Super Riemann surfaces, metrics, and gravitinos
Jürgen Jost, Enno Keßler, and Jürgen Tolksdorf
Contact the author: Please use for correspondence this email.
Submission date: 18. Dec. 2014 (revised version: December 2015)
Download full preprint: PDF (510 kB)
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.