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(Anti-)Brane backreaction beyond perturbation theory

Johan Blåbäck, Ulf H. Danielsson, Daniel Junghans, Thomas Van Riet, Timm Wrase, Marco Zagermann

TL;DR

This work analyzes the full nonperturbative backreaction of anti-D6-branes in a flux background that is mutually BPS with D6-branes, avoiding both brane smearing and perturbative expansions. By leveraging a SO(3) symmetric localised ansatz and a near-brane expansion, the authors reduce the problem to a set of ODEs and systematically classify the possible boundary conditions allowed by the equations of motion. A topological constraint from previous work rules out most boundary data, leaving a unique non-standard boundary condition that evades the constraint and features a diverging but integrable $H$ flux energy density, $e^{-\phi} H^2 \propto \theta^{-1/8}$. The results suggest that fully backreacted anti-brane configurations generically exhibit flux singularities not directly sourced by the branes, pointing to either open-string resolutions via brane-flux transitions or a fundamental dynamical instability that challenges anti-brane uplifting scenarios in KS-like geometries.

Abstract

We improve on the understanding of the backreaction of anti-D6-branes in a flux background that is mutually BPS with D6-branes. This setup is analogous to the study of the backreaction of anti-D3-branes inserted in the KS throat, but does not require us to smear the anti-branes or do a perturbative analysis around the BPS background. We solve the full equations of motion near the anti-D6-branes and show that only two boundary conditions are consistent with the equations of motion. Upon invoking a topological argument we eliminate the boundary condition with regular H flux since it cannot lead to a solution that approaches the right kind of flux away from the anti-D6-brane. This leaves us with a boundary condition which has singular, but integrable, H flux energy density.

(Anti-)Brane backreaction beyond perturbation theory

TL;DR

This work analyzes the full nonperturbative backreaction of anti-D6-branes in a flux background that is mutually BPS with D6-branes, avoiding both brane smearing and perturbative expansions. By leveraging a SO(3) symmetric localised ansatz and a near-brane expansion, the authors reduce the problem to a set of ODEs and systematically classify the possible boundary conditions allowed by the equations of motion. A topological constraint from previous work rules out most boundary data, leaving a unique non-standard boundary condition that evades the constraint and features a diverging but integrable flux energy density, . The results suggest that fully backreacted anti-brane configurations generically exhibit flux singularities not directly sourced by the branes, pointing to either open-string resolutions via brane-flux transitions or a fundamental dynamical instability that challenges anti-brane uplifting scenarios in KS-like geometries.

Abstract

We improve on the understanding of the backreaction of anti-D6-branes in a flux background that is mutually BPS with D6-branes. This setup is analogous to the study of the backreaction of anti-D3-branes inserted in the KS throat, but does not require us to smear the anti-branes or do a perturbative analysis around the BPS background. We solve the full equations of motion near the anti-D6-branes and show that only two boundary conditions are consistent with the equations of motion. Upon invoking a topological argument we eliminate the boundary condition with regular H flux since it cannot lead to a solution that approaches the right kind of flux away from the anti-D6-brane. This leaves us with a boundary condition which has singular, but integrable, H flux energy density.

Paper Structure

This paper contains 12 sections, 77 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Review of previous results
  3. The smeared solution
  4. The ansatz for the localised solution
  5. A topological constraint
  6. Boundary conditions
  7. Summary and interpretation of results
  8. Type IIA supergravity with $D6/\overline{ D6}$-branes
  9. Determining the boundary conditions
  10. Leading order behaviour
  11. Sub-leading order behaviour
  12. Determining the sources

Figures (1)

  • Figure 1: a) This plot shows the boundary conditions (\ref{['bc3']}) that evade the constraint \ref{['eq:topological']} provided that $\alpha(0)>0$ (solid line). For $\alpha(0)<0$ (dashed line), boundary condition (\ref{['bc3']}) would not work, because $\alpha$ would have to violate \ref{['eq:topological']} in order to become positive to cancel the global $\overline{D6}$ tadpole. b) This plot shows that the usual BPS boundary conditions near the $\overline{D6}$ are likewise excluded due to the forbidden extrema (crosses) that would be necessary to ensure overall tadpole cancellation.