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Dual geometries for a set of 3-charge microstates

Stefano Giusto, Samir D. Mathur, Ashish Saxena

TL;DR

This work constructs extremal D1-D5-P geometries by taking carefully controlled limits of nonextremal 3-charge solutions, yielding completely smooth, horizonless spacetimes that dualize to spectral-flowed Ramond microstates of the D1-D5 CFT. The gravity solutions are shown to be regular, free of closed timelike curves, and horizonless, with the dilaton and RR fields well-behaved; the near-region geometry remains AdS$_3\times$S$^3$ under spectral flow, matching the expected CFT states. A detailed extremal limit is developed, including the introduction of a new radial coordinate and precise handling of divergences to produce a robust class of microstate geometries, and these results are compared to concurrent constructions (e.g., Lunin et al.). Overall, the paper strengthens the fuzzball program by demonstrating explicit, smooth gravity duals for a family of 3-charge microstates and highlighting the role of spectral flow in relating CFT states to smooth geometries.

Abstract

We construct a set of extremal D1-D5-P solutions, by taking appropriate limits in a known family of nonextremal 3-charge solutions. The extremal geometries turn out to be completely smooth, with no horizon and no singularity. The solutions have the right charges to be the duals of a family of CFT microstates which are obtained by spectral flow from the NS vacuum.

Dual geometries for a set of 3-charge microstates

TL;DR

This work constructs extremal D1-D5-P geometries by taking carefully controlled limits of nonextremal 3-charge solutions, yielding completely smooth, horizonless spacetimes that dualize to spectral-flowed Ramond microstates of the D1-D5 CFT. The gravity solutions are shown to be regular, free of closed timelike curves, and horizonless, with the dilaton and RR fields well-behaved; the near-region geometry remains AdSS under spectral flow, matching the expected CFT states. A detailed extremal limit is developed, including the introduction of a new radial coordinate and precise handling of divergences to produce a robust class of microstate geometries, and these results are compared to concurrent constructions (e.g., Lunin et al.). Overall, the paper strengthens the fuzzball program by demonstrating explicit, smooth gravity duals for a family of 3-charge microstates and highlighting the role of spectral flow in relating CFT states to smooth geometries.

Abstract

We construct a set of extremal D1-D5-P solutions, by taking appropriate limits in a known family of nonextremal 3-charge solutions. The extremal geometries turn out to be completely smooth, with no horizon and no singularity. The solutions have the right charges to be the duals of a family of CFT microstates which are obtained by spectral flow from the NS vacuum.

Paper Structure

This paper contains 18 sections, 80 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The CFT states
  3. The D1-D5 CFT
  4. The states we consider
  5. Explicit representation of the states
  6. Constructing the gravity duals
  7. Spectral flow in the gravity description
  8. The nonextremal 3-charge solution, with angular momentum
  9. The Extremal Limit
  10. Conserved charges
  11. Taking the extremal limit
  12. Regularity of the Solution
  13. Regularity of the metric
  14. Absence of closed timelike curves
  15. Regularity of $\Phi, C_{AB}$
  16. ...and 3 more sections

Figures (1)

  • Figure 1: (a) Naive geometry of 2-charge D1-D5. (b) Actual geometries of 2-charge D1-D5; the area of the surface shown by the dashed line gives ${A\over 4G}\sim \sqrt{n_1n_5}$. (c) Naive geometry of 3-charge D1-D5-P; there is a horizon at $r=0$ and a singularity past the horizon. (d) Expected geometries for D1-D5-P; the area at the dashed line will give ${A\over 4G}=2\pi\sqrt{n_1n_5n_p}$.