Fixing moduli in exact Type IIA flux vacua

TL;DR

This paper provides a detailed ten-dimensional analysis of Type IIA flux vacua with O6-planes, demonstrating exact solutions that stabilize all moduli and connect to previous four-dimensional effective theory results.

Contribution

It presents explicit ten-dimensional supersymmetric solutions for Type IIA flux compactifications with O6-planes, including both smooth and localized charge distributions, confirming moduli stabilization.

Findings

Exact supersymmetric solutions with stabilized moduli

Calabi-Yau geometry for smooth O6-charge distribution

Half-flat, non-Calabi-Yau geometry for localized case

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 supersymmetric solutions in the case when the O6-charge is smoothly distributed: the geometry is Calabi-Yau and the dilaton is constant. In the localized case, the solution is a half-flat, non-Calabi-Yau metric but still with constant dilaton. Finally, using the ten dimensional description we show how all moduli are stabilized and reproduce precisely the results of de Wolfe et al. Based on arXiv:hep-th/0607223.