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:2609.18944

Reading Topological Hair from Black-Hole Entanglement

Kumar Ghosh

hep-thgr-qcquant-phSubmitted Jul 17, 2026• Announced Jul 20, 2026• 0 citations
arXivHTMLPDF

Abstract

Black-hole hair can affect boundary mixed-state entanglement through local stress-energy and through topological information invisible to the classical metric. We separate these channels for a Nielsen--Olesen vortex on a nonrotating BTZ black hole. A superselection theorem shows that Shannon sector entropy cancels from the Markov gap, while standard $U(1)$ symmetry-resolved reflected entropy in a thermal $U(1)_k$ CFT is equipartitioned at leading order, excluding a universal $\log|n|$ term in the imbalance-resolved gap. We therefore define a Wilson-threaded reflected moment in a probe $U(1)_k$ Chern--Simons completion coupled to the compact vortex-flux class. In a reflected-replica sector with linking number $ν$, its normalised phase is $2πκpnν/k$, where $κ\in\mathbb Z$ is the mixed topological coupling; for $\gcd(κν,k)=1$, a discrete Fourier transform reconstructs $n\bmod k$. The RT connectivity transition switches the specified linked contour on or off, whereas the independent scale $\ell_\star r_+/L^2=1.128378\ldots$ determines the direction of the vortex-induced shift of that transition. The charged-moment modulus and the ordinary Markov gap remain geometric observables and are computed from a horizon-anchored Einstein-Abelian-Higgs solution with a complete first-variation kernel including the motion of the entanglement-wedge cross-section endpoints. This phase and modulus separation distinguishes topological hair from gravitational dressing without assigning an unsupported winding-dependent entropy.

Comments
18 pages 3 figures

Related papers

Holonomy Separation and Anyonic Hair in AdS$_3$

Kumar Ghosh

Three-dimensional Einstein gravity and Chern-Simons-Higgs matter both admit Chern-Simons descriptions, but their holonomies encode different physics. We prove that charge conjugation reverses the vortex winding $n\to-n$ while leaving the metric and the gravitational connections pointwise unchanged, so every closed gravitational holonomy character, the BTZ charges, the Bañados data and the leading geometric mixed-state hierarchy are exactly even in $n$. On a fixed marked Euclidean replica filling the same change of variables gives $Z_q[n;\mathcal J_+]=Z_q[-n;\mathcal J_+]$, so the uncharged Rényi hierarchy, the Faulkner-Lewkowycz-Maldacena one-loop correction, the renormalized generalized entropy and the quantum extremal surfaces coincide for the two orientations. The complementary sector is fixed exactly: with an Aharonov-Bohm angle $μ$ conjugate to the entangling-region charge, $Z_q[n;μ]=Z_q[-n;-μ]$, so the symmetry-resolved spectrum obeys $\mathcal Z_q(\mathcal Q;n)=\mathcal Z_q(-\mathcal Q;-n)$ and every odd charged cumulant reverses with the winding. The orientation is therefore stored entirely in the charge asymmetry of the entanglement spectrum, and is read at topological order by a linked charged matter line. The pair is a bulk logical qubit on which the neutral gravitational-replica algebra acts as a multiple of the identity. Exact BTZ cross sections show that the purification plateau and the entanglement wedge disconnection transition are orientation blind, the latter closing with the cutoff-independent jump $(c/3)\log(1+\sqrt2)$. Numerical Bogomolny solutions verify odd flux and even energy and spin; used as linearized charge-matching data they give the even asymptotic shifts $δ\widehat M=16πGv^2|n|$ and $|δ\widehat j|=16πGv^2n^2/(mL)$ and, conditionally, a finite continuous winding envelope.

arXiv:2609.29562•Aug 26, 2026•0 citations

Reflected entropy for communicating black holes II: Planck braneworlds

Mir Afrasiar, Jaydeep Kumar Basak, Ashish Chandra +1 more

Abstract We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in finite-sized non-gravitating reservoirs described by $$CFT_2$$ C F T 2 s each coupled to two quantum dots at their boundaries in the large central charge limit through a replica technique. These field theory results are substantiated through a holographic computation involving the entanglement wedge cross section in the dual bulk BTZ black hole geometry truncated by two Planck branes. The two Planck branes are the holographic duals of the quantum dots described by $$AdS_2$$ A d S 2 slices with JT black holes. Our result reproduce the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the $$AdS_3/CFT_2$$ A d S 3 / C F T 2 correspondence. Subsequently we analyze the behaviour of the holographic Markov gap between the reflected entropy and the mutual information for different scenarios involving the subsystem sizes and time.

arXiv:2302.12810•The European Physical Journal C•Mar 9, 2024•6 citations

Information Flow from Zero-Energy Boundary Modes: Exact Quantum-Nondemolition Dynamics of Soft Hair in a Solvable Gauge Model

Mustafa Boudjerada

The black-hole soft-hair proposal raises a central dynamical question: can zero-energy boundary degrees of freedom become correlated with radiation in a way that preserves and reveals information, or are such modes permanently decoupled from observable physics? This work studies that question in an exactly solvable minimal charge-locked emission model derived from the soft-hair structure of the Schwinger model. The model provides a controlled setting to analyze information transfer between boundary hair degrees of freedom and emitted radiation without uncontrolled approximations. The analysis shows that the hair variable acts as a quantum-nondemolition degree of freedom: the hair charge is conserved during emission, while the radiation acquires a coherent record of the initial sector. The emitted radiation remains phase-locked to the vacuum-sector label, and the decay of hair coherences follows an exact closed-form decoherence law. The information flow is characterized using mutual information and explicit state reconstruction. The radiation record approaches a perfect distinguishable record of the hair sector, and pretty-good-measurement decoding achieves exponentially improving recovery accuracy, reaching errors below 10⁻¹² in the verified regime. A central result is an operator-class separation theorem within the model: neutral radiation observables remain completely insensitive to the hair information at all times, while charged observables can access the encoded phase information. Thus, the question of whether soft hair carries information is resolved in this solvable setting by distinguishing the operator algebra available to the observer. The result provides an exactly computable benchmark for discussions of soft hair, information transfer, superselection sectors, and quantum reference frames. The work does not claim a black-hole evaporation solution: the model has no gravitational backreaction, no Page-curve dynamics, and is formulated in a 1+1-dimensional gauge-theory setting. All analytic results, numerical checks, and verification procedures are accompanied by reproducibility materials.

•Aug 25, 2026•0 citations

Reflected entropy for communicating black holes. Part I. Karch-Randall braneworlds

Mir Afrasiar, Jaydeep Kumar Basak, Ashish Chandra +1 more

A bstract We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in BCFT 2 s with two distinct boundaries through a replica technique in the large central charge limit. Subsequently these field theory results are reproduced from bulk computations involving the entanglement wedge cross section in the dual BTZ black hole geometry truncated by two Karch-Randall branes. Our result confirms the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the AdS 3 / BCFT 2 scenario. We further investigate the critical issue of the holographic Markov gap between the reflected entropy and the mutual information for these configurations from the bulk braneworld geometry and study its variation with subsystem sizes and time.

arXiv:2211.13246•Journal of High Energy Physics•Feb 20, 2023•15 citations

Topological Entanglement Entropy of Black Hole Interiors

Eric M. Howard

Recent theoretical progress shows that ([Formula: see text]) black hole solution manifests long-range topological quantum entanglement similar to exotic non-Abelian excitations with fractional quantum statistics. In topologically ordered systems, there is a deep connection between physics of the bulk and that at the boundaries. Boundary terms play an important role in explaining the black hole entropy in general. We find several common properties between BTZ black holes and the Quantum Hall effect in ([Formula: see text])-dimensional bulk/boundary theories. We calculate the topological entanglement entropy of a ([Formula: see text]) black hole and recover the Bekenstein–Hawking entropy, showing that black hole entropy and topological entanglement entropy are related. Using Chern–Simons and Liouville theories, we find that long-range entanglement describes the interior geometry of a black hole and identify it with the boundary entropy as the bond required by the connectivity of spacetime, gluing the short-range entanglement described by the area law. The IR bulk–UV boundary correspondence can be realized as a UV low-excitation theory on the bulk matching the IR long-range excitations on the boundary theory. Several aspects of the current findings are discussed.

Reports in Advances of Physical Sciences•Feb 19, 2020•2 citations

Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure

Marius Gerbershagen

Abstract We define a generalized entanglement measure in the context of the AdS/CFT correspondence. Compared to the ordinary entanglement entropy for a spatial subregion dual to the area of the Ryu-Takayanagi surface, we take into account both entanglement between spatial degrees of freedom as well as between different fields of the boundary theory. Moreover, we resolve the contribution to the entanglement entropy of strings with different winding numbers in the bulk geometry. We then calculate this generalized entanglement measure in a thermal state dual to the BTZ black hole in the setting of the D1/D5 system at and close to the orbifold point. We find that the entanglement entropy defined in this way is dual to the length of a geodesic with non-zero winding number. Such geodesics probe the entire bulk geometry, including the entanglement shadow up to the horizon in the one-sided black hole as well as the wormhole growth in the case of a two-sided black hole for an arbitrarily long time. Therefore, we propose that the entanglement structure of the boundary state is enough to reconstruct asymptotically AdS3 geometries up to extremal surface barriers.

arXiv:2105.01097•Journal of High Energy Physics•Oct 22, 2021•9 citations
Black-hole hair can affect boundary mixed-state entanglement through local stress-energy and through topological information invisible to the classical metric. We separate these channels for a Nielsen--Olesen vortex on a nonrotating BTZ black hole. A superselection theorem shows that Shannon sector entropy cancels from the Markov gap, while standard U(1)U(1)U(1) symmetry-resolved reflected entropy in a thermal U(1)kU(1)_kU(1)k​ CFT is equipartitioned at leading order, excluding a universal log⁡∣n∣\log|n|log∣n∣ term in the imbalance-resolved gap. We therefore define a Wilson-threaded reflected moment in a probe U(1)kU(1)_kU(1)k​ Chern--Simons completion coupled to the compact vortex-flux class. In a reflected-replica sector with linking number ννν, its normalised phase is 2πκpnν/k2πκpnν/k2πκpnν/k, where κ∈Zκ\in\mathbb Zκ∈Z is the mixed topological coupling; for gcd⁡(κν,k)=1\gcd(κν,k)=1gcd(κν,k)=1, a discrete Fourier transform reconstructs n mod kn\bmod knmodk. The RT connectivity transition switches the specified linked contour on or off, whereas the independent scale ℓ⋆r+/L2=1.128378…\ell_\star r_+/L^2=1.128378\ldotsℓ⋆​r+​/L2=1.128378… determines the direction of the vortex-induced shift of that transition. The charged-moment modulus and the ordinary Markov gap remain geometric observables and are computed from a horizon-anchored Einstein-Abelian-Higgs solution with a complete first-variation kernel including the motion of the entanglement-wedge cross-section endpoints. This phase and modulus separation distinguishes topological hair from gravitational dressing without assigning an unsupported winding-dependent entropy.
Holonomy Separation and Anyonic Hair in AdS3_33​
Three-dimensional Einstein gravity and Chern-Simons-Higgs matter both admit Chern-Simons descriptions, but their holonomies encode different physics. We prove that charge conjugation reverses the vortex winding n→−nn\to-nn→−n while leaving the metric and the gravitational connections pointwise unchanged, so every closed gravitational holonomy character, the BTZ charges, the Bañados data and the leading geometric mixed-state hierarchy are exactly even in nnn. On a fixed marked Euclidean replica filling the same change of variables gives Zq[n;J+]=Zq[−n;J+]Z_q[n;\mathcal J_+]=Z_q[-n;\mathcal J_+]Zq​[n;J+​]=Zq​[−n;J+​], so the uncharged Rényi hierarchy, the Faulkner-Lewkowycz-Maldacena one-loop correction, the renormalized generalized entropy and the quantum extremal surfaces coincide for the two orientations. The complementary sector is fixed exactly: with an Aharonov-Bohm angle μμμ conjugate to the entangling-region charge, Zq[n;μ]=Zq[−n;−μ]Z_q[n;μ]=Z_q[-n;-μ]Zq​[n;μ]=Zq​[−n;−μ], so the symmetry-resolved spectrum obeys Zq(Q;n)=Zq(−Q;−n)\mathcal Z_q(\mathcal Q;n)=\mathcal Z_q(-\mathcal Q;-n)Zq​(Q;n)=Zq​(−Q;−n) and every odd charged cumulant reverses with the winding. The orientation is therefore stored entirely in the charge asymmetry of the entanglement spectrum, and is read at topological order by a linked charged matter line. The pair is a bulk logical qubit on which the neutral gravitational-replica algebra acts as a multiple of the identity. Exact BTZ cross sections show that the purification plateau and the entanglement wedge disconnection transition are orientation blind, the latter closing with the cutoff-independent jump (c/3)log⁡(1+2)(c/3)\log(1+\sqrt2)(c/3)log(1+2​). Numerical Bogomolny solutions verify odd flux and even energy and spin; used as linearized charge-matching data they give the even asymptotic shifts δM^=16πGv2∣n∣δ\widehat M=16πGv^2|n|δM=16πGv2∣n∣ and ∣δj^∣=16πGv2n2/(mL)|δ\widehat j|=16πGv^2n^2/(mL)∣δj​∣=16πGv2n2/(mL) and, conditionally, a finite continuous winding envelope.
Abstract We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in finite-sized non-gravitating reservoirs described by CFT2CFT_2CFT2​ C F T 2 s each coupled to two quantum dots at their boundaries in the large central charge limit through a replica technique. These field theory results are substantiated through a holographic computation involving the entanglement wedge cross section in the dual bulk BTZ black hole geometry truncated by two Planck branes. The two Planck branes are the holographic duals of the quantum dots described by AdS2AdS_2AdS2​ A d S 2 slices with JT black holes. Our result reproduce the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the AdS3/CFT2AdS_3/CFT_2AdS3​/CFT2​ A d S 3 / C F T 2 correspondence. Subsequently we analyze the behaviour of the holographic Markov gap between the reflected entropy and the mutual information for different scenarios involving the subsystem sizes and time.
The black-hole soft-hair proposal raises a central dynamical question: can zero-energy boundary degrees of freedom become correlated with radiation in a way that preserves and reveals information, or are such modes permanently decoupled from observable physics? This work studies that question in an exactly solvable minimal charge-locked emission model derived from the soft-hair structure of the Schwinger model. The model provides a controlled setting to analyze information transfer between boundary hair degrees of freedom and emitted radiation without uncontrolled approximations. The analysis shows that the hair variable acts as a quantum-nondemolition degree of freedom: the hair charge is conserved during emission, while the radiation acquires a coherent record of the initial sector. The emitted radiation remains phase-locked to the vacuum-sector label, and the decay of hair coherences follows an exact closed-form decoherence law. The information flow is characterized using mutual information and explicit state reconstruction. The radiation record approaches a perfect distinguishable record of the hair sector, and pretty-good-measurement decoding achieves exponentially improving recovery accuracy, reaching errors below 10⁻¹² in the verified regime. A central result is an operator-class separation theorem within the model: neutral radiation observables remain completely insensitive to the hair information at all times, while charged observables can access the encoded phase information. Thus, the question of whether soft hair carries information is resolved in this solvable setting by distinguishing the operator algebra available to the observer. The result provides an exactly computable benchmark for discussions of soft hair, information transfer, superselection sectors, and quantum reference frames. The work does not claim a black-hole evaporation solution: the model has no gravitational backreaction, no Page-curve dynamics, and is formulated in a 1+1-dimensional gauge-theory setting. All analytic results, numerical checks, and verification procedures are accompanied by reproducibility materials.
A bstract We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in BCFT 2 s with two distinct boundaries through a replica technique in the large central charge limit. Subsequently these field theory results are reproduced from bulk computations involving the entanglement wedge cross section in the dual BTZ black hole geometry truncated by two Karch-Randall branes. Our result confirms the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the AdS 3 / BCFT 2 scenario. We further investigate the critical issue of the holographic Markov gap between the reflected entropy and the mutual information for these configurations from the bulk braneworld geometry and study its variation with subsystem sizes and time.
Recent theoretical progress shows that ([Formula: see text]) black hole solution manifests long-range topological quantum entanglement similar to exotic non-Abelian excitations with fractional quantum statistics. In topologically ordered systems, there is a deep connection between physics of the bulk and that at the boundaries. Boundary terms play an important role in explaining the black hole entropy in general. We find several common properties between BTZ black holes and the Quantum Hall effect in ([Formula: see text])-dimensional bulk/boundary theories. We calculate the topological entanglement entropy of a ([Formula: see text]) black hole and recover the Bekenstein–Hawking entropy, showing that black hole entropy and topological entanglement entropy are related. Using Chern–Simons and Liouville theories, we find that long-range entanglement describes the interior geometry of a black hole and identify it with the boundary entropy as the bond required by the connectivity of spacetime, gluing the short-range entanglement described by the area law. The IR bulk–UV boundary correspondence can be realized as a UV low-excitation theory on the bulk matching the IR long-range excitations on the boundary theory. Several aspects of the current findings are discussed.
Abstract We define a generalized entanglement measure in the context of the AdS/CFT correspondence. Compared to the ordinary entanglement entropy for a spatial subregion dual to the area of the Ryu-Takayanagi surface, we take into account both entanglement between spatial degrees of freedom as well as between different fields of the boundary theory. Moreover, we resolve the contribution to the entanglement entropy of strings with different winding numbers in the bulk geometry. We then calculate this generalized entanglement measure in a thermal state dual to the BTZ black hole in the setting of the D1/D5 system at and close to the orbifold point. We find that the entanglement entropy defined in this way is dual to the length of a geodesic with non-zero winding number. Such geodesics probe the entire bulk geometry, including the entanglement shadow up to the horizon in the one-sided black hole as well as the wormhole growth in the case of a two-sided black hole for an arbitrarily long time. Therefore, we propose that the entanglement structure of the boundary state is enough to reconstruct asymptotically AdS3 geometries up to extremal surface barriers.