Localization for CS manifolds and volume of homogeneous superspaces

TL;DR

This paper extends the Schwarz-Zaboronsky localization theorem to CS manifolds and applies it to compute volumes of homogeneous superspaces associated with super-Lie groups without real forms.

Contribution

It introduces a localization theorem for CS manifolds and provides volume calculations for certain homogeneous superspaces, expanding the mathematical toolkit for supergeometry.

Findings

Localization theorem for CS manifolds established

Volume formulas for superspaces without real forms derived

Application to super-Lie groups enhances understanding of supergeometry

Abstract

We prove the Schwarz-Zaboronsky localization theorem for CS manifolds and use this to give a volume calculation for homogeneous superspaces for super-Lie groups that lack a real form.