The Special Role of Toroidal Black Holes in Holography

TL;DR

This paper investigates the unique role of toroidal black holes in holography, revealing their special properties near extremality and implications for boundary field theories, with insights from the Weak Gravity Conjecture and black hole emission.

Contribution

It demonstrates that small toroidal black holes are uniquely relevant in holography and explores their behavior near extremality, including black hole emission and effects on boundary correlators.

Findings

Small emitted black holes are always of the small type near extremality.

Dependence of one-point functions on fall time drops out for emitted toroidal black holes.

Toroidal black holes have a special role in the holographic dictionary near extremality.

Abstract

In the standard holographic ``dictionary'', the deep infrared of the strongly coupled boundary field theory is studied by examining the bulk region near to the event horizon of a simple AdS-Reissner-Nordstr\"{o}m black hole, near to extremality. Recently Horowitz et al. have argued that this is not correct, \emph{except} in the case of small toroidal black holes, which are therefore revealed to be particularly interesting and important. On the other hand, the Weak Gravity Conjecture postulates that black holes (including toroidal black holes) which are extremely near to extremality spontaneously emit black holes of the same kind. We show that, in the toroidal case, these ``emitted'' black holes are always small in the sense of Horowitz et al. As an application, we discuss the Grinberg-Maldacena analysis of the way one-point functions, evaluated outside an AdS-Reissner-Nordstr\"{o}m black hole, depend on the proper time of fall from the event horizon to the Cauchy horizon. We find that, for emitted toroidal black holes, this dependence effectively drops out.