Doubled space and extended supersymmetry

TL;DR

This paper extends the doubled formulation of string theory to include $ ext{N}=(2,2)$ supersymmetry, providing a unified description of bi-Hermitian and generalized Kähler target spaces with explicit T-duality symmetry.

Contribution

It introduces a doubled-generalized Kähler potential framework for $ ext{N}=(2,2)$ supersymmetric string theories, incorporating T-duality explicitly.

Findings

Constructs a doubled $ ext{N}=(2,2)$ superspace formulation.

Provides examples including T-folds within this framework.

Demonstrates the manifest T-duality symmetry in supersymmetric models.

Abstract

The doubled formulation of the worldsheet provides a description of string theory in which T-duality is promoted to a manifest symmetry. Here we extend this approach to $\mathcal{N}=(2,2)$ superspace providing a doubled formulation for bi-Hermitian/generalised K\"ahler target spaces. The theory is described by a single function, a doubled-generalised K\"ahler potential, supplemented with a manifestly $\mathcal{N}=(2,2)$ constraint. Several examples serve to illustrate this construction, including a discussion of the $\mathcal{N}=(2,2)$ description of T-folds.