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:2203.10103 · SciPost Physics

Radiation, entanglement and islands from a boundary local quench

Lorenzo Bianchi, Stefano De Angelis, Marco Meineri

Published Jun 8, 2023• 10 citations
arXivHTMLPDF

Abstract

We study the entanglement and the energy density of the radiation emitted after a local quench in a boundary conformal field theory. We use the operator product expansion (OPE) to predict the early- and late-time behavior of the entanglement entropy and we find, under mild assumptions, a universal form for the leading term, which we test on some treatable two-dimensional examples. We also derive a general upper bound on the entanglement, valid along the full time evolution. In two dimensions, the bound is computed analytically, while in higher dimensions it is evaluated at early and late time via the OPE. These CFT predictions are then compared with a doubly-holographic setup where the CFT is interpreted as a reservoir for the radiation produced on an end-of-the-world brane. After finding the gravitational dual of a boundary local quench, we compute the time evolution of the holographic entanglement entropy, whose late-time behavior is in perfect agreement with the CFT predictions. In the brane+bath picture, unitarity of the time evolution is preserved thanks to the formation of an island. The holographic results can be recovered explicitly from the island formula, in the limit where the tension of the brane is close to the maximal value.

DOI
10.21468/scipostphys.14.6.148

Related papers

The entropy of radiation for local quenches in higher dimensions

Lorenzo Bianchi, Andrea Mattiello, Jacopo Sisti

A bstract We investigate the real time dynamics of the radiation produced by a local quench in a d -dimensional conformal field theory (CFT) with d > 2. Using the interpretation of the higher-dimensional twist operator as a conformal defect, we study the time evolution of the entanglement entropy of the radiation across a spherical entangling surface. We provide an analytic estimate for the early- and late-time behavior of the entanglement entropy and derive an upper bound valid at all times. We extend our analysis to the case of a boundary CFT (BCFT) and derive similar results through a detailed discussion of the setup with two conformal defects (the boundary and the twist operator). We conclude with a holographic analysis of the process, computing the time evolution of the holographic entanglement entropy (HEE) as the area of the Ryu-Takayanagi surface in a backreacted geometry. This gives a Page-like curve in agreement with the early- and late-time results obtained with CFT methods. The extension to a holographic BCFT setup is generically hard and we consider the case of a tensionless end-of-the-world brane.

arXiv:2502.00105•Journal of High Energy Physics•Jun 4, 2025•1 citation

Evolution of entanglement entropy in the D1-D5 brane system

Curtis T. Asplund, Steven G. Avery

We calculate the evolution of the geometric entanglement entropy following a local quench in the D1-D5 conformal field theory, a two-dimensional theory that describes a particular bound state of D1 and D5 branes. The quench corresponds to a localized insertion of the exactly marginal operator that deforms the field theory off of the orbifold (free) point in its moduli space. This deformation ultimately leads to thermalization of the system. We find an exact analytic expression for the entanglement entropy of any spatial interval as a function of time after the quench and analyze its properties. This process is holographically dual to one stage in the formation of a stringy black hole.

arXiv:1108.2510•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Dec 27, 2011•38 citations

Holographic entanglement entropy of local quenches in AdS4/CFT3: a finite-element approach

Alexander Jahn, Tadashi Takayanagi

Abstract Understanding quantum entanglement in interacting higher-dimensional conformal field theories is a challenging task, as direct analytical calculations are often impossible to perform. With holographic entanglement entropy, calculations of entanglement entropy turn into a problem of finding extremal surfaces in a curved spacetime, which we tackle with a numerical finite-element approach. In this paper, we compute the entanglement entropy between two half-spaces resulting from a local quench, triggered by a local operator insertion in a CFT 3 . We find that the growth of entanglement entropy at early time agrees with the prediction from the first law, as long as the conformal dimension Δ of the local operator is small. Within the limited time region that we can probe numerically, we observe deviations from the first law and a transition to sub-linear growth at later time. In particular, the time dependence at large Δ shows qualitative differences to the simple logarithmic time dependence familiar from the CFT 2 case. We hope that our work will motivate further studies, both numerical and analytical, on entanglement entropy in higher dimensions.

arXiv:1705.04705•Journal of Physics A Mathematical and Theoretical•Sep 7, 2017•13 citations

Entanglement entropy in holographic CFTs with generic boundaries

Fabio Ori, Peng-Xiang Hao

Entanglement entropy in holographic conformal field theories with boundaries of generic spacetime signature cannot be described entirely within the standard holographic duality to a real bulk spacetime. We show, both in static and time-dependent setups, that an exact match with the conformal field theory predictions in two boundary dimensions entails an extension of the dual spacetime to complex coordinates. As a consequence, relevant bulk objects such as Ryu-Takayanagi surfaces and branes are in general complex, yet anchored on a real asymptotic boundary preserving the physical meaning of field-theoretical quantities. We also provide a third numerical check of the holographic prediction with a two-dimensional system of free Gaussian fermions exhibiting the same asymptotic regimes across different entanglement phases.

hep-thCross-listedarXiv:2609.21370•Sep 21, 2026•0 citations

Holographic entanglement entropy from 2d CFT: heavy states and local quenches

Curtis T. Asplund, Alice Bernamonti, Federico Galli +1 more

We consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-dimensional gravity. High-energy eigenstates are dual to microstates of the BTZ black hole, so the corresponding holographic calculation is a geodesic length in the black hole geometry; agreement between these two answers demonstrates that these individual microstates of holographic CFTs effectively thermalize at the level of the single-interval entanglement entropy. For local quenches, the dual geometry is a highly boosted black hole or conical defect. On the CFT side, the rise in entanglement entropy after a quench is directly related to the monodromy of a Virasoro conformal block.

arXiv:1410.1392•Journal of High Energy Physics•Feb 1, 2015•279 citations

Entanglement Dynamics by (Non-)Unitary Local Operator Quenches in a 2D Holographic CFT

Weibo Mao, Akihiro Miyata, Masahiro Nozaki +1 more

In this paper, we investigate the time evolution of entanglement entropy and mutual information for the spatially-infinite systems where we act with a primary operator on the vacuum state and then time-evolve it with the sequence of the Euclidean and Lorentzian time evolutions. Two-dimensional holographic conformal field theories describe the systems under consideration in this paper. The Euclidean time evolution is induced by the Rindler Hamiltonian and behaves as the regulator that tames the divergence induced by the local operator, while the Lorentzian one is induced by the uniform Hamiltonian. Under these time evolutions, we investigate the time ordering effect of the Rindler Euclidean and uniform Lorentzian time evolution operators. Consequently, we find the remarkable differences between those time evolutions are induced by whether those are unitary or non-unitary. Especially, we find that the unitary time evolution induces the late-time logarithmic growth of the entanglement entropy, while the non-unitary time evolution induces the late-time constant behavior. Furthermore, we investigate the dual gravity of the systems under consideration. Especially, we investigate the gravity duals of the systems with the insertion of the heavy primary operator and show that it is a black brane with a spacetime-dependent horizon.

hep-thCross-listedarXiv:2512.18781•Physical review. D/Physical review. D.•Dec 23, 2025•0 citations
We study the entanglement and the energy density of the radiation emitted after a local quench in a boundary conformal field theory. We use the operator product expansion (OPE) to predict the early- and late-time behavior of the entanglement entropy and we find, under mild assumptions, a universal form for the leading term, which we test on some treatable two-dimensional examples. We also derive a general upper bound on the entanglement, valid along the full time evolution. In two dimensions, the bound is computed analytically, while in higher dimensions it is evaluated at early and late time via the OPE. These CFT predictions are then compared with a doubly-holographic setup where the CFT is interpreted as a reservoir for the radiation produced on an end-of-the-world brane. After finding the gravitational dual of a boundary local quench, we compute the time evolution of the holographic entanglement entropy, whose late-time behavior is in perfect agreement with the CFT predictions. In the brane+bath picture, unitarity of the time evolution is preserved thanks to the formation of an island. The holographic results can be recovered explicitly from the island formula, in the limit where the tension of the brane is close to the maximal value.
A bstract We investigate the real time dynamics of the radiation produced by a local quench in a d -dimensional conformal field theory (CFT) with d > 2. Using the interpretation of the higher-dimensional twist operator as a conformal defect, we study the time evolution of the entanglement entropy of the radiation across a spherical entangling surface. We provide an analytic estimate for the early- and late-time behavior of the entanglement entropy and derive an upper bound valid at all times. We extend our analysis to the case of a boundary CFT (BCFT) and derive similar results through a detailed discussion of the setup with two conformal defects (the boundary and the twist operator). We conclude with a holographic analysis of the process, computing the time evolution of the holographic entanglement entropy (HEE) as the area of the Ryu-Takayanagi surface in a backreacted geometry. This gives a Page-like curve in agreement with the early- and late-time results obtained with CFT methods. The extension to a holographic BCFT setup is generically hard and we consider the case of a tensionless end-of-the-world brane.
We calculate the evolution of the geometric entanglement entropy following a local quench in the D1-D5 conformal field theory, a two-dimensional theory that describes a particular bound state of D1 and D5 branes. The quench corresponds to a localized insertion of the exactly marginal operator that deforms the field theory off of the orbifold (free) point in its moduli space. This deformation ultimately leads to thermalization of the system. We find an exact analytic expression for the entanglement entropy of any spatial interval as a function of time after the quench and analyze its properties. This process is holographically dual to one stage in the formation of a stringy black hole.
Abstract Understanding quantum entanglement in interacting higher-dimensional conformal field theories is a challenging task, as direct analytical calculations are often impossible to perform. With holographic entanglement entropy, calculations of entanglement entropy turn into a problem of finding extremal surfaces in a curved spacetime, which we tackle with a numerical finite-element approach. In this paper, we compute the entanglement entropy between two half-spaces resulting from a local quench, triggered by a local operator insertion in a CFT 3 . We find that the growth of entanglement entropy at early time agrees with the prediction from the first law, as long as the conformal dimension Δ of the local operator is small. Within the limited time region that we can probe numerically, we observe deviations from the first law and a transition to sub-linear growth at later time. In particular, the time dependence at large Δ shows qualitative differences to the simple logarithmic time dependence familiar from the CFT 2 case. We hope that our work will motivate further studies, both numerical and analytical, on entanglement entropy in higher dimensions.
Entanglement entropy in holographic conformal field theories with boundaries of generic spacetime signature cannot be described entirely within the standard holographic duality to a real bulk spacetime. We show, both in static and time-dependent setups, that an exact match with the conformal field theory predictions in two boundary dimensions entails an extension of the dual spacetime to complex coordinates. As a consequence, relevant bulk objects such as Ryu-Takayanagi surfaces and branes are in general complex, yet anchored on a real asymptotic boundary preserving the physical meaning of field-theoretical quantities. We also provide a third numerical check of the holographic prediction with a two-dimensional system of free Gaussian fermions exhibiting the same asymptotic regimes across different entanglement phases.
We consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-dimensional gravity. High-energy eigenstates are dual to microstates of the BTZ black hole, so the corresponding holographic calculation is a geodesic length in the black hole geometry; agreement between these two answers demonstrates that these individual microstates of holographic CFTs effectively thermalize at the level of the single-interval entanglement entropy. For local quenches, the dual geometry is a highly boosted black hole or conical defect. On the CFT side, the rise in entanglement entropy after a quench is directly related to the monodromy of a Virasoro conformal block.
In this paper, we investigate the time evolution of entanglement entropy and mutual information for the spatially-infinite systems where we act with a primary operator on the vacuum state and then time-evolve it with the sequence of the Euclidean and Lorentzian time evolutions. Two-dimensional holographic conformal field theories describe the systems under consideration in this paper. The Euclidean time evolution is induced by the Rindler Hamiltonian and behaves as the regulator that tames the divergence induced by the local operator, while the Lorentzian one is induced by the uniform Hamiltonian. Under these time evolutions, we investigate the time ordering effect of the Rindler Euclidean and uniform Lorentzian time evolution operators. Consequently, we find the remarkable differences between those time evolutions are induced by whether those are unitary or non-unitary. Especially, we find that the unitary time evolution induces the late-time logarithmic growth of the entanglement entropy, while the non-unitary time evolution induces the late-time constant behavior. Furthermore, we investigate the dual gravity of the systems under consideration. Especially, we investigate the gravity duals of the systems with the insertion of the heavy primary operator and show that it is a black brane with a spacetime-dependent horizon.