Topological Sigma Models On Supermanifolds

TL;DR

This paper develops topological sigma models for maps from super Riemann surfaces to supermanifolds, defining A and B models with BRST symmetry and computing correlation functions via supersymmetric localization.

Contribution

It introduces a general framework for topological sigma models on supermanifolds, including definitions of A and B models and their correlation functions using supergeometry.

Findings

Correlation functions expressed as integrals over supermoduli space

Formulation of A and B models on super Riemann surfaces

Use of supergeometry to analyze topological field theories

Abstract

This paper concerns constructing topological sigma models governing maps from semirigid super Riemann surfaces to general target supermanifolds. We define both the A model and B model in this general setup by defining suitable BRST operators and physical observables. Using supersymmetric localization, we express correlation functions in these theories as integrals over suitable supermanifolds. In the case of the A model, we obtain an integral over the supermoduli space of "superinstantons". The language of supergeometry is used extensively throughout this paper.