Attractors and Black Rings

TL;DR

This paper extends the attractor mechanism to five-dimensional BPS black rings, showing how moduli are fixed by dipole charges through an attractor function, with explicit formulas derived.

Contribution

It provides a general derivation of the attractor mechanism in five dimensions, highlighting the role of dipole charges in fixing moduli for BPS black rings.

Findings

Moduli can be fixed by dipole charges, not just conserved charges.

Explicit expressions for the fixed moduli are derived.

The analysis clarifies when dipole versus conserved charges determine moduli.

Abstract

The attractor mechanism is usually thought of as the fixing of the near horizon moduli of a BPS black hole in terms of conserved charges measured at infinity. Recent progress in understanding BPS solutions in five dimensions indicates that this is an incomplete story. Moduli can instead be fixed in terms of dipole charges, and their corresponding values can be found by extremizing a certain attractor function built out of these charges. BPS black rings provide an example of this phenomenon. We give a general derivation of the attractor mechanism in five dimensions based on the recently developed classification of BPS solutions. This analysis shows when it is the dipole charges versus the conserved charges that fix the moduli. It also yields explicit expressions for the fixed moduli.