Deforming super Riemann surfaces with gravitinos and super Schottky groups

TL;DR

This paper explores the deformation of super Riemann surfaces using gravitinos and super Schottky groups, linking their cohomological descriptions and period matrices, and discusses their construction via puncture gluing.

Contribution

It introduces a cohomological framework for deformations of super Riemann surfaces via super Schottky groups and relates period matrices to gravitino and Beltrami parameters.

Findings

Super Schottky group formula for period matrices matches gravitino-based expressions.

Deformations by gravitinos and Beltrami parameters are recast in super Schottky group cohomology.

Relationship between super Schottky groups and puncture gluing construction is clarified.

Abstract

The (super) Schottky uniformization of compact (super) Riemann surfaces is briefly reviewed. Deformations of super Riemann surface by gravitinos and Beltrami parameters are recast in terms of super Schottky group cohomology. It is checked that the super Schottky group formula for the period matrix of a non-split surface matches its expression in terms of a gravitino and Beltrami parameter on a split surface. The relationship between (super) Schottky groups and the construction of surfaces by gluing pairs of punctures is discussed in an appendix.