Flux Compactifications of String Theory on Twisted Tori

TL;DR

This work reframes Scherk–Schwarz dimensional reductions as compactifications on compact group-manifold quotients ${\cal G}/\Gamma$, enabling consistent truncations and mass gaps when cocompact discrete subgroups exist. It extends the framework to string theory by including flux on twisted tori, yielding an ${O(d,d)}$-covariant low-energy theory in the common sector and clarifying how the gauge algebra emergent from flux and twists is embedded in $O(d,d)$ and how it breaks spontaneously. The paper also analyzes reductions with duality twists, distinguishing geometric twists (reducible to twisted tori) from non-geometric twists, and presents explicit ${SL}(2)$-twist examples to illustrate the landscape of possible backgrounds. It provides a detailed gauge-algebra analysis, showing how fluxes alter the commutators and mass spectrum, and outlines how these results generalize to M-theory and F-theory contexts, with discussion of the interplay between gauge symmetry and T-duality. Overall, the results unify warped reductions, flux compactifications, and duality twists within a covariant group-theoretic framework and illuminate the conditions under which such reductions yield consistent, mass-gapped string backgrounds.

Abstract

Global aspects of Scherk-Schwarz dimensional reduction are discussed and it is shown that it can usually be viewed as arising from a compactification on the compact space obtained by identifying a (possibly non-compact) group manifold G under a discrete subgroup Gamma, followed by a truncation. This allows a generalisation of Scherk-Schwarz reductions to string theory or M-theory as compactifications on G/Gamma, but only in those cases in which there is a suitable discrete subgroup of G. We analyse such compactifications with flux and investigate the gauge symmetry and its spontaneous breaking. We discuss the covariance under O(d,d), where d is the dimension of the group G, and the relation to reductions with duality twists. The compactified theories promote a subgroup of the O(d,d) that would arise from a toroidal reduction to a gauge symmetry, and we discuss the interplay between the gauge symmetry and the O(d,d,Z) T-duality group, suggesting the role that T-duality should play in such compactifications.