Control Issues of KKLT

Abstract

We analyze to which extent the KKLT proposal for the construction of de Sitter vacua in string theory is quantitatively controlled. Our focus is on the quality of the 10d supergravity approximation. As our main finding, we uncover and quantify an issue which one may want to call the "singular-bulk problem". In particular, we show that, requiring the curvature to be small in the conifold region, one is generically forced into a regime where the warp factor becomes negative in a significant part of the Calabi-Yau orientifold. This implies true singularities, independent of the familiar, string-theoretically controlled singularities of this type in the vicinity of O-planes. We also discuss possible escape routes as well as other control issues, related to the need for a large tadpole and hence for a complicated topology.

On de Sitter string vacua from anti-d3-branes in the large volume scenario

“…More recently a new kind of potential singularity, named bulk singularity, was identified [59] (see also [60]). This corresponds to the fact that the picture of a CY with warped throat is consistent if the size R throat of the region that is warped is smaller than the radius R CY of the CY.…”

Moduli Stabilization with Non‐Geometric Fluxes — Comments on Tadpole Contributions and de‐Sitter Vacua

“…In Equation () we have defined tadpole charges , which play an important role for moduli stabilization. They connect the open‐ and closed‐string sectors to each other and give rise to strong restrictions (see for instance [39–47] for recent discussions of this question). In this section we present arguments that the should contribute to the tadpole cancellation conditions () in the same way as D‐branes and not as anti‐D‐branes.…”

“…Such configurations exists – but these usually have a complicated topology and hence a large number of moduli have to be stabilized. Problems related to the latter issue have been discussed recently for instance in [44–46]. …”

Oh, wait, O8 de Sitter may be unstable!

“…where γ α are 9-dimensional purely-imaginary γ-matrices with Minkowskian signature. 12 With these conventions, the 10d chirality matrix can be written as:…”

“…An efficient way to construct such vacua is to use an effective four-dimensional theory that incorporates String-Theory ingredients [2]. However, the embedding of these ingredients in the full String Theory and their interactions therein are nontrivial, and have opened a rich debate about the validity of these constructions [3][4][5][6][7][8][9][10][11][12]. In parallel to these top-down investigations, there also exist bottom-up arguments and conjectures suggesting that metastable String-Theory compactifications with a positive cosmological constant cannot be constructed [13][14][15][16].…”