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

Understand

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.