Calabi-Yau Black Holes and Enhancement of Supersymmetry in Five Dimensions

TL;DR

The paper addresses BPS black holes in five-dimensional $N=2$ supergravity arising from M-theory compactifications on Calabi–Yau manifolds. It leverages very special geometry and the attractor mechanism to express electric and magnetic solutions in terms of harmonic functions and horizon data, showing that horizon values extremize central charges $Z_e$ and $Z_m$ and yield distinct near-horizon geometries $AdS_{2}\times S^{3}$ and $AdS_{3}\times S^{2}$ with supersymmetry enhanced at the horizon. The authors provide explicit Killing spinor constructions for these near-horizon geometries and derive the field configurations, including the metric forms governed by the cubic prepotential ${\cal V}$ and the harmonic functions. These results deepen the understanding of Calabi–Yau compactifications in M-theory, illustrating how horizon data fixes moduli and supports the attractor picture in $d=5$, $N=2$ theories with vector multiplets.

Abstract

BPS electric and magnetic black hole solutions which break half of supersymmetry in the theory of N=2 five-dimensional supergravity are discussed. For models which arise as compactifications of M-theory on a Calabi-Yau manifold, these solutions correspond, respectively, to the two and five branes wrapping around the homology cycles of the Calabi-Yau compact space. The electric solutions are reviewed and the magnetic solutions are constructed. The near-horizon physics of these solutions is examined and in particular the phenomenon of the enhancement of supersymmetry. The solutions for the supersymmetric Killing spinor of the near horizon geometry, identified as $AdS_{3}\times S^{2}$ and $AdS_{2} \times S^{3}$ are also given.