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 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.
Highlights
In many classes of microstate geometries, the infinitely-long throat of an extremal black hole is replaced by a cap at the end of a long, but finite throat [7,8,9] (See figure 1)
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
Summary
The most general supersymmetric solution to N = 2 five-dimensional Supergravity coupled to nV extra gauge fields with structure constant CIJK, admitting a time-like Killing vector ∂t are characterized by nV +1 electric warp factors ZI , nV +1 magnetic self-dual twoforms ΘI , an angular momentum one-form ω, and a space-like hyper-Kähler manifold B. The second set of nV +1 equations (2.7) determine the electric warp factors, sourced by the magnetic fields. The last equation (2.8) tells that the angular momentum ω is sourced by electric and magnetic fields, recalling the Poynting vector in electromagnetism. We consider B to be a four-dimensional Gibbons-Hawking space. The potential V is sourced by a set of n Gibbons-Hawking centres labeled by j, of charge qj:.
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