A microstate for the 3-charge black ring

TL;DR

This paper constructs a smooth, normalizable perturbation on a 2-charge D1-D5 ring geometry, providing a concrete example of black ring 'hair' with three charges, and explores its implications for D0-D6 binding.

Contribution

It presents the first explicit example of a smooth perturbation adding momentum to a 2-charge black ring, revealing new insights into black ring microstates and D0-D6 interactions.

Findings

Found a smooth perturbation adding one unit of momentum to the D1-D5 ring.

Demonstrated the perturbation as a form of black ring 'hair' with three charges.

Provided insights into D0-D6 flux bound states at the threshold.

Abstract

We start with a 2-charge D1-D5 BPS geometry that has the shape of a ring; this geometry is regular everywhere. In the dual CFT there exists a perturbation that creates one unit of excitation for left movers, and thus adds one unit of momentum P. This implies that there exists a corresponding normalizable perturbation on the near-ring D1-D5 geometry. We find this perturbation, and observe that it is smooth everywhere. We thus find an example of `hair' for the black ring carrying three charges -- D1, D5 and one unit of P. The near-ring geometry of the D1-D5 supertube can be dualized to a D6 brane carrying fluxes corresponding to the `true' charges, while the quantum of P dualizes to a D0 brane. We observe that the fluxes on the D6 brane are at the threshold between bound and unbound states of D0-D6, and our wavefunction helps us learn something about binding at this threshold.