# Understanding KKLT from a 10d perspective

## TL;DR

This paper critically examines the KKLT de Sitter vacuum construction in string theory from a 10-dimensional perspective, arguing that recent challenges based on 10d Einstein equations are not conclusive.

## Contribution

It relates 10d Einstein equations to 4d effective potential extremization and defends the consistency of KKLT uplift scenarios using a finite, perfect-square 10d action.

## Key findings

- The 10d Einstein equation relates to the 4d effective potential extremization.
- The 10d action with gaugino condensation is consistent and does not hinder uplift.
- KKLT de Sitter constructions are not invalidated by the integrated 10d equations.

## Abstract

Some of the most well-celebrated constructions of metastable de Sitter vacua from string theory, such as the KKLT proposal, involve the interplay of gaugino condensation on a D7-brane stack and an uplift by a positive tension object. These constructions have recently been challenged using arguments that rely on the trace-reversed and integrated 10d Einstein equation. We give a critical assessment of such concerns. We first relate an integrated 10d Einstein equation to the extremization condition for a 10d-derived 4d effective potential. Then we argue how to obtain the latter from a 10d action which incorporates gaugino condensation in a (recently proposed) manifestly finite, perfect-square form. This effective potential is consistent with 4d supergravity and does not present obstacles for an uplifted minimum. Moreover, within standard approximations, we understand the uplift explicitly in one of the popular versions of the integrated 10d equation. Our conclusion is that de Sitter constructions of the KKLT type cannot be dismissed simply based on the integrated 10d equations considered so far.