Geometry of the N=2 supersymmetric sigma model with Euclidean worldsheet

Abstract

We investigate the target space geometry of supersymmetric sigma models in two dimensions with Euclidean signature, and the conditions for N=2 supersymmetry. For a real action, the geometry for the N=2 model is not the generalized Kahler geometry that arises for Lorentzian signature, but is an interesting modification of this which is not a complex geometry.