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AdS/CFT duality and the black hole information paradox

Oleg Lunin, Samir D. Mathur

TL;DR

The paper investigates the AdS/CFT correspondence in the D1-D5 system, focusing on Ramond-sector ground states and their dual throat geometries. It demonstrates a precise CFT–supergravity match below the black-hole threshold, including identical time delays and emission rates, and shows how throat endings, dictated by microstate structure, encode information about the CFT state. It argues that semiclassical gravity can break down when multiple excitations populate a single component string, offering a concrete link to a proposed information-paradox resolution via the stretching of spacelike slices and a density-of-degrees-of-freedom argument. By mapping D1-D5 states to FP configurations and exploring hair, singularities, and generic j configurations, the work provides a unified microscopic–macroscopic picture connecting microstate geometries to information retrieval while clarifying the limits of the semiclassical approximation. Overall, the results suggest that information leakage in Hawking radiation can be realized within a unitary, string-theoretic framework without invoking nonlocal physics beyond holography.

Abstract

Near-extremal black holes are obtained by exciting the Ramond sector of the D1-D5 CFT, where the ground state is highly degenerate. We find that the dual geometries for these ground states have throats that end in a way that is characterized by the CFT state. Below the black hole threshold we find a detailed agreement between propagation in the throat and excitations of the CFT. We study the breakdown of the semiclassical approximation and relate the results to the proposal of gr-qc/0007011 for resolving the information paradox: semiclassical evolution breaks down if hypersurfaces stretch too much during an evolution. We find that a volume V stretches to a maximum throat depth of V/2G.

AdS/CFT duality and the black hole information paradox

TL;DR

The paper investigates the AdS/CFT correspondence in the D1-D5 system, focusing on Ramond-sector ground states and their dual throat geometries. It demonstrates a precise CFT–supergravity match below the black-hole threshold, including identical time delays and emission rates, and shows how throat endings, dictated by microstate structure, encode information about the CFT state. It argues that semiclassical gravity can break down when multiple excitations populate a single component string, offering a concrete link to a proposed information-paradox resolution via the stretching of spacelike slices and a density-of-degrees-of-freedom argument. By mapping D1-D5 states to FP configurations and exploring hair, singularities, and generic j configurations, the work provides a unified microscopic–macroscopic picture connecting microstate geometries to information retrieval while clarifying the limits of the semiclassical approximation. Overall, the results suggest that information leakage in Hawking radiation can be realized within a unitary, string-theoretic framework without invoking nonlocal physics beyond holography.

Abstract

Near-extremal black holes are obtained by exciting the Ramond sector of the D1-D5 CFT, where the ground state is highly degenerate. We find that the dual geometries for these ground states have throats that end in a way that is characterized by the CFT state. Below the black hole threshold we find a detailed agreement between propagation in the throat and excitations of the CFT. We study the breakdown of the semiclassical approximation and relate the results to the proposal of gr-qc/0007011 for resolving the information paradox: semiclassical evolution breaks down if hypersurfaces stretch too much during an evolution. We find that a volume V stretches to a maximum throat depth of V/2G.

Paper Structure

This paper contains 41 sections, 47 equations, 9 figures.

Table of Contents

  1. Introduction.
  2. Review of some basic issues
  3. Results
  4. R ground states in the CFT and dual metrics for a special family
  5. The states in the CFT
  6. Chiral primaries in the NS sector.
  7. Ground states in the R sector.
  8. Pictorial description of R ground states.
  9. A special family of metrics for the D1-D5 system
  10. CFT states and their dual supergravity throats
  11. Microscopic model used for black hole absorption computations.
  12. Time delay and its microscopic interpretation.
  13. General values of $j$.
  14. The rate of radiation.
  15. Generic microstates and the dual throat geometries
  16. ...and 26 more sections

Figures (9)

  • Figure 1: (a) The state with one component string wrapped $n_1n_5$ times around the direction $y$; (b) A generic state with several component strings. The arrows indicate the spins of the component strings.
  • Figure 2: (a) A graviton is incident on the component string; (b) The graviton is converted to a pair of vibration modes; (c) The vibration modes meet again at B.
  • Figure 3: Component strings for the state $[\sigma_{N/m}^{--}]^m$. The spins are all aligned to give $j=m/2$.
  • Figure 4: (a) Component strings for the D1-D5 microstate $[\sigma_2^{--}]^{N/2}$. (b) The fundamental string in the dual FP system, oscillating in the harmonic $n=2$, shown opened up to its full length $2\pi n_w R'$. (c) The string of (b) as it actually appears due to the identification $y'\rightarrow y'+2\pi R'$. (d) The cross section of the singularity created by the strands in (c) in the classical limit.
  • Figure 5: (a) Component strings with spins not all aligned; (b) The shape of the singularity.
  • ...and 4 more figures