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

José Calderón-Infante, Gongrui Cheng, Alvaro Herráez, Thomas Van Riet

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--Nuñez 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--Nuñez 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.

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

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--Nuñez 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--Nuñez 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-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.
Paper Structure (21 sections, 100 equations, 1 figure)

This paper contains 21 sections, 100 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Domain wall flows and Singularity Criteria
  3. Ansatz and effective actions: General Formulae
  4. Singularity Criteria: Gubser and Maldacena-Nuñez
  5. Dynamical Cobordisms and End-of-the-World Singularities
  6. ETW Singularities in Moduli Space Flows
  7. Domain wall flows in moduli space
  8. Confronting moduli space flows with Gubser and Maldacena-Nuñez
  9. Gubser's criteria
  10. Maldacena-Nuñez criteria
  11. A UV-complete ETW singularity in moduli space and its generalization
  12. ETW Singularities Outside Moduli Space
  13. A Singularity Criterion from Dynamical Cobordisms
  14. Klebanov-Tseytlin and Klebanov-Strassler solutions
  15. Massive Type IIA flow
  16. ...and 6 more sections

Figures (1)

  • Figure 1: The flow of the scalars towards the horizon at finite temperature.