Black Holes and the Swampland: the Deep Throat revelations

TL;DR

This paper explores the relationship between black hole microstate geometries in supergravity and the Swampland Distance Conjecture, revealing a mismatch in moduli space distance computations with implications for quantum gravity theories.

Contribution

It establishes a connection between the scaling limit of microstate geometries and the Swampland Distance Conjecture, highlighting discrepancies in moduli space distance measures.

Findings

The proper length of the throat relates to the moduli space distance in the naive conjecture.

A second distance measure using quiver quantum mechanics does not match the first.

The mismatch has implications for understanding the Swampland criteria in quantum gravity.

Abstract

Multi-centered bubbling solutions are black hole microstate geometries that arise as smooth solutions of 5-dimensional $\mathcal{N}=2$ Supergravity. When these solutions reach the scaling limit, their resulting geometries develop an infinitely deep throat and look arbitrarily close to a black hole geometry. We depict a connection between the scaling limit in the moduli space of Microstate Geometries and the Swampland Distance Conjecture. The naive extension of the Distance Conjecture implies that the distance in moduli space between a reference point and a point approaching the scaling limit is set by the proper length of the throat as it approaches the scaling limit. Independently, we also compute a distance in the moduli space of 3-centre solutions, from the K\"ahler structure of its phase space using quiver quantum mechanics. We show that the two computations of the distance in moduli space do not agree and comment on the physical implications of this mismatch.