Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2409.05850

A Bottom-Up Approach to Black Hole Microstates

Vaibhav Burman, Chethan Krishnan

Published Sep 9, 2024• 0 citations
arXivHTMLPDF

Abstract

In arXiv:2312.14108, we argued that a sliver at the black hole mass in the Hilbert space of a quantum field theory on an AdS black hole with a stretched horizon, has many desirable features of black hole microstates. A key observation is that the stretched horizon requires a finite Planck length, i.e., finite-$N$. Therefore it is best viewed as a ``quantum horizon" -- a proxy for the UV-complete bulk description, and not directly an element in the bulk EFT. It was shown in arXiv:2312.14108 that despite the manifest absence of the interior, the 2-point function in the sliver is indistinguishable from the smooth horizon correlator, up to the Page time. In this paper, instead of boundary correlators, we work directly in the bulk, and demonstrate the appearance of the bulk Hartle-Hawking correlator in the large-$N$ limit. This is instructive because it shows that the analytic continuation across the horizon is emergent. It is a $bulk$ transition to a Type III algebra and provides a structural distinction between black holes and weakly coupled thermal systems. We also identify a mechanism for universal code subspaces and interior tensor factors to appear via a quantum horizon version of thermal factorization. Our claims apply directly only within a ``Page window", so they are not in immediate tension with firewall arguments. During a Page window, typical heavy microstates probed by light single trace operators respond with effectively smooth horizons in low-point correlators. We work in 2+1 dimensions to be concrete, but expect our results to hold in all higher dimensions. We discuss some important differences between our approach and the conventional fuzzball program, and also argue that probe-notions (like infalling boundary conditions) must be distinguished from microstate-notions (like size of the Einstein-Rosen bridge) to make meaningful statements about post-Page smoothness.

DOI
10.48550/arxiv.2409.05850

Related papers

Stretched horizon from conformal field theory

Suchetan Das

A bstract Recently, it has been observed that the Hartle-Hawking correlators, a signature of smooth horizon, can emerge from certain heavy excited state correlators in the (manifestly non-smooth) BTZ stretched horizon background, in the limit when the stretched horizon approaches the real horizon. In this note, we develop a framework of quantizing the CFT modular Hamiltonian, that explains the necessity of introducing a stretched horizon and the emergence of thermal features in the AdS-Rindler and (planar) BTZ backgrounds. In more detail, we quantize vacuum modular Hamiltonian on a spatial segment of S 1 , which can be written as a particular linear combination of sl(2,ℝ) generators. Unlike radial quantization, (Euclidean) time circles emerge naturally here which can be contracted smoothly to the ‘fixed points’(end points of the interval) of this quantization thus providing a direct link to thermal physics. To define a Hilbert space with discrete normalizable states and to construct a Virasoro algebra with finite central extension, a natural regulator ( ϵ ) is needed around the fixed points. Eventually, in the dual description the fixed points correspond to the horizons of AdS-Rindler patch or (planar) BTZ and the cut-off being the stretched horizon. We construct a (Lorentzian) highest weight representation of that Virasoro algebra where vacuum can be identified with certain boundary states on the cut-off surface. We further demonstrate that two point function in a (vacuum) descendant state of the regulated Hilbert space will reproduce thermal answer in ϵ → 0 limit which is analogous to the recent observation of emergent thermality in (planar) BTZ stretched horizon background. We also argue the thermal entropy of this quantization coincides with entanglement entropy of the subregion. Conversely, the microcanonical entropy corresponding to high energy density of states exactly reproduce the BTZ entropy. Quite remarkably, all these dominant high lying microstates are defined only at finite ϵ in the regulated Hilbert space. We expect that all our observations can be generalized to BTZ in stretched horizon background where the boundary spatial coordinate is compactified.

arXiv:2406.10879•Journal of High Energy Physics•Nov 6, 2024•7 citations

On black hole interior reconstruction, singularities and the emergence of time

de Boer, Jan, Daniel Louis Jafferis, Lampros Lamprou

We propose a CFT definition of local observables in both the exterior and interior of bulk black holes, whenever such an interior exists. We achieve this by introducing a small microcanonical black hole as a "probe" and using its modular flow to propagate operators from the asymptotic boundary to the interior of other black holes along its worldline, elaborating on the ideas of [2009.04476]. The key conceptual advance is a CFT criterion for selecting states whose modular flow acts as geometric proper time translation in the bulk, which we dub "local equilibrium" states. Our interior reconstruction depends on the choice of code subspace but not on the specific black hole microstate and does not suffer from the "frozen vacuum" problem of other approaches. By virtue of our construction, the question of firewall typicality reduces to a technical problem we articulate and we identify a CFT correlator that is expected to signal the approach to the black hole singularity via a universal divergence. We end with comments on the utility of our framework to the quest for a quantum description of de Sitter cosmologies.

arXiv:2211.16512•Nov 29, 2022•4 citations

Learning the Alpha-bits of black holes

Patrick M. Hayden, Geoff Penington

Abstract When the bulk geometry in AdS/CFT contains a black hole, boundary subregions may be sufficient to reconstruct certain bulk operators if and only if the black hole microstate is known, an example of state dependence. Reconstructions exist for any microstate, but no reconstruction works for all microstates. We refine this dichotomy, demonstrating that the same boundary operator can often be used for large subspaces of black hole microstates, corresponding to a constant fraction α of the black hole entropy. In the Schrödinger picture, the boundary subregion encodes the α-bits (a concept from quantum information) of a bulk region containing the black hole and bounded by extremal surfaces. These results have important consequences for the structure of AdS/CFT and for quantum information. Firstly, they imply that the bulk reconstruction is necessarily only approximate and allow us to place non-perturbative lower bounds on the error when doing so. Second, they provide a simple and tractable limit in which the entanglement wedge is state dependent, but in a highly controlled way. Although the state dependence of operators comes from ordinary quantum error correction, there are clear connections to the Papadodimas-Raju proposal for understanding operators behind black hole horizons. In tensor network toy models of AdS/CFT, we see how state dependence arises from the bulk operator being ‘pushed’ through the black hole itself. Finally, we show that black holes provide the first ‘explicit’ examples of capacity-achieving α-bit codes. Unintuitively, Hawking radiation always reveals the α-bits of a black hole as soon as possible. In an appendix, we apply a result from the quantum information literature to prove that entanglement wedge reconstruction can be made exact to all orders in 1/N.

arXiv:1807.06041•Journal of High Energy Physics•Dec 1, 2019•125 citations

Where in the Island is the Information?

Tom Banks

The Island Formula for Quantum Extremal Surfaces of large AdS black holes, which are made to evaporate by coupling the CFT of the AdS/CFT correspondence to an external system, demonstrates that the space time picture can reproduce the quantum mechanically required Page curve of the CFT/bath system if a region in the interior of the black hole has become entangled with the external radiation by the Page time. In an effective quantum field theory (EFT) description in ``nice slice" coordinates, this appears to imply paradoxical entanglement between degrees of freedom that have been causally disconnected since long before the Page time. We will give two arguments that all of the quantum information in the island is in fact concentrated in a tiny space-like portion of the island very close to the black hole horizon at the Page time. The first applies the covariant entropy bound\cite{fsb} (CEB) to the causal diamonds of geodesics originating on the space-like region that becomes the island, but on a time slice just before the Page time. All points on the island except those in a stretched horizon region very close to the horizon have entropy bounds that are tiny fractions of the black hole entropy. The second argument uses standard quantum statistical mechanics combined with the tensor network renormalization group regularization of CFT to argue that the wave function of a typical pure state in the microcanonical evaporating black hole always has most of its probability concentrated in a small range of wavelengths corresponding to a small range of radii in the dual tensor network/AdS slice.

arXiv:2610.02406•Oct 1, 2026•0 citations

Interior of a unitarily evaporating black hole

Yasunori Nomura A

We study microscopic operators describing the experience of an observer falling into the horizon of a unitarily evaporating black hole. For a young black hole, these operators can be taken to act only on the degrees of freedom in the black hole region: the soft---or stretched horizon---modes as well as the semiclassical modes in the zone region. On the other hand, for an old black hole, the operators must also involve radiation emitted earlier; the difference between the two cases comes from statistics associated with the coarse graining performed to obtain the effective theory of the interior. We find that the operators relevant for the interior theory can be defined globally as standard linear operators throughout the microstates, which obey the correct algebra up to corrections exponentially suppressed in the ratio of excitation energy to the Hawking temperature. We conjecture that the existence of such global operators is required for the emergence of the semiclassical picture. We also elucidate the relation between the present construction and entanglement wedge reconstruction of the interior.

arXiv:1911.13120•Physical review. D/Physical review. D.•Jul 1, 2020•22 citations

Quantum microstate counting from Brownian motion: From many-body systems to black holes

Enzo Bavaro, Javier M. Magán, Leandro Martinek

We introduce a new way to produce infinite families of bases of a quantum system's Hilbert space, as well as methods to find its dimension. These families are constructed via Brownian motions in the Hilbert space, defined using disordered, time-dependent couplings. The dimension spanned by them has zero variance over the ensemble of disordered couplings, and it is determined by certain replica partition functions. We apply these methods to finite dimensional $q$-local systems (spin clusters and SYK) and black holes. For $q$-local systems we find exact expressions at finite $q$, $N$, and $t$, for replica partition functions, together with universal behavior at large times and a semiclassical analysis at large-$N$ in appropriate master field variables. The right Hilbert space dimension is obtained for any time $t>0$, $q>1$ and $N>0$. For black holes, the Brownian motions prepare quantitatively generic ensembles of black hole microstates, and the Bekenstein-Hawking entropy is universally reproduced by counting those. There the $n$-replica partition functions are constructed by gluing $n$-traversable womrholes at their future and past. This method demonstrates the robustness of black hole microstate counting methods, avoiding several limitations of previous constructions, including the non-genericity of the microstates and associated interiors, implicit statistics of heavy operators, limited microscopic control over overlaps, and the need for specific limits in the calculation.

arXiv:2512.15854•Physical review. D/Physical review. D.•Oct 26, 2026•0 citations
In arXiv:2312.14108, we argued that a sliver at the black hole mass in the Hilbert space of a quantum field theory on an AdS black hole with a stretched horizon, has many desirable features of black hole microstates. A key observation is that the stretched horizon requires a finite Planck length, i.e., finite-NNN. Therefore it is best viewed as a quantum horizon" -- a proxy for the UV-complete bulk description, and not directly an element in the bulk EFT. It was shown in arXiv:2312.14108 that despite the manifest absence of the interior, the 2-point function in the sliver is indistinguishable from the smooth horizon correlator, up to the Page time. In this paper, instead of boundary correlators, we work directly in the bulk, and demonstrate the appearance of the bulk Hartle-Hawking correlator in the large-$N$ limit. This is instructive because it shows that the analytic continuation across the horizon is emergent. It is a $bulk$ transition to a Type III algebra and provides a structural distinction between black holes and weakly coupled thermal systems. We also identify a mechanism for universal code subspaces and interior tensor factors to appear via a quantum horizon version of thermal factorization. Our claims apply directly only within a Page window", so they are not in immediate tension with firewall arguments. During a Page window, typical heavy microstates probed by light single trace operators respond with effectively smooth horizons in low-point correlators. We work in 2+1 dimensions to be concrete, but expect our results to hold in all higher dimensions. We discuss some important differences between our approach and the conventional fuzzball program, and also argue that probe-notions (like infalling boundary conditions) must be distinguished from microstate-notions (like size of the Einstein-Rosen bridge) to make meaningful statements about post-Page smoothness.
A bstract Recently, it has been observed that the Hartle-Hawking correlators, a signature of smooth horizon, can emerge from certain heavy excited state correlators in the (manifestly non-smooth) BTZ stretched horizon background, in the limit when the stretched horizon approaches the real horizon. In this note, we develop a framework of quantizing the CFT modular Hamiltonian, that explains the necessity of introducing a stretched horizon and the emergence of thermal features in the AdS-Rindler and (planar) BTZ backgrounds. In more detail, we quantize vacuum modular Hamiltonian on a spatial segment of S 1 , which can be written as a particular linear combination of sl(2,ℝ) generators. Unlike radial quantization, (Euclidean) time circles emerge naturally here which can be contracted smoothly to the ‘fixed points’(end points of the interval) of this quantization thus providing a direct link to thermal physics. To define a Hilbert space with discrete normalizable states and to construct a Virasoro algebra with finite central extension, a natural regulator ( ϵ ) is needed around the fixed points. Eventually, in the dual description the fixed points correspond to the horizons of AdS-Rindler patch or (planar) BTZ and the cut-off being the stretched horizon. We construct a (Lorentzian) highest weight representation of that Virasoro algebra where vacuum can be identified with certain boundary states on the cut-off surface. We further demonstrate that two point function in a (vacuum) descendant state of the regulated Hilbert space will reproduce thermal answer in ϵ → 0 limit which is analogous to the recent observation of emergent thermality in (planar) BTZ stretched horizon background. We also argue the thermal entropy of this quantization coincides with entanglement entropy of the subregion. Conversely, the microcanonical entropy corresponding to high energy density of states exactly reproduce the BTZ entropy. Quite remarkably, all these dominant high lying microstates are defined only at finite ϵ in the regulated Hilbert space. We expect that all our observations can be generalized to BTZ in stretched horizon background where the boundary spatial coordinate is compactified.
We propose a CFT definition of local observables in both the exterior and interior of bulk black holes, whenever such an interior exists. We achieve this by introducing a small microcanonical black hole as a "probe" and using its modular flow to propagate operators from the asymptotic boundary to the interior of other black holes along its worldline, elaborating on the ideas of [2009.04476]. The key conceptual advance is a CFT criterion for selecting states whose modular flow acts as geometric proper time translation in the bulk, which we dub "local equilibrium" states. Our interior reconstruction depends on the choice of code subspace but not on the specific black hole microstate and does not suffer from the "frozen vacuum" problem of other approaches. By virtue of our construction, the question of firewall typicality reduces to a technical problem we articulate and we identify a CFT correlator that is expected to signal the approach to the black hole singularity via a universal divergence. We end with comments on the utility of our framework to the quest for a quantum description of de Sitter cosmologies.
Abstract When the bulk geometry in AdS/CFT contains a black hole, boundary subregions may be sufficient to reconstruct certain bulk operators if and only if the black hole microstate is known, an example of state dependence. Reconstructions exist for any microstate, but no reconstruction works for all microstates. We refine this dichotomy, demonstrating that the same boundary operator can often be used for large subspaces of black hole microstates, corresponding to a constant fraction α of the black hole entropy. In the Schrödinger picture, the boundary subregion encodes the α-bits (a concept from quantum information) of a bulk region containing the black hole and bounded by extremal surfaces. These results have important consequences for the structure of AdS/CFT and for quantum information. Firstly, they imply that the bulk reconstruction is necessarily only approximate and allow us to place non-perturbative lower bounds on the error when doing so. Second, they provide a simple and tractable limit in which the entanglement wedge is state dependent, but in a highly controlled way. Although the state dependence of operators comes from ordinary quantum error correction, there are clear connections to the Papadodimas-Raju proposal for understanding operators behind black hole horizons. In tensor network toy models of AdS/CFT, we see how state dependence arises from the bulk operator being ‘pushed’ through the black hole itself. Finally, we show that black holes provide the first ‘explicit’ examples of capacity-achieving α-bit codes. Unintuitively, Hawking radiation always reveals the α-bits of a black hole as soon as possible. In an appendix, we apply a result from the quantum information literature to prove that entanglement wedge reconstruction can be made exact to all orders in 1/N.
The Island Formula for Quantum Extremal Surfaces of large AdS black holes, which are made to evaporate by coupling the CFT of the AdS/CFT correspondence to an external system, demonstrates that the space time picture can reproduce the quantum mechanically required Page curve of the CFT/bath system if a region in the interior of the black hole has become entangled with the external radiation by the Page time. In an effective quantum field theory (EFT) description in ``nice slice" coordinates, this appears to imply paradoxical entanglement between degrees of freedom that have been causally disconnected since long before the Page time. We will give two arguments that all of the quantum information in the island is in fact concentrated in a tiny space-like portion of the island very close to the black hole horizon at the Page time. The first applies the covariant entropy bound\cite{fsb} (CEB) to the causal diamonds of geodesics originating on the space-like region that becomes the island, but on a time slice just before the Page time. All points on the island except those in a stretched horizon region very close to the horizon have entropy bounds that are tiny fractions of the black hole entropy. The second argument uses standard quantum statistical mechanics combined with the tensor network renormalization group regularization of CFT to argue that the wave function of a typical pure state in the microcanonical evaporating black hole always has most of its probability concentrated in a small range of wavelengths corresponding to a small range of radii in the dual tensor network/AdS slice.
We study microscopic operators describing the experience of an observer falling into the horizon of a unitarily evaporating black hole. For a young black hole, these operators can be taken to act only on the degrees of freedom in the black hole region: the soft---or stretched horizon---modes as well as the semiclassical modes in the zone region. On the other hand, for an old black hole, the operators must also involve radiation emitted earlier; the difference between the two cases comes from statistics associated with the coarse graining performed to obtain the effective theory of the interior. We find that the operators relevant for the interior theory can be defined globally as standard linear operators throughout the microstates, which obey the correct algebra up to corrections exponentially suppressed in the ratio of excitation energy to the Hawking temperature. We conjecture that the existence of such global operators is required for the emergence of the semiclassical picture. We also elucidate the relation between the present construction and entanglement wedge reconstruction of the interior.
We introduce a new way to produce infinite families of bases of a quantum system's Hilbert space, as well as methods to find its dimension. These families are constructed via Brownian motions in the Hilbert space, defined using disordered, time-dependent couplings. The dimension spanned by them has zero variance over the ensemble of disordered couplings, and it is determined by certain replica partition functions. We apply these methods to finite dimensional qqq-local systems (spin clusters and SYK) and black holes. For qqq-local systems we find exact expressions at finite qqq, NNN, and ttt, for replica partition functions, together with universal behavior at large times and a semiclassical analysis at large-NNN in appropriate master field variables. The right Hilbert space dimension is obtained for any time t>0t>0t>0, q>1q>1q>1 and N>0N>0N>0. For black holes, the Brownian motions prepare quantitatively generic ensembles of black hole microstates, and the Bekenstein-Hawking entropy is universally reproduced by counting those. There the nnn-replica partition functions are constructed by gluing nnn-traversable womrholes at their future and past. This method demonstrates the robustness of black hole microstate counting methods, avoiding several limitations of previous constructions, including the non-genericity of the microstates and associated interiors, implicit statistics of heavy operators, limited microscopic control over overlaps, and the need for specific limits in the calculation.