# K\"ahler moduli stabilization from ten dimensions

## TL;DR

This paper investigates how gaugino condensates influence Kähler moduli stabilization in supersymmetric AdS4 string compactifications, revealing that the cycle volume remains finite due to the cosmological constant, aligning with KKLT results.

## Contribution

It provides a ten-dimensional supergravity perspective on Kähler moduli stabilization, connecting geometric effects with the effective field theory approach of KKLT.

## Key findings

- Gaugino condensates prevent cycle shrinking in AdS compactifications.
- A relation between cycle size and cosmological constant is established.
- The results match KKLT's effective field theory predictions.

## Abstract

We describe the back-reaction of gaugino condensates in supersymmetric AdS$_4$ Type II String Theory compactifications with fluxes. We use generalized complex geometry to capture the modification of the ten-dimensional supersymmetry equations and show that the cosmological constant prevents the cycle wrapped by the branes with gaugino condensation from shrinking to zero size. Thus, unlike in ordinary geometric transitions in flat space, the volume of this cycle remains finite. For D7 branes with gaugino condensation, this gives a ten-dimensional account of K\"ahler moduli stabilization. Furthermore, by matching the ten-dimensional supergravity solutions near and far from the cycle wrapped by the D7 branes, we find a relation between the size of this cycle and the cosmological constant. This relation agrees with the supersymmetric AdS vacuum condition obtained by KKLT using effective field theory.