Supersymmetric localization in GLSMs for supermanifolds

2018/07/31 by Wei Gu, Hao Zou
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #Partition function (quantum field theory) #Sigma #Sigma model #Supermanifold #Superpotential #Supersymmetry #hep-th

paper · pdf · doi:10.1007/jhep05(2019)019

31 pages, no figures

openalex created_date 2018/08/03 · arxiv created 2019/04/29 · openalex publication_date 2019/05/01 · arxiv updated 2019/05/22 · openalex updated_date 2026/08/05

Abstract

A bstract 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 [1, 2]. Furthermore, we explore elliptic genera and (0,2) deformations and find similar phenomena.

Citations

• Supermanifolds, Rigid Manifolds and Mirror Symmetry
• Sigma-models having supermanifolds as target spaces
• A topologically twisted index for three-dimensional supersymmetric theories
• Superconformal symmetry in linear sigma model on supermanifolds
• Phases of N = 2 theories in two dimensions
• Notes on Certain (0,2) Correlation Functions
• Comments on N N = (2, 2) supersymmetry on two-manifolds