Semichiral Fields on S^2 and Generalized K\"ahler Geometry

TL;DR

This paper investigates 2D N=(2,2) supersymmetric gauge theories with semichiral multiplets, computes their S^2 partition functions via localization, and explores their connection to generalized K"ahler geometry with flux.

Contribution

It provides the first exact localization computation for theories with semichiral multiplets and links these to generalized K"ahler target spaces with flux.

Findings

Instanton contributions are deformation-insensitive.

Partition functions encode generalized K"ahler geometry.

Results extend understanding of supersymmetric gauge theories on curved spaces.

Abstract

We study a class of two-dimensional N=(2,2) supersymmetric gauge theories, given by semichiral multiplets coupled to the standard vector multiplet. In the UV, these theories are traditional gauge theories deformed by a gauged Wess-Zumino term. In the IR, they give rise to nonlinear sigma models on noncompact generalized K\"ahler manifolds, which contain a three-form flux H and whose metric is not K\"ahler. We place these theories on S^2 and compute their partition function exactly with localization techniques. We find that the contribution of instantons to the partition function that we define is insensitive to the deformation, and discuss our results from the point of view of the generalized K\"ahler target space.