Poisson-Sigma-Models: A Generalization of 2-D Gravity Yang-Mills-Systems

TL;DR

This paper introduces a new class of two-dimensional integrable field theories based on Poisson manifolds, unifying gravity-Yang-Mills systems and gauged Wess-Zumino models, with classical solutions and initial quantization schemes.

Contribution

It presents the formulation of a general class of 2D integrable models using Poisson geometry, including classical solutions and a framework for quantization.

Findings

Classical solutions of the models are derived.

A scheme for Hamiltonian quantization is proposed.

Partial results on the partition function on Riemann surfaces are discussed.

Abstract

A new class of two dimensional integrable field theories, based on the mathematical notion of Poisson manifolds, and containing gravity-Yang-Mills systems as well as the G/G gauged Wess-Zumino Witten-model, are presented. The local solutions of the classical equations of motions as well as a scheme for the quantization in a Hamiltonian formulation is presented for the general model. Partial results of a calculation of the partition function on arbitrary Riemann surfaces via path integral techniques are given. (Contribution to the proceedings of the Conference on Integrable Systems at the JINR, Dubna, July 1994).