Super Riemann Surfaces and the Super Conformal Action Functional

TL;DR

This paper explores super Riemann surfaces, extending harmonic action functionals to them, and discusses their implications for understanding the moduli space in super geometry.

Contribution

It introduces an extension of the harmonic action functional to super Riemann surfaces and analyzes its applications to their moduli space.

Findings

Super Riemann surfaces can be viewed as Riemann surfaces with an additional gravitino field.

The extended harmonic action functional provides new tools for studying super moduli space.

Applications to the moduli space of super Riemann surfaces are discussed.

Abstract

Riemann surfaces are two-dimensional manifolds with a conformal class of metrics. It is well known that the harmonic action functional and harmonic maps are tools to study the moduli space of Riemann surfaces. Super Riemann surfaces are an analogue of Riemann surfaces in the world of super geometry. After a short introduction to super differential geometry we will compare Riemann surfaces and super Riemann surfaces. We will see that super Riemann surfaces can be viewed as Riemann surfaces with an additional field, the gravitino. An extension of the harmonic action functional to super Riemann surfaces is presented and applications to the moduli space of super Riemann surfaces are considered.