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

Iosif Bena, Mariana Grana, Nick Halmagyi

TL;DR

The paper investigates whether anti-D3 branes in the KS background can backreact to produce a metastable vacuum by analyzing linearized, symmetry-preserving deformations around KS within the Papadopoulos-Tseytlin framework. Using the Borokhov-Gubser first-order formalism, the authors solve for the full space of perturbations, identify a single deformation parameter X1 that controls the force on a probe D3-brane, and show that requiring UV-consistent anti-D3 boundary conditions forces IR singularities in NS- and RR-flux densities. Depending on whether such IR singularities are deemed admissible, the work concludes either that a backreacted metastable KS vacuum exists (if the singularity is allowed) or that no metastable KS vacuum exists (if it is forbidden), with profound implications for KKLT-type constructions. The analysis also clarifies the role of ISD flux, the universal form of the probe-force, and the UV/IR structure of perturbations, offering a precise holographic handle on the metastability question in string theory.

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.

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

TL;DR

The paper investigates whether anti-D3 branes in the KS background can backreact to produce a metastable vacuum by analyzing linearized, symmetry-preserving deformations around KS within the Papadopoulos-Tseytlin framework. Using the Borokhov-Gubser first-order formalism, the authors solve for the full space of perturbations, identify a single deformation parameter X1 that controls the force on a probe D3-brane, and show that requiring UV-consistent anti-D3 boundary conditions forces IR singularities in NS- and RR-flux densities. Depending on whether such IR singularities are deemed admissible, the work concludes either that a backreacted metastable KS vacuum exists (if the singularity is allowed) or that no metastable KS vacuum exists (if it is forbidden), with profound implications for KKLT-type constructions. The analysis also clarifies the role of ISD flux, the universal form of the probe-force, and the UV/IR structure of perturbations, offering a precise holographic handle on the metastability question in string theory.

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 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.

Paper Structure

This paper contains 31 sections, 122 equations, 1 table.

Table of Contents

  1. Introduction
  2. Strategy and Results
  3. Perturbations around a supersymmetric solution
  4. The First Order Formalism
  5. Papadopoulos-Tseytlin ansatz for the perturbation
  6. The zero-th order solution: Klebanov-Strassler
  7. $\xi_i$ Equations
  8. $\phi^i$ Equations
  9. Imaginary (anti)-Self Duality of The Three Form Flux
  10. The Force on a Probe D3 Brane
  11. The Space of Solutions
  12. Solving the $\xi_i$ Equations for $X_1=0$
  13. Solution for $X_1 \neq 0$, UV and IR expansions
  14. Solving the $\phi^i$ Equations
  15. The Space of Solutions
  16. ...and 16 more sections