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

Abstract

We study the situation when the T-dual of a toric K\"ahler geometry is a generalized K\"ahler 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 K\"ahler geometry of the $\eta$-deformed $\mathbb{CP}^{n-1}$ model, relating it to the K\"ahler geometry of its T-dual.