A microstate for the 3-charge black ring

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.