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On classical de Sitter and Minkowski solutions with intersecting branes

David Andriot

TL;DR

This work analyzes classical de Sitter and Minkowski backgrounds in ten-dimensional type II supergravity with intersecting Dp/O_p sources, focusing on how the pattern of overlaps between different source sets constrains or enables solutions. It derives multiple expressions for the four-dimensional Ricci scalar R_4 by combining flux Bianchi identities and Einstein equations, yielding strong no-go results for de Sitter in several cases (notably p=7,8 and D3/O3/D7/O7 configurations) and revealing that intersecting sources introduce new, overlap-sensitive terms. For Minkowski solutions, the paper identifies structural features and proposes a calibration-inspired flux ansatz that may realize R_4=0, though full general solutions remain challenging; group-manifold geometries and homogeneous overlap play a key role in determining viability. Overall, the results highlight the central importance of how intersecting Dp/O_p stacks overlap in internal directions and how this overlap governs the existence and nature of classical de Sitter and Minkowski backgrounds, guiding future efforts in model-building and stability analyses.

Abstract

Motivated by the connection of string theory to cosmology or particle physics, we study solutions of type II supergravities having a four-dimensional de Sitter or Minkowski space-time, with intersecting Dp-branes and orientifold Op-planes. Only few such solutions are known, and we aim at a better characterisation. Modulo a few restrictions, we prove that there exists no classical de Sitter solution for any combination of D3/O3 and D7/O7, while we derive interesting constraints for intersecting D5/O5 or D6/O6, or combinations of D4/O4 and D8/O8. Concerning classical Minkowski solutions, we understand some typical features, and propose a solution ansatz. Overall, a central information appears to be the way intersecting Dp/Op overlap each other, a point we focus on.

On classical de Sitter and Minkowski solutions with intersecting branes

TL;DR

This work analyzes classical de Sitter and Minkowski backgrounds in ten-dimensional type II supergravity with intersecting Dp/O_p sources, focusing on how the pattern of overlaps between different source sets constrains or enables solutions. It derives multiple expressions for the four-dimensional Ricci scalar R_4 by combining flux Bianchi identities and Einstein equations, yielding strong no-go results for de Sitter in several cases (notably p=7,8 and D3/O3/D7/O7 configurations) and revealing that intersecting sources introduce new, overlap-sensitive terms. For Minkowski solutions, the paper identifies structural features and proposes a calibration-inspired flux ansatz that may realize R_4=0, though full general solutions remain challenging; group-manifold geometries and homogeneous overlap play a key role in determining viability. Overall, the results highlight the central importance of how intersecting Dp/O_p stacks overlap in internal directions and how this overlap governs the existence and nature of classical de Sitter and Minkowski backgrounds, guiding future efforts in model-building and stability analyses.

Abstract

Motivated by the connection of string theory to cosmology or particle physics, we study solutions of type II supergravities having a four-dimensional de Sitter or Minkowski space-time, with intersecting Dp-branes and orientifold Op-planes. Only few such solutions are known, and we aim at a better characterisation. Modulo a few restrictions, we prove that there exists no classical de Sitter solution for any combination of D3/O3 and D7/O7, while we derive interesting constraints for intersecting D5/O5 or D6/O6, or combinations of D4/O4 and D8/O8. Concerning classical Minkowski solutions, we understand some typical features, and propose a solution ansatz. Overall, a central information appears to be the way intersecting Dp/Op overlap each other, a point we focus on.

Paper Structure

This paper contains 18 sections, 79 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Formalities
  3. Deriving expressions for ${\cal R}_4$
  4. First derivation and no-go theorem for $p=7,8$
  5. Second derivation
  6. Second derivation
  7. No-go theorems for $p=4,5,6$
  8. First considerations and the $p=4$ case
  9. The case of homogeneous overlap
  10. On group manifolds
  11. Towards Minkowski solutions
  12. Foreword
  13. New derivation and comments
  14. Towards solutions
  15. Sources of multiple sizes: no-go theorem for $p=3\, \&\, 7$
  16. ...and 3 more sections

Figures (2)

  • Figure 1: Typical potential of a single field inflation model in agreement with observational constraints. The end-point is a stable de Sitter solution, while the inflation phase is almost an (unstable) de Sitter solution.
  • Figure 2: Each set $I=1,2$ is made of parallel $D_p/O_p$, and the different sets intersect each other. The $N=2$ sets have $N_o=1$ common (internal) direction, where their sources overlap.