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Massless black holes and black rings as effective geometries of the D1-D5 system

Vijay Balasubramanian, Per Kraus, Masaki Shigemori

TL;DR

This work analyzes how typical Ramond-ground-state microstates of the D1-D5 CFT map to emergent bulk geometries via AdS$_3$/CFT$_2$ correlators. By computing two-point functions in typical states and comparing them to bulk propagators, the authors show that for large central charge and finite times, the effective description is given by the massless BTZ geometry, while late-time behavior reveals microstate-specific details and quasi-periodicity. For zero R-charge the emergent geometry is the M=0 BTZ (naive AdS$_3$ with a periodic direction), whereas nonzero R-charge leads to a singular black ring as the effective bulk geometry. Overall, the paper supports viewing black hole geometries as coarse-grained, universal descriptions valid for certain measurements, which break down when probing the full microstate structure.

Abstract

We compute correlation functions in the AdS/CFT correspondence to study the emergence of effective spacetime geometries describing complex underlying microstates. The basic argument is that almost all microstates of fixed charges lie close to certain "typical" configurations. These give a universal response to generic probes, which is captured by an emergent geometry. The details of the microstates can only be observed by atypical probes. We compute two point functions in typical ground states of the Ramond sector of the D1-D5 CFT, and compare with bulk two-point functions computed in asymptotically AdS_3 geometries. For large central charge (which leads to a good semiclassical limit), and sufficiently small time separation, a typical Ramond ground state of vanishing R-charge has the M=0 BTZ black hole as its effective description. At large time separation this effective description breaks down. The CFT correlators we compute take over, and give a response whose details depend on the microstate. We also discuss typical states with nonzero R-charge, and argue that the effective geometry should be a singular black ring. Our results support the argument that a black hole geometry should be understood as an effective coarse-grained description that accurately describes the results of certain typical measurements, but breaks down in general.

Massless black holes and black rings as effective geometries of the D1-D5 system

TL;DR

This work analyzes how typical Ramond-ground-state microstates of the D1-D5 CFT map to emergent bulk geometries via AdS/CFT correlators. By computing two-point functions in typical states and comparing them to bulk propagators, the authors show that for large central charge and finite times, the effective description is given by the massless BTZ geometry, while late-time behavior reveals microstate-specific details and quasi-periodicity. For zero R-charge the emergent geometry is the M=0 BTZ (naive AdS with a periodic direction), whereas nonzero R-charge leads to a singular black ring as the effective bulk geometry. Overall, the paper supports viewing black hole geometries as coarse-grained, universal descriptions valid for certain measurements, which break down when probing the full microstate structure.

Abstract

We compute correlation functions in the AdS/CFT correspondence to study the emergence of effective spacetime geometries describing complex underlying microstates. The basic argument is that almost all microstates of fixed charges lie close to certain "typical" configurations. These give a universal response to generic probes, which is captured by an emergent geometry. The details of the microstates can only be observed by atypical probes. We compute two point functions in typical ground states of the Ramond sector of the D1-D5 CFT, and compare with bulk two-point functions computed in asymptotically AdS_3 geometries. For large central charge (which leads to a good semiclassical limit), and sufficiently small time separation, a typical Ramond ground state of vanishing R-charge has the M=0 BTZ black hole as its effective description. At large time separation this effective description breaks down. The CFT correlators we compute take over, and give a response whose details depend on the microstate. We also discuss typical states with nonzero R-charge, and argue that the effective geometry should be a singular black ring. Our results support the argument that a black hole geometry should be understood as an effective coarse-grained description that accurately describes the results of certain typical measurements, but breaks down in general.

Paper Structure

This paper contains 27 sections, 123 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. The D1-D5 system and its geometric dual
  3. The D1-D5 CFT and its Ramond sector ground states
  4. Map to the FP system and microstate geometries
  5. Bulk geometries and correlators
  6. Conical defect
  7. Naive geometry
  8. Non-rotating BTZ
  9. Comparison
  10. Typical states
  11. Statistics and typical states
  12. Typical twist distribution with $J={\widetilde{J}}=0$
  13. Typical twist distribution with $J\neq 0$ and $\tilde{J} = 0$
  14. The effective geometry
  15. Two-point functions of the D1-D5 CFT
  16. ...and 12 more sections

Figures (1)

  • Figure 1: