Geometric and Non-Geometric Compactifications of IIB Supergravity

TL;DR

This work analyzes both geometric and non-geometric compactifications of IIB supergravity. It develops a Scherk–Schwarz framework on identified group manifolds ${\cal X}=G/\Gamma$, yielding a gauge theory with a Lie algebroid structure and flux-induced moduli potentials, and it systematically studies the accompanying symmetry breaking and mass generation. It then extends the analysis to nine-dimensional reductions with S‑duality twists, showing how duality-covariant gaugings arise and how certain vacua yield massless graviphotons, with a clear link to F‑Theory through non-geometric twists. Together, the results illuminate how IIB reductions can realize both geometric, algebroid-based gauge structures and non-geometric backgrounds that admit F‑Theory interpretations, with implications for moduli stabilization and duality in lower dimensions.

Abstract

Complimentary geometric and non-geometric consistent reductions of IIB supergravity are studied. The geometric reductions on the identified group manifold X are found to have a gauge symmetry with Lie algebroid structure, generalising that found in similar reductions of the Bosonic string theory and eleven-dimensional supergravity. Examples of such compactifications are considered and the symmetry breaking in each case is analysed. Complimentary to the reductions on X are the nine-dimensional S-duality twisted reductions considered in the second half of the paper. The general reduced theory is given and symmetry breaking is investigated. The non-geometric S-duality twisted reductions and their relation to geometric reductions of F-Theory on X is briefly discussed.