End-of-the-World Singularities: The Good, the Bad, and the Heated-up

TL;DR

This paper examines end-of-the-world curvature singularities in string theory, proposing new criteria to assess their physical relevance and exploring their implications for the Distance Conjecture and finite-temperature behavior.

Contribution

It introduces a novel geometric criterion for singularities, compares existing criteria, and extends the understanding of singularities in dynamical cobordisms and their relation to string theory.

Findings

Singularities can satisfy Gubser's and Maldacena--Nuñez criteria without being resolved.

EFT strings and D7-branes fail Gubser's potential criterion despite having UV completions.

A finite-temperature relation between black brane temperature and field-space distance is established.

Abstract

We revisit codimension-one End-of-the-World curvature singularities that drive scalars to infinite distance in field-space and have appeared in the context of dynamical cobordisms. We confront them with Gubser's horizon and potential criteria and with the Maldacena--Nu\~nez criterion. Moduli-space flows do not admit a near-extremal horizon generalization. Still, they satisfy Gubser's potential criterion and, in representative string realizations, the Maldacena--Nu\~nez criterion in ten dimensions. Together with an explicit uplift of this type of solution to a consistent string theory background, this suggests that such singularities should not be discarded. For flows with non-trivial scalar potential, we argue that the fate of the singularity is tied to the infinite-distance limit probed near the singularity. The Klebanov--Tseytlin and Klebanov--Strassler solutions illustrate that a modification that obstructs or modifies the field excursion should not be understood as a UV-resolution of the original singularity. We show that EFT strings and D7-branes fail Gubser's potential criterion despite having a sensible UV completion. Motivated by this, and inspired by dynamical cobordisms, we propose a novel criterion that bounds the divergence of the Ricci scalar as the flow explores infinite distance in field-space. Our criterion can be viewed as a geometrization Gubser's one that, while capturing all examples accepted by the latter, also admits EFT strings and D7-branes. Both criteria reject the massive Type IIA strong coupling End-of-the-World singularity. Finally, we analyze black D$p$-branes reduced to codimension one as representatives of flows that admit near-extremal generalizations, and find an exponential relation between temperature and field-space distance. This suggests a finite-temperature extension of the Distance Conjecture for dynamical cobordisms.