Dynamical Cobordism and Swampland Distance Conjectures

TL;DR

This paper explores how dynamical solutions in string theory with tadpoles relate to the Swampland Distance Conjecture, revealing new scaling relations and boundary behaviors that connect spacetime geometry with moduli space properties.

Contribution

It introduces a framework linking dynamical cobordism solutions to the Swampland Distance Conjecture, including new scaling relations and insights into boundary phenomena in string theory.

Findings

Scalar fields run to infinite distance near cobordism walls.

Walls at finite moduli space distance separate cobordant theories.

Explicit examples in massive IIA, M-theory, and non-supersymmetric strings support the framework.

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.