On the existence of meta-stable vacua in Klebanov-Strassler

Abstract

We solve for the complete space of linearized deformations of the KlebanovStrassler background consistent with the symmetries preserved by a stack of anti-D3 branes smeared on the S 3 of the deformed conifold. We find that the only solution whose UV physics is consistent with that of a perturbation produced by anti-D3 branes must have a singularity in the infrared, coming from NS and RR three-form field strengths whose energy density diverges. If this singularity is admissible, our solution describes the backreaction of the anti-D3 branes, and is thus likely to be dual to the conjectured metastable vacuum in the Klebanov-Strassler field theory. If this singularity is not admissible, then our analysis strongly suggests that anti-D3 branes do not give rise to metastable Klebanov-Strassler vacua, which would have dramatic consequences for some string theory constructions of de Sitter space. Key to this result is a simple, universal form for the force on a probe D3-brane in our ansatz.

Inflation and String Theory

“…The linearized solution describing p anti-D3-branes smeared around the tip of a Klebanov-Strassler throat has been obtained in [427,429,430], and passes multiple consistency checks [428,439]. The three-form flux in this solution is singular near the source [427].…”

“…The idea of antibrane uplifting has recently been challenged [427]. In particular, it was observed that the known, approximate solutions for p anti-D3-branes in a KS background are singular.…”

“…If one could establish that the corresponding full, exact solution manifests unphysical singularities, this would imply that anti-D3-branes in a KS throat do not provide a consistent metastable supersymmetry-breaking configuration. To discuss this important point [427][428][429][430][431][432][433][434][435][436][437][438][439][440][441], we first have to explain the sense in which the known solutions are approximations (see also §4.1.4).…”

“…Of course, the divergence in the energy of the electric field is removed in the quantum theory. The question, then, is whether the singularities seen in [427,429,430] are expected, and therefore plausibly resolved in the exact solution. A central concern raised by [427] is that the singularities in three-form flux "do not appear to have a distinct physical origin" [427].…”

“…The question, then, is whether the singularities seen in [427,429,430] are expected, and therefore plausibly resolved in the exact solution. A central concern raised by [427] is that the singularities in three-form flux "do not appear to have a distinct physical origin" [427]. That is, according to [427] it is not obvious how the anti-D3-brane can serve as a source for singular three-form flux, and correspondingly these singularities are unexpected.…”