Holography and the KKLT Scenario

TL;DR

This paper uses holography to argue that constructing the initial supersymmetric AdS vacuum in the KKLT string theory scenario is fundamentally impossible due to bounds on the AdS radius related to the internal Calabi-Yau geometry.

Contribution

It provides a holographic argument establishing a bound on the AdS radius, challenging the feasibility of the first step in the KKLT dS vacua construction.

Findings

Bound on AdS radius: $l_{AdS}^2 ot o ext{large}$

Relation between $l_{AdS}$ and Calabi-Yau Euler characteristic

Implication that the AdS vacuum would be highly curved and beyond EFT validity

Abstract

The KKLT scenario, one of the few ideas to realize dS vacua in string theory, consists of two steps: the first involves the construction of a supersymmetric AdS vacuum with a small negative cosmological constant, and the second involves breaking supersymmetry and uplifting the energy to achieve dS. In this paper we use conventional holography to argue why it is not possible to complete the first step. We obtain this by putting a bound on the central charge of the dual theory which involves branes wrapping special Lagrangian cycles in CY 4-folds. We find that $l_{\rm AdS}^2 \lesssim \chi(CY_4)$. Since $l_{\rm species}^2\gtrsim \chi(CY_4)$ this leads to $l_{\rm AdS}/l_{\rm species}\lesssim 1$ leading at best to a highly curved AdS which is beyond the validity of the EFT.