Enhancement of Supersymmetry Near 5d Black Hole Horizon

TL;DR

The paper investigates enhancement of unbroken supersymmetry near the horizon of five-dimensional black holes in $N=2$ supergravity with vector multiplets. By identifying supersymmetric Killing spinors with geometric Killing spinors on $AdS_2 \times S^3$, it shows an SUSY enhancement from partial to full near-horizon supersymmetry and derives the horizon area from the volume of $S^3$ in terms of charges and the intersection form $C_{IJK}$. The analysis leverages very special geometry to obtain a precise area-entropy formula $A = \frac{\pi^2}{3} \{ (C^{IJ} q_I q_J)_{\partial i Z=0} \}^{3/4}$ and confirms this in the truncation to $N=2$ with one vector multiplet, reproducing the Strominger–Vafa result for the SV black hole. The results unify the near-horizon SUSY structure with entropy expressions across $N=2$ and truncated $N=4$ theories, and discuss extensions to other near-horizon geometries. The work clarifies the link between central-charge extremization, horizon area, and supersymmetry enhancement, providing a framework for analyzing similar setups in higher dimensions.

Abstract

Geometric Killing spinors which exist on AdS_{p+2} X S^{d-p-2} sometimes may be identified with supersymmetric Killing spinors. This explains the enhancement of unbroken supersymmetry near the p-brane horizon in d dimensions. The corresponding p-brane interpolates between two maximally supersymmetric vacua, at infinity and at the horizon. New case is studied here: p=0, d=5. The details of supersymmetric version of the very special geometry are presented. We find the area-entropy formula of the supersymmetric 5d black holes via the volume of S^3 which depends on charges and intersection matrix.