Curvature Couplings in $\mathcal{N}=(2,2)$ Nonlinear Sigma Models on $S^2$

TL;DR

This paper investigates curvature couplings in two-dimensional  supersymmetric nonlinear sigma models on a sphere, highlighting differences from four-dimensional theories and discussing topological twists.

Contribution

It derives curvature couplings for  sigma models with superpotential on S^2, expanding understanding of supersymmetric theories on curved backgrounds.

Findings

Curvature couplings depend on target space geometry.

No constraints on Kahler forms in 2D theories, unlike 4D.

Discussion of topological twist issues.

Abstract

Following recent work on GLSM localization, we work out curvature couplings for rigidly supersymmetric nonlinear sigma models with superpotential for general target spaces, describing both ordinary and twisted chiral superfields on round two-sphere worldsheets. We briefly discuss why, unlike four-dimensional theories, there are no constraints on Kahler forms in these theories. We also briefly discuss general issues in topological twists of such theories.