Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Polchinski-Strassler does not uplift Klebanov-Strassler

Iosif Bena, Mariana Grana, Stanislav Kuperstein, Stefano Massai

TL;DR

This work analyzes the backreaction of smeared anti-D3 branes in the KS background and shows that IR three-form flux singularities cannot be resolved by Polchinski-Strassler-type polarization into D5 branes wrapping the conifold's $S^2$. By employing the Papadopoulos-Tseytlin ansatz and a two-fold first-order formalism with conjugate momenta $oldsymbol{\xi}$, it proves that no IR-regular solution exists that connects to KS in the UV; a global argument and a detailed irreguar analysis confirm the same obstruction. The D5 polarization potential for a probe D5 with dissolved anti-D3 charge has no metastable minimum for any IR data, indicating that brane polarization does not cure the singularity and that anti-D3 uplifting of AdS to dS is unlikely in this setup. The results strengthen the view that anti-branes in flux backgrounds do not yield metastable vacua and call for alternative uplift mechanisms. Overall, the paper provides a robust no-go for polarization-based resolution and emphasizes the need to reassess claims of a large dS landscape in string theory.

Abstract

Anti-D3-branes at the tip of the Klebanov-Strassler solution with D3-charge dissolved in fluxes give rise, in the probe approximation, to a metastable state. The fully back-reacted smeared solution has singular three-form fluxes in the IR, whose presence suggests a stringy resolution by brane polarization a la Polchinski-Strassler. In this paper we show that there is no polarization into anti-D5-branes wrapping the $S^2$ of the conifold at a finite radius. The singularities therefore do not seem to be physical, signaling that antibranes cannot be used to uplift AdS and obtain a very large landscape of de Sitter vacua in string theory.

Polchinski-Strassler does not uplift Klebanov-Strassler

TL;DR

This work analyzes the backreaction of smeared anti-D3 branes in the KS background and shows that IR three-form flux singularities cannot be resolved by Polchinski-Strassler-type polarization into D5 branes wrapping the conifold's . By employing the Papadopoulos-Tseytlin ansatz and a two-fold first-order formalism with conjugate momenta , it proves that no IR-regular solution exists that connects to KS in the UV; a global argument and a detailed irreguar analysis confirm the same obstruction. The D5 polarization potential for a probe D5 with dissolved anti-D3 charge has no metastable minimum for any IR data, indicating that brane polarization does not cure the singularity and that anti-D3 uplifting of AdS to dS is unlikely in this setup. The results strengthen the view that anti-branes in flux backgrounds do not yield metastable vacua and call for alternative uplift mechanisms. Overall, the paper provides a robust no-go for polarization-based resolution and emphasizes the need to reassess claims of a large dS landscape in string theory.

Abstract

Anti-D3-branes at the tip of the Klebanov-Strassler solution with D3-charge dissolved in fluxes give rise, in the probe approximation, to a metastable state. The fully back-reacted smeared solution has singular three-form fluxes in the IR, whose presence suggests a stringy resolution by brane polarization a la Polchinski-Strassler. In this paper we show that there is no polarization into anti-D5-branes wrapping the of the conifold at a finite radius. The singularities therefore do not seem to be physical, signaling that antibranes cannot be used to uplift AdS and obtain a very large landscape of de Sitter vacua in string theory.

Paper Structure

This paper contains 18 sections, 53 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The setup
  3. The Papadopoulos-Tseytlin Ansatz
  4. The KS and anti-KS solutions
  5. The first-order formalism
  6. A regular solution does not exist
  7. Regular boundary conditions for anti-D3 branes
  8. The first proof
  9. The second proof
  10. The singular anti-D3 solution
  11. D5 polarization
  12. The D5 potential
  13. The mean field argument
  14. Validity of approximations
  15. Discussion
  16. ...and 3 more sections

Figures (2)

  • Figure 1: Left: localized anti-D3 branes at the north pole of the $S^3$ can polarize into a NS5 brane wrapping a two sphere $S^2 \subset S^3$ and into a D5 brane wrapping the shrinking $S^2$ of the conifold. Right: smearing the anti-D3 branes on the $S^3$ wipes out the KPV channel but the D5 channel still survives.
  • Figure 2: The function $\xi_1(\tau)$ is positive for small $\tau$ but cannot have a zero (left) at finite $\tau=\tau_\star$, since $\dot{\xi}_1(\tau) < 0$ is not allowed. As a consequence, it will be everywhere positive (right). Notice that it goes to zero at infinity, otherwise we do not get asymptotic KS solution.