Nongeometry, Duality Twists, and the Worldsheet

TL;DR

The paper develops a worldsheet framework for nongeometric backgrounds produced by duality twists, using interpolating orbifolds to realize monodromies in the perturbative duality group. It shows that some backgrounds are pseudo asymmetric (dual to geometric ones) while others are truly asymmetric with no geometric dual, and it provides explicit modular-invariant partition functions for several cases including circle twists, $T^2$ fibrations, and monodromies with modular shifts. It discusses moduli fixing via monodromies, the role of boundary conditions, and subtle order- and sector-summation issues necessary for consistency, offering a path toward a broader classification and links to generalized geometry. The work thus tightens the bridge between spacetime duality twists and worldsheet CFT constructions, with implications for understanding nongeometric flux backgrounds in string theory.

Abstract

In this paper, we use orbifold methods to construct nongeometric backgrounds, and argue that they correspond to the spacetimes discussed in \cite{dh,wwf}. More precisely, we make explicit through several examples the connection between interpolating orbifolds and spacetime duality twists. We argue that generic nongeometric backgrounds arising from duality twists will not have simple orbifold constructions and then proceed to construct several examples which do have a consistent worldsheet description.