Nongeometric Flux Compactifications

TL;DR

This paper extends flux compactifications to include nongeometric NS-NS fluxes, constructing a T-duality–invariant four-dimensional superpotential for type II theories on a symmetric T^6. By incorporating geometric, H-flux, and nongeometric Q and R fluxes, the authors demonstrate a duality-consistent mapping between IIA and IIB vacua and propose a framework that potentially generalizes mirror symmetry to backgrounds with arbitrary H-flux. They derive explicit tadpole and Bianchi-type constraints, discuss the physical interpretation of Q- and R-fluxes as nongeometric data, and outline future directions toward a fully U-duality invariant description and a broader understanding of the string landscape.

Abstract

We investigate a simple class of type II string compactifications which incorporate nongeometric "fluxes" in addition to "geometric flux" and the usual H-field and R-R fluxes. These compactifications are nongeometric analogues of the twisted torus. We develop T-duality rules for NS-NS geometric and nongeometric fluxes, which we use to construct a superpotential for the dimensionally reduced four-dimensional theory. The resulting structure is invariant under T-duality, so that the distribution of vacua in the IIA and IIB theories is identical when nongeometric fluxes are included. This gives a concrete framework in which to investigate the possibility that generic string compactifications may be nongeometric in any duality frame. The framework developed in this paper also provides some concrete hints for how mirror symmetry can be generalized to compactifications with arbitrary H-flux, whose mirrors are generically nongeometric.