Fixing Moduli in Exact Type IIA Flux Vacua

TL;DR

The paper provides a concrete ten-dimensional realization of Type IIA flux vacua with $O6$-planes, showing that the exact localized solution is not Calabi–Yau but can be described by a half-flat $SU(3)$ structure, while a smeared approximation yields a Calabi–Yau background with flux. By solving the SUSY conditions and modified Bianchi identities, the authors demonstrate that all geometric moduli and B-axions are stabilized at tree level in AdS$_4$ vacua and recover the moduli-stabilization results of deWolfe et al. The work connects smeared CY solutions to localized, backreacted geometries and highlights a topology-change transition required when moving from smeared to localized sources. The analysis covers both a concrete example, the T^6/(Z3)^2 orientifold, and a general Calabi–Yau with fluxes, establishing a robust framework for moduli stabilization in exact ten-dimensional Type IIA flux vacua with O6-planes.

Abstract

Type IIA flux compactifications with O6-planes have been argued from a four dimensional effective theory point of view to admit stable, moduli free solutions. We discuss in detail the ten dimensional description of such vacua and present exact solutions in the case when the O6-charge is smoothly distributed. In the localised case, the solution is a half-flat, non-Calabi-Yau metric. Finally, using the ten dimensional description we show how all moduli are stabilised and reproduce precisely the results of de Wolfe et al.