First-order supersymmetric sigma models and target space geometry

TL;DR

This paper explores the geometric conditions enabling N=(1,1) supersymmetric sigma models to extend to N=(2,2), revealing a framework that includes generalized complex geometry, with implications for understanding target space structures.

Contribution

It introduces a geometric framework connecting supersymmetry extension conditions to generalized complex geometry, aiding analysis of complex sigma models.

Findings

Extended supersymmetry linked to target space complex geometry.

Developed a language for analyzing supersymmetric sigma models.

Uncovered a geometric framework encompassing generalized complex geometry.

Abstract

We study the conditions under which N=(1,1) generalized sigma models support an extension to N=(2,2). The enhanced supersymmetry is related to the target space complex geometry. Concentrating on a simple situation, related to Poisson sigma models, we develop a language that may help us analyze more complicated models in the future. In particular, we uncover a geometrical framework which contains generalized complex geometry as a special case.