Flux backgrounds from Twists

TL;DR

The paper develops a coordinate‑dependent $O(d,d)$ twist within Generalized Geometry to directly relate flux backgrounds with different topology, including IIB nilmanifold compactifications and heterotic torsional backgrounds. By acting on generalized vielbeins and pure spinors, the authors derive explicit transformations of the metric, $B$‑field, dilaton, and RR/NS fluxes, and demonstrate SUSY‑preserving mappings between ${\cal B}\times \mathbb{T}^n$ and twisted fibrations. The work provides concrete examples (e.g., mapping $\mathbb{T}^6$ with O3 to nilmanifolds with O5/D5, and relating heterotic $SU(3)$ structures) and discusses iterated twists that generate further nilmanifolds, while situating these twists in the Courant bracket framework as coordinate‑dependent automorphisms. It shows that such twists extend the conventional $O(n,n;\mathbb{Z})$ dualities, enabling topology change and new links in the landscape of flux compactifications, including NSNS–RR mixing and gauge‑bundle transformations. The results offer a direct, geometric mechanism for transitioning between apparently distinct supersymmetric backgrounds and highlight the broader symmetry structure behind flux compactifications.

Abstract

It is well known that a constant O(n,n,Z) transformation can relate different string backgrounds with n commuting isometries that have very different geometric and topological properties. Here we construct discrete families of (flux) backgrounds on internal manifolds of different topologies by performing certain coordinate dependent O(d,d) transformations, where d is the dimension of the internal manifold. Our two principal examples include respectively the family of type IIB compactifications with D5 branes and O5 planes on six-dimensional nilmanifolds, and the heterotic torsional backgrounds.