Semirigid Geometry

TL;DR

This paper introduces an intrinsic framework for semirigid super Riemann surfaces, linking their geometry to integrable reductions and exploring their moduli spaces in the context of topological gravity.

Contribution

It provides a new intrinsic description of semirigid super Riemann surfaces and analyzes their moduli spaces, connecting geometric structures to physical theories.

Findings

Semirigid surfaces are characterized by integrable reductions of complex supermanifolds.

The moduli spaces of TN-SR surfaces are related to those of N-super Riemann surfaces.

The geometric framework has applications in topological gravity and supergravity.

Abstract

We provide an intrinsic description of $N$-super \RS s and $TN$-\SR\ surfaces. Semirigid surfaces occur naturally in the description of topological gravity as well as topological supergravity. We show that such surfaces are obtained by an integrable reduction of the structure group of a complex supermanifold. We also discuss the \s moduli spaces of $TN$-\SR\ surfaces and their relation to the moduli spaces of $N$-\s\ \RS s.