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

TL;DR

This paper explores the unique target space geometry of N=2 supersymmetric sigma models with Euclidean worldsheet signature, revealing a novel geometric structure distinct from the Lorentzian case.

Contribution

It identifies a new geometric structure for N=2 supersymmetric sigma models in Euclidean signature, differing from the generalized Kahler geometry known in Lorentzian cases.

Findings

The geometry is a modification of generalized Kahler geometry.

The geometry is not a complex geometry.

Conditions for N=2 supersymmetry are established.

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.