin Theories: Generalising Third-Way, Yang-Mills and Integrable Sigma Models