T-duality for toric manifolds in $\mathcal{N}=(2, 2)$ superspace

We study the situation when the T-dual of a toric Kähler geometry is a generalized Kähler geometry involving semi-chiral fields. We explain that this situation is generic for polycylinders, tori and related geometries. Gauging multiple isometries in this case requires the introduction of semi-chiral gauge fields on top of the standard ones. We then apply this technology to the generalized Kähler geometry of the $η$-deformed $\mathbb{CP}^{n-1}$ model, relating it to the Kähler geometry of its T-dual.

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