Holography and the KKLT scenario
Severin Lüst, Cumrun Vafa, Max Wiesner, Kai Xu
Abstract
A bstract 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 $$ {l}_{\textrm{AdS}}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>l</mml:mi> <mml:mi>AdS</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> ≲ χ ( CY 4 ). Since $$ {l}_{\textrm{species}}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>l</mml:mi> <mml:mtext>species</mml:mtext> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> ≳ χ ( CY 4 ) this leads to l AdS /l species ≲ 1 leading at best to a highly curved AdS which is beyond the validity of the EFT.