Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Dynamical Cobordism and Swampland Distance Conjectures

Ginevra Buratti, José Calderón-Infante, Matilda Delgado, Angel M. Uranga

Abstract

We consider spacetime-dependent solutions to string theory models with tadpoles for dynamical fields, arising from non-trivial scalar potentials. The solutions have necessarily finite extent in spacetime, and are capped off by boundaries at a finite distance, in a dynamical realization of the Cobordism Conjecture. We show that as the configuration approaches these cobordism walls of nothing, the scalar fields run off to infinite distance in moduli space, allowing to explore the implications of the Swampland Distance Conjecture. We uncover new interesting scaling relations linking the moduli space distance and the SDC tower scale to spacetime geometric quantities, such as the distance to the wall and the scalar curvature. We show that walls at which scalars remain at finite distance in moduli space correspond to domain walls separating different (but cobordant) theories/vacua; this still applies even if the scalars reach finite distance singularities in moduli space, such as conifold points. We illustrate our ideas with explicit examples in massive IIA theory, M-theory on CY threefolds, and 10d non-supersymmetric strings. In 4d $\mathcal{N}=1$ theories, our framework reproduces a recent proposal to explore the SDC using 4d string-like solutions.

Dynamical Cobordism and Swampland Distance Conjectures

Abstract

We consider spacetime-dependent solutions to string theory models with tadpoles for dynamical fields, arising from non-trivial scalar potentials. The solutions have necessarily finite extent in spacetime, and are capped off by boundaries at a finite distance, in a dynamical realization of the Cobordism Conjecture. We show that as the configuration approaches these cobordism walls of nothing, the scalar fields run off to infinite distance in moduli space, allowing to explore the implications of the Swampland Distance Conjecture. We uncover new interesting scaling relations linking the moduli space distance and the SDC tower scale to spacetime geometric quantities, such as the distance to the wall and the scalar curvature. We show that walls at which scalars remain at finite distance in moduli space correspond to domain walls separating different (but cobordant) theories/vacua; this still applies even if the scalars reach finite distance singularities in moduli space, such as conifold points. We illustrate our ideas with explicit examples in massive IIA theory, M-theory on CY threefolds, and 10d non-supersymmetric strings. In 4d theories, our framework reproduces a recent proposal to explore the SDC using 4d string-like solutions.

Paper Structure

This paper contains 14 sections, 72 equations, 3 figures.

Table of Contents

  1. Introduction and Conclusions
  2. Cobordism walls in massive IIA theory
  3. Cobordism walls in M-theory on CY3
  4. M-theory on CY3 with $G_4$ flux
  5. Traveling across finite distance singularities in moduli space
  6. ${\bf {S}}^1$ compactification of 4d ${\cal {N}}=1$ theories and EFT strings
  7. Cobordism walls in 4d ${\cal {N}}=1$ theories on a circle
  8. Comparison with EFT strings
  9. 4d ${\cal {N}}=1$ theories with flux-induced superpotentials
  10. Walls in 10d non-supersymmetric strings
  11. Final remarks
  12. Holographic examples
  13. Domain wall to a new vacuum
  14. Domain wall to a new running solution

Figures (3)

  • Figure 1: Domain wall interpolating between the conifold theory with fractional branes, and an AdS vacuum. Figure a) shows a heuristic intermediate step of a KS solution with a number $P$ of left-over probe D3-branes. If $P$ is large, the appropriate description requires including the backreaction of the D3-branes, which lead to a further AdS throat, to the left of the picture in Figure b). Hence the running of the dynamical tadpole in the right hand side ends in a domain wall separating it from an AdS vacuum.
  • Figure 2: The quiver and dimer diagrams describing the gauge theory on D3-branes at the tip of the complex cone over $dP_3$.
  • Figure 3: a) Web diagram of the complex cone over $dP_3$ splitting into three sub-webs. b) Rank assignment (fractional branes) that trigger those complex deformations.