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A microstate for the 3-charge black ring

Stefano Giusto, Samir D. Mathur, Yogesh K. Srivastava

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.

A microstate for the 3-charge black ring

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.

Paper Structure

This paper contains 39 sections, 162 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The CFT state
  3. The 2-charge geometry
  4. The 'inner' region
  5. Constructing the chiral primary
  6. The state $J^-_0|\psi\rangle_{NS}~\leftrightarrow~J^-_{- 1}|\psi\rangle_R$
  7. The near ring limit
  8. The Taub-NUT space
  9. The scalar $w$ in the near-ring limit
  10. The perturbation equations
  11. Reducing to equations on TN
  12. The equations to be solved
  13. Harmonics on Taub-NUT
  14. Symmetries of Taub-NUT
  15. Harmonics on the squashed sphere
  16. ...and 24 more sections

Figures (3)

  • Figure 1: (a) The D1-D5 geometry for large values of $R_y$, the radius of $S^1$; there is a large AdS region (b) The geometry for small $R_y$; the metric is close to flat outside a thin ring (c) In the near ring limit we approximate the segment of the ring by a straight line along $z$.
  • Figure 2: (a) The NS1 carrying a transverse oscillation profile in the covering space of $S^1$. (b) The strands of the NS1 as they appear in the actual space.
  • Figure 3: The winding and momentum charges of a segment of the NS1; we have used a multiple cover of the $S^1$ so that the NS1 looks like a diagonal line.