Poisson sigma models on surfaces with boundary: classical and quantum aspects

TL;DR

This thesis explores classical and quantum aspects of Poisson sigma models, including branes, Poisson-Lie groups, and supersymmetric extensions, highlighting their geometric and algebraic structures.

Contribution

It provides a comprehensive analysis of branes in Poisson sigma models, studies Poisson-Lie groups, and examines supersymmetric twisted models, advancing understanding of their geometric and quantum properties.

Findings

Classified consistent branes at classical and quantum levels.

Analyzed Poisson-Lie group structures within sigma models.

Connected supersymmetric models with twisted generalized complex geometry.

Abstract

The topics covered in this thesis may be divided into three parts. Firstly, we perform a study on the most general branes which are consistent with the Poisson sigma model, both at the classical and quantum levels. The second part is devoted to the particular case in which the target Poisson manifold is a Poisson-Lie group. Finally, we investigate the supersymmetric version of the twisted Poisson sigma model and its connection with twisted generalized complex geometry.