Supersymmetric Localization in GLSMs for Supermanifolds

TL;DR

This paper uses supersymmetric localization to connect GLSMs for supermanifolds with those for hypersurfaces, showing their correlation functions and partition functions are equivalent under certain conditions, extending previous results.

Contribution

It demonstrates the equivalence of correlation functions and partition functions between GLSMs for supermanifolds and hypersurfaces, extending the understanding of supersymmetric localization in these models.

Findings

A-twisted GLSM correlation functions match for supermanifolds and hypersurfaces.

Physical two-sphere partition functions are identical for these target spaces.

Similar phenomena observed in elliptic genera and (0,2) deformations.

Abstract

In this paper we apply supersymmetric localization to study gauged linear sigma models (GLSMs) describing supermanifold target spaces. We use the localization method to show that A-twisted GLSM correlation functions for certain supermanifolds are equivalent to A-twisted GLSM correlation functions for hypersurfaces in ordinary spaces under certain conditions. We also argue that physical two-sphere partition functions are the same for these two types of target spaces. Therefore, we reproduce the claim of arXiv:hep-th/9404186, arXiv:hep-th/9506070. Furthermore, we explore elliptic genera and (0,2) deformations and find similar phenomena.