Super Riemann surfaces, metrics, and gravitinos

TL;DR

This paper explores the geometric structure of super Riemann surfaces, focusing on their metrics and gravitinos, and connects these to the action functional in super symmetric sigma models and string theory.

Contribution

It provides a geometric interpretation of the super symmetric action functional on the moduli space of super Riemann surfaces, linking physics and super geometry.

Findings

Infinitesimal deformations involve both the Riemann surface and gravitino.

The super symmetric action functional is derived from a geometric functional.

Invariances of the action are explained via super geometric terms.

Abstract

The underlying even manifold of a super Riemann surface is a Riemann surface with a spinor valued differential form called gravitino. Consequently infinitesimal deformations of super Riemann surfaces are certain infinitesimal deformations of the Riemann surface and the gravitino. Furthermore the action functional of non-linear super symmetric sigma models, the action functional underlying string theory, can be obtained from a geometric action functional on super Riemann surfaces. All invariances of the super symmetric action functional are explained in super geometric terms and the action functional is a functional on the moduli space of super Riemann surfaces.