Moduli Stabilization in Non-Geometric Backgrounds

TL;DR

Becker–Becker–Vafa–Walcher show that in type IIB string theory, fluxes can stabilize all complex-structure moduli and the dilaton in non-geometric LG backgrounds, yielding Minkowski or AdS vacua with no Kahler moduli. They formulate a concrete flux framework via the Gukov–Vafa–Witten superpotential $W = \int G \wedge \Omega$ and prove a non-renormalization theorem ensuring $W$ is exact to all orders, enabling explicit, fully stabilized vacua at $g_s \sim O(1)$. The authors construct and solve explicit SUSY equations subject to tadpole cancellation in two Gepner-model examples, 1^9 (Minkowski) and 2^6 (AdS/Kahler-free), providing detailed flux configurations and brane/orientifold data. Their results demonstrate that moduli stabilization can occur without geometric moduli, offering new, highly symmetric vacua and suggesting further connections to the landscape and mirror-symmetric AdS constructions in the presence of fluxes. Overall, the work presents the first explicit realizations of all-moduli stabilization by fluxes in non-geometric backgrounds, with potential implications for phenomenology and the understanding of string vacua.

Abstract

Type II orientifolds based on Landau-Ginzburg models are used to describe moduli stabilization for flux compactifications of type II theories from the world-sheet CFT point of view. We show that for certain types of type IIB orientifolds which have no Kahler moduli and are therefore intrinsically non-geometric, all moduli can be explicitly stabilized in terms of fluxes. The resulting four-dimensional theories can describe Minkowski as well as Anti-de-Sitter vacua. This construction provides the first string vacuum with all moduli frozen and leading to a 4D Minkowski background.

Figures (1)

• Figure 1: The piece of cake picture of Lagrangian (A-type) D-branes in LG model $x^3$.