Supersymmetric Sigma Models and Generalized Complex Geometry

Abstract

In this thesis we look at a physical model that consists of maps from a surface to a compact manifold M. After introducing the concept of supersymmetry in two dimensions, we discuss what kind of structure is needed on M in order for this model to have supersymmetric representations on it. These structures are naturally described by a field in mathematics known as Generalized Complex Geometry, which includes complex and symplectic geometry as special cases. We review the topological twist in the presence of flux, which is a procedure to obtain out of these sigma-models so-called topological theories.