Lectures on Generalized Complex Geometry and Supersymmetry

TL;DR

This paper provides an introductory overview of generalized complex geometry, its relation to supersymmetry, and its applications in two-dimensional field theories and string theory, highlighting recent mathematical and physical developments.

Contribution

It offers a comprehensive introduction to generalized complex geometry, connecting mathematical structures with supersymmetry and physical theories, including generalized Kahler and Calabi-Yau manifolds.

Findings

Relation between generalized complex geometry and supersymmetry explained

Overview of generalized Kahler and Calabi-Yau manifolds in physics

Connections to two-dimensional field theories elucidated

Abstract

These are the lecture notes from the 26th Winter School "Geometry and Physics", Czech Republic, Srni, January 14 - 21, 2006. These lectures are an introduction into the realm of generalized geometry based on the tangent plus the cotangent bundle. In particular we discuss the relation of this geometry to physics, namely to two-dimensional field theories. We explain in detail the relation between generalized complex geometry and supersymmetry. We briefly review the generalized Kahler and generalized Calabi-Yau manifolds and explain their appearance in physics.