On T-folds, G-structures and Supersymmetry

TL;DR

This work develops a framework to determine the amount of supersymmetry preserved when Type II supergravity is compactified on T-folds, non-geometric backgrounds patched by T-duality transformations. It extends traditional G-structure-based SUSY counting to the non-geometric setting by introducing two distinct, field-dependent spin bundles for the left- and right-moving worldsheet sectors and deriving how supersymmetry parameters transform under T-duality. The authors illustrate their approach with explicit reductions on a $T^d$ fibration over $S^1$, showing that monodromies in $SO(d,d;\mathbb{Z})$ generate massive lower-dimensional supergravities and alter the possible amount of preserved SUSY. They propose a practical criterion based on singlets under the structure groups to count preserved supersymmetry in these T-fold reductions and discuss the implications for moduli and potential links to generalized geometry. Overall, the paper provides a concrete method to classify supersymmetry in non-geometric compactifications and lays groundwork for further connections to broader mathematical structures and phenomenological applications.

Abstract

We describe how to calculate the amount of supersymmetry associated to a class of supergravity theories obtained by compactification on T-folds. We illustrate our discussion by calculating the degree of supersymmetry enjoyed by a particular set of massive supergravities which have been obtained in the literature by compactifying type II supergravity on such backgrounds. Our discussion involves a modification of the usual arguments, based upon G-structures, for the amount of supersymmetry preserved by geometric compactifications.