  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.
