String Sigma Models on Curved Supermanifolds

TL;DR

This paper employs integral forms to analyze two-dimensional sigma models on supermanifolds, demonstrating how to formulate actions and extend definitions from flat to curved supermanifolds using superfield techniques.

Contribution

It introduces a method to formulate sigma models on curved supermanifolds using integral forms and superfields, extending flat supermanifold techniques to curved cases.

Findings

Formulation of sigma model actions as integrals of top integral forms.

Interpolation between different superspace actions.

Extension of flat supermanifold definitions to curved supermanifolds.

Abstract

We use the techniques of integral forms to analyse the easiest example of two dimensional sigma models on a supermanifold. We write the action as an integral of a top integral form over a D=2 supermanifold and we show how to interpolate between different superspace actions. Then, we consider curved supermanifolds and we show that the definitions used for flat supermanifold can also be used for curved supermanifolds. We prove it by first considering the case of a curved rigid supermanifold and then the case of a generic curved supermanifold described by a single superfield $E$.