Lectures on Nongeometric Flux Compactifications

TL;DR

The notes argue that nongeometric fluxes, generated by T-duality from familiar NS-NS flux backgrounds, are essential components of string compactifications. They develop a duality-invariant superpotential that incorporates geometric and nongeometric fluxes, enabling stabilization of all moduli in a broad class of backgrounds, and they connect these four-dimensional theories to worldsheet descriptions via asymmetric orbifolds and Hull's doubled torus. The work highlights the H→f→Q→R flux chain, the associated Bianchi-like constraints, and the challenges and prospects of fully embedding such backgrounds in string theory. It emphasizes that understanding nongeometric fluxes—especially the mysterious R flux—and extending these ideas beyond toroidal cases are important directions for future research.

Abstract

These notes present a pedagogical review of nongeometric flux compactifications. We begin by reviewing well-known geometric flux compactifications in Type II string theory, and argue that one must include nongeometric "fluxes" in order to have a superpotential which is invariant under T-duality. Additionally, we discuss some elementary aspects of the worldsheet description of nongeometric backgrounds. This review is based on lectures given at the 2007 RTN Winter School at CERN.