Black holes and the swampland: the deep throat revelations

Abstract

Multi-centered bubbling solutions are black hole microstate geometries that arise as smooth solutions of 5-dimensional $$ \mathcal{N} $$ 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 Kähler 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.

An Alliance in the Tripartite Conflict over Moduli Space

“…In this letter, we have compared the distance in moduli space between two bubbling geometries of different throat lengths, using the DeWitt distance. Our computation in Section III shows an agreement between the distance to the scaling limit according to the phase-space distance (3) computed in [27] and to the DeWitt distance (6). Both formulas, (11) and (30), give a finite result for this distance.…”

“…In the scaling limit, the redshift becomes stronger and stronger, so the energy measured at spatial infinity gets more and more suppressed. Moreover, this decay is ex-ponential with respect to the throat length, L throat [27]:…”

“…Knowing the Swampland distance conjecture (8), it appeared natural to propose that the distance to the scaling limit in moduli space is given by the argument of the decreasing exponential, up to some constant factor of order 1 [27]:…”

“…But it was also shown from [27] that the distance to the scaling limit according to the phase-space definition (3) would give a finite distance. This distance was derived at weak string coupling from quiver quantum mechanics, and, according to [28], can be extrapolated to strong coupling thanks to a non-renormalization theorem [28,29].…”

Gravitational footprints of black holes and their microstate geometries

“…where δ micro 1 is the scale of the solution which characterizes how "close" in moduli space the microstate geometry is to the black hole [25,26]. When δ micro → 0, the microstate geometry becomes identical to the black hole.…”