Sharpened Dynamical Cobordism

TL;DR

This paper refines the concept of Dynamical Cobordism by linking the physical structure of a theory to the allowed critical exponents, providing a criterion to distinguish true transitions from obstructions, with applications to string theory and black hole solutions.

Contribution

It introduces a sharpened version of Dynamical Cobordism that determines allowed ranges of critical exponents based on the physical structure, incorporating higher-form gauge fields and testing against various examples.

Findings

The allowed range of critical exponents changes with the inclusion of higher-form gauge fields.

The sharpened conjecture aligns with known string theory configurations like O8-planes.

It successfully applies to black hole solutions and D-brane distributions, confirming its consistency.

Abstract

We propose a sharpened version of Dynamical Cobordism, where the physical structure $\xi$ of the theory in question determines an allowed range $R^\xi$ for the critical exponent $\delta$. We interpret a singularity with $\delta \in R^\xi$ as a true transition-to-nothing, i.e., a configuration ending spacetime, while a singularity with $\delta \notin R^\xi$ indicates some obstruction to such a transition, i.e., the presence of a non-trivial cobordism global charge, which is incompatible with a theory of quantum gravity. In the spirit of the original Cobordism Conjecture, this apparent inconsistency of the theory can be alleviated via the modification of the structure, for instance by introducing new degrees of freedom and associated defects. Inspired by the Gubser criterion for good singularities, we propose a way to determine $R^\xi$. As a proof-of-concept we show explicitly how the introduction of a higher-form gauge field changes the allowed range of $\delta$ compared to an EFT with only scalars. We test this sharpened version of Dynamical Cobordism against several examples, such as massive IIA string theory, where it is notably compatible with the presence of O8-planes; the Janis-Newman-Winicour and Garfinkle-Horowitz-Strominger black hole solutions; and certain singular distributions of D-branes. In all these cases, the Sharpened Dynamical Cobordism Conjecture leads to results consistent with our expectations.