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3-charge geometries and their CFT duals

Stefano Giusto, Samir D. Mathur, Ashish Saxena

TL;DR

This work strengthens the fuzzball paradigm by constructing two families of smooth, extremal D1-D5-P geometries that cap off without horizons, supporting a nontrivial black hole interior. It extends the D1-D5 CFT via spectral flow and S,T dualities to generate explicit gravity duals, analyzes conical defects and orbifold singularities, and uses a scalar wave test to connect throat travel times and absorption to underlying CFT excitations. By matching the gravity travel times and absorption thresholds to component-string data (m, k, and per-string excitations), the authors map 3-charge microstates to precise CFT states, revealing invariants under dualities and uncovering subtle integrality puzzles in orbifold theories. The results reinforce the fuzzball picture while highlighting ongoing challenges in fully classifying the dual CFT states and understanding orbifold point dynamics.

Abstract

We consider two families of D1-D5-P states and find their gravity duals. In each case the geometries are found to `cap off' smoothly near r=0; thus there are no horizons or closed timelike curves. These constructions support the general conjecture that the interior of black holes is nontrivial all the way up to the horizon.

3-charge geometries and their CFT duals

TL;DR

This work strengthens the fuzzball paradigm by constructing two families of smooth, extremal D1-D5-P geometries that cap off without horizons, supporting a nontrivial black hole interior. It extends the D1-D5 CFT via spectral flow and S,T dualities to generate explicit gravity duals, analyzes conical defects and orbifold singularities, and uses a scalar wave test to connect throat travel times and absorption to underlying CFT excitations. By matching the gravity travel times and absorption thresholds to component-string data (m, k, and per-string excitations), the authors map 3-charge microstates to precise CFT states, revealing invariants under dualities and uncovering subtle integrality puzzles in orbifold theories. The results reinforce the fuzzball picture while highlighting ongoing challenges in fully classifying the dual CFT states and understanding orbifold point dynamics.

Abstract

We consider two families of D1-D5-P states and find their gravity duals. In each case the geometries are found to `cap off' smoothly near r=0; thus there are no horizons or closed timelike curves. These constructions support the general conjecture that the interior of black holes is nontrivial all the way up to the horizon.

Paper Structure

This paper contains 43 sections, 183 equations, 1 figure.

Table of Contents

  1. Introduction
  2. D1-D5-P states from spectral flow of D1-D5 states
  3. The D1-D5 CFT
  4. A subclass of states
  5. Spectral flow
  6. The states we consider
  7. Explicit representations of the states
  8. Gravity duals
  9. Duals of 2-charge states
  10. Duals of 3-charge states obtained by spectral flow of 2-charge states
  11. Obtaining new solutions by S,T dualities
  12. Conical defect angles
  13. The physics of conical defects
  14. Singularity structure of 3-charge metrics
  15. Geometries obtained by spectral flow: orbifold singularities
  16. ...and 28 more sections

Figures (1)

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