On the Existence of Meta-stable Vacua in Klebanov-Strassler

TL;DR

This paper investigates whether anti-D3 branes can create metastable vacua in the Klebanov-Strassler background, finding that the only consistent solutions involve singularities, which challenges the existence of such vacua.

Contribution

The authors provide a complete classification of linearized deformations of the Klebanov-Strassler background with anti-D3 branes and analyze their physical viability.

Findings

Only solutions with singular IR behavior are consistent with anti-D3 branes.

If the singularity is acceptable, it indicates a metastable vacuum; if not, such vacua likely do not exist.

The analysis introduces a universal force formula for probe D3-branes in this setup.

Abstract

We solve for the complete space of linearized deformations of the Klebanov-Strassler 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.