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

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.