Charge Orbits of Symmetric Special Geometries and Attractors

TL;DR

This paper classifies charge orbits and attractor solutions in N=2 supergravity, revealing three classes of regular black hole solutions with distinct properties linked to the symmetry of the charge space.

Contribution

It identifies three classes of regular attractor solutions in symmetric special geometries and characterizes their charge orbits and associated mass spectra.

Findings

Three classes of regular attractor solutions are identified.

Charge orbits are classified by their invariants and symmetry properties.

Different attractor classes exhibit distinct scalar fluctuation spectra.

Abstract

We study the critical points of the black hole scalar potential $V_{BH}$ in N=2, d=4 supergravity coupled to $n_{V}$ vector multiplets, in an asymptotically flat extremal black hole background described by a 2(n_{V}+1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special K\"{a}hler manifold. For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with non-vanishing Bekenstein-Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2(n_{V}+1)-dimensional representation $R_{V}$ of the U-duality group. Such orbits are non-degenerate, namely they have non-vanishing quartic invariant (for rank-3 spaces). Other than the 1/2-BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge. The three species of solutions to the N=2 extremal black hole attractor equations give rise to different mass spectra of the scalar fluctuations, whose pattern can be inferred by using invariance properties of the critical points of $V_{BH}$ and some group theoretical considerations on homogeneous symmetric special K\"{a}hler geometry.