4d/5d Correspondence for the Black Hole Potential and its Critical Points

TL;DR

This paper establishes a correspondence between four-dimensional and five-dimensional black hole potentials in N=2 supergravity, revealing how critical points and entropies relate across dimensions for various geometries.

Contribution

It derives explicit relations between 4d and 5d black hole potentials and critical points, including for non-symmetric cubic geometries, extending previous understanding of dimensional correspondence.

Findings

4d black hole potential expressed in 5d special geometry data

Relation between 4d and 5d critical points and entropies

Validity for generic configurations and non-symmetric geometries

Abstract

We express the d=4, N=2 black hole effective potential for cubic holomorphic F functions and generic dyonic charges in terms of d=5 real special geometry data. The 4d critical points are computed from the 5d ones, and their relation is elucidated. For symmetric spaces, we identify the BPS and non-BPS classes of attractors and the respective entropies. These are related by simple formulae, interpolating between four and five dimensions, depending on the volume modulus and on the 4d magnetic (or electric) charges, and holding true also for generic field configurations and for non-symmetric cubic geometries.