A note on T-folds and T3 fibrations

TL;DR

This paper investigates T-folds with T^3 fibrations, analyzing their geometric structure, monodromies, and the effects of winding sector corrections on local solutions within string theory.

Contribution

It provides a geometric model for T-folds with T^3 fibrations, linking duality monodromies to large diffeomorphisms of a four-torus, and discusses corrections from winding modes.

Findings

Derived the fibration data for T-folds from geometric models.

Described monodromies around duality defects and their effects.

Argued that winding sector corrections influence local solutions.

Abstract

We study stringy modifications of $T^3$-fibered manifolds, where the fiber undergoes a monodromy in the T-duality group. We determine the fibration data defining such T-folds from a geometric model, by using a map between the duality group and the group of large diffeomorphisms of a four-torus. We describe the monodromies induced around duality defects where such fibrations degenerate and we argue that local solutions receive corrections from the winding sector, dual to the symmetry-breaking modes that correct semi-flat metrics.