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The problematic backreaction of SUSY-breaking branes

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

TL;DR

This work critically evaluates the localisation of SUSY-breaking branes in a non-BPS $AdS_7\times S^3$ background of massive IIA with smeared ${D6}/{\overline{D6}}$-branes. By contrasting delta-function sources with regularised profiles, the authors derive a strong no-go: for a wide range of boundary conditions, fully localised branes cannot support a static flux vacuum, and the smeared solution is the unique regular brane profile. Their analysis, including a perturbative left-invariant stability check and a detailed localisation attempt, suggests that smeared constructions may not have reliable localised counterparts in non-BPS setups, with significant implications for de Sitter model-building in string theory. The results underscore the need for caution when employing smeared sources in non-BPS flux vacua and motivate further exploration of boundary conditions and generalised brane configurations.

Abstract

In this paper we investigate the localisation of SUSY-breaking branes which, in the smeared approximation, support specific non-BPS vacua. We show, for a wide class of boundary conditions, that there is no flux vacuum when the branes are described by a genuine delta-function. Even more, we find that the smeared solution is the unique solution with a regular brane profile. Our setup consists of a non-BPS AdS_7 solution in massive IIA supergravity with smeared anti-D6-branes and fluxes T-dual to ISD fluxes in IIB supergravity.

The problematic backreaction of SUSY-breaking branes

TL;DR

This work critically evaluates the localisation of SUSY-breaking branes in a non-BPS background of massive IIA with smeared -branes. By contrasting delta-function sources with regularised profiles, the authors derive a strong no-go: for a wide range of boundary conditions, fully localised branes cannot support a static flux vacuum, and the smeared solution is the unique regular brane profile. Their analysis, including a perturbative left-invariant stability check and a detailed localisation attempt, suggests that smeared constructions may not have reliable localised counterparts in non-BPS setups, with significant implications for de Sitter model-building in string theory. The results underscore the need for caution when employing smeared sources in non-BPS flux vacua and motivate further exploration of boundary conditions and generalised brane configurations.

Abstract

In this paper we investigate the localisation of SUSY-breaking branes which, in the smeared approximation, support specific non-BPS vacua. We show, for a wide class of boundary conditions, that there is no flux vacuum when the branes are described by a genuine delta-function. Even more, we find that the smeared solution is the unique solution with a regular brane profile. Our setup consists of a non-BPS AdS_7 solution in massive IIA supergravity with smeared anti-D6-branes and fluxes T-dual to ISD fluxes in IIB supergravity.

Paper Structure

This paper contains 17 sections, 55 equations, 5 figures.

Table of Contents

  1. Introduction
  2. A simple non-BPS setup on $AdS_7 \times S^3$
  3. Type IIA supergravity and smeared $D6/\overline{ D6}$-branes
  4. The smeared solution
  5. Perturbative stability
  6. The left-invariant closed string moduli
  7. Open string moduli
  8. Localisation
  9. The ansatz
  10. Delta-function sources
  11. Regularised sources
  12. Summary of results
  13. Discussion
  14. Smeared non-BPS solutions for general $d$ and $\eta$
  15. The ansatz
  16. ...and 2 more sections

Figures (5)

  • Figure 1: Configuration of a single $\overline{D6}$-brane and flux. The solid line corresponds to the usual boundary condition of a BPS $\overline{D6}$-brane, whereas the dashed lines represent more general boundary conditions consistent with net 'IASD' flux near the $\overline{D6}$-brane. Global tadpole cancellation then enforces the forbidden extrema marked by the crosses.
  • Figure 2: A configuration with a $\overline{D6}$-brane at each pole with assumed 'IASD' flux near the branes, again leading to forbidden extrema.
  • Figure 3: BPS configuration with orientifold-planes.
  • Figure 4: Alternative boundary conditions.
  • Figure 5: A brane source that is a step function.