The Geometry of Sigma-Models with Twisted Supersymmetry

TL;DR

This paper explores the geometric structures underlying two-dimensional sigma models with various supersymmetries, providing superspace formulations and analyzing twisted supersymmetry in models with different signatures.

Contribution

It introduces superspace formulations for twisted and untwisted supersymmetry in two-dimensional sigma models with arbitrary signature target spaces.

Findings

Superspace formulations for (p,q) heterotic sigma-models are developed.

Extended superspace formulations are provided for twisted (2,1) and pseudo-Kähler sigma models.

The relation between supersymmetry and geometry in diverse signatures is clarified.

Abstract

We investigate the relation between supersymmetry and geometry for two dimensional sigma models with target spaces of arbitrary signature, and Lorentzian or Euclidean world-sheets. In particular, we consider twisted forms of the two-dimensional $(p,q)$ supersymmetry algebra. Superspace formulations of the $(p,q)$ heterotic sigma-models with twisted or untwisted supersymmetry are given. For the twisted (2,1) and the pseudo-K\"{a}hler sigma models, we give extended superspace formulations.