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

TL;DR

This paper explores the relationship between T-duality and generalized K"ahler geometry in toric manifolds within $ abla=(2, 2)$ superspace, highlighting the role of semi-chiral fields and gauge fields in this context.

Contribution

It demonstrates that T-duality often leads to generalized K"ahler geometries involving semi-chiral fields and introduces methods for gauging multiple isometries with semi-chiral gauge fields.

Findings

T-duality can produce generalized K"ahler geometries with semi-chiral fields.

Gauging multiple isometries requires semi-chiral gauge fields.

Application to $ ext{eta}$-deformed $ ext{CP}^{n-1}$ model links it to T-dual K"ahler geometry.

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.