# de Sitter Vacua from Ten Dimensions

## TL;DR

This paper rigorously derives de Sitter vacua in string theory from ten-dimensional supergravity, confirming the consistency of the KKLT construction with the ten-dimensional equations of motion.

## Contribution

It provides an exact ten-dimensional derivation of de Sitter vacua, validating the KKLT scenario through detailed supergravity analysis.

## Key findings

- Exact agreement between ten-dimensional and four-dimensional descriptions.
- Derivation of stress-energy from gaugino condensation on D7-branes.
- Confirmation that anti-D3-branes and gaugino effects produce consistent de Sitter solutions.

## Abstract

We analyze the de Sitter construction of \cite{KKLT} using ten-dimensional supergravity, finding exact agreement with the four-dimensional effective theory. Starting from the fermionic couplings in the D7-brane action, we derive the ten-dimensional stress-energy due to gaugino condensation on D7-branes. We demonstrate that upon including this stress-energy, as well as that due to anti-D3-branes, the ten-dimensional equations of motion require the four-dimensional curvature to take precisely the value determined by the four-dimensional effective theory of \cite{KKLT}.