We model the Hayden-Preskill (HP) information recovery protocol in 2d CFTs via local joining quenches. Euclidean path integrals with slits prepare the HP subsystems: the message $\textit{M}$, its reference $\textit{N}$, the Page-time black hole $\textit{B}$, the early radiation $\textit{E}$, and the late radiation $\textit{R}$; the remaining black hole after emitting $\textit{R}$ is denoted as $\textit{B}$ . The single-slit geometry provides an analytically tractable toy model, while the bounded-slit geometry more closely captures the HP setup. In the free Dirac fermion 2d CFT, the mutual information $\textit{I}$($\textit{N}$ : $\textit{B}$ ) shows quasi-particle dynamics with partial or full revivals, whereas that in holographic 2d CFTs, which are expected to be maximally chaotic, exhibits sharp transitions: in the bounded-slit case, when the size of the late radiation becomes comparable to that of the reference $\textit{N}$, $\textit{I}$($\textit{N}$ : $\textit{B}$ ) vanishes at late time, otherwise it remains finite. This contrast between free CFTs and holographic CFTs gives a clear characterization of the HP recovery threshold.

China

Weibo Mao

Japan

Tadashi Takayanagi

Hayden-Preskill model via local quenches

We consider the evolution of entanglement entropy in a two-dimensional conformal field theory with a holographic dual. Specifically, we are interested in a class of excited states produced by a combination of pure-state (local operator) and mixed-state local quenches. We employ a method that allows us to determine the full time evolution analytically. While a single insertion of a local operator gives rise to a logarithmic time profile of entanglement entropy relative to the vacuum, we find that this growth is heavily suppressed in the presence of a mixed-state quench, reducing it to a time-independent constant bump. The degree of suppression depends on the relative position of the quenches as well as the ratio of regularization parameters associated with the quenches. This work sheds light on the interesting properties of gravitational scattering involving black holes.

Kazuki Doi

Entanglement suppression due to black hole scattering

We explore the reconstruction of bulk local states in three-dimensional flat spacetime (Flat ) using states from two-dimensional Carrollian conformal field theories (CCFT ), proposed as dual field theories in one lower dimension. For massive scalar-type bulk excitations, reconstruction is achieved through states in the induced representation. This method successfully reproduces the bulk massive scalar spectrum and the bulk-to-bulk propagator. Additionally, we identify a new flat limit from AdS and dS spacetimes, further validating our proposal for scalar reconstruction in Flat /CCFT .

Peng-Xiang Hao

Kotaro Shinmyo

Yu-ki Suzuki

Shunta Takahashi

Bulk reconstruction of scalar excitations in Flat

We study the Ryu-Takayanagi (RT) surfaces associated with timelike subregions in static spacetimes with a horizon. It is possible to find the analytical continuation of the RT surfaces that can extend into the horizon, allowing us to probe the interior of the black hole. The horizon typically divides the RT surface into two distinct parts. We demonstrate that the area of the surface inside the horizon can be reconstructed from the contributions of the surfaces outside the horizon, along with additional RT surfaces for spacelike subregions that are causally related to the timelike subregions. This result provides a concrete realization of black hole complementarity at the level of classical metric, where the spacetime in the black hole interior can be reconstructed from the degrees of freedom outside the horizon.

Wu-zhong Guo

Jin Xu

Duality of Ryu-Takayanagi surfaces inside and outside the horizon

In this paper, we study a new class of AdS/BCFT setups, where the world-volumes of end-of-the-world branes (EOW branes) are given by flat spaces, to explore flat space holography from an AdS bulk. We show that they provide gravity duals of CFTs in the presence of null boundaries. Our holographic calculations lead to many new predictions on entanglement entropy, correlation functions and partition functions for CFTs with null boundaries. By considering a bulk region between two EOW branes, we present an AdS/BCFT explanation that the flat space gravity is dual to a Carrollian CFT (CCFT), including the swing surface calculation of entanglement entropy.

Naoki Ogawa

Takahiro Waki

Flat space holography via AdS/BCFT

We study a class of quantum states involving multiple entangled CFTs in AdS /CFT , associated with multi-boundary black hole geometries, and demonstrate that the Ryu-Takayanagi (RT) formula for entanglement entropy can be derived using only boundary CFT data. Approximating the OPE coefficients by their Gaussian moments within the 2D large-$\textit{c}$ CFT ensemble, we show that both the norm of the states and the entanglement entropies associated with various bipartitions — reproducing the expected bulk dual results — can be computed purely from the CFT. All $\textit{macroscopic geometric}$ structures arising from gravitational saddles emerge entirely from the universal statistical moments of the $\textit{microscopic algebraic}$ CFT data, revealing a statistical-mechanical mechanism underlying semiclassical gravity. We establish a precise correspondence between the CFT norm, the Liouville partition function with ZZ boundary conditions, and the exact gravitational path integral over 3D multi-boundary black hole geometries. For entanglement entropy, each RT phase arises from a distinct leading-order Gaussian contraction, with phase transitions — analogous to replica wormholes — emerging naturally from varying dominant statistical patterns in the CFT ensemble. Our derivation elucidates how the general mechanism behind holographic entropy, namely a boundary replica direction that elongates and becomes contractible in the bulk dual, is encoded explicitly in the statistical structure of the CFT data.

United States

Ning Bao

Hao Geng

Yikun Jiang

Ryu-Takayanagi formula for multi-boundary black holes from 2D large-$\textit{c}$ CFT ensemble

Holographic duality describes gravitational theories in terms of quantum many-body systems. In holography, quantum information theory provides a crucial tool that directly connects microscopic structures of these systems to the geometries of gravitational spacetimes. One manifestation is that the entanglement entropy in quantum many-body systems can be calculated from the area of an extremal surface in the corresponding gravitational spacetime. This implies that a gravitational spacetime can emerge from an enormous number of entangled qubits. In this Essay, I will discuss open problems in this area of research, considering recent developments and outlining future prospects towards a complete understanding of quantum gravity. The first step in this direction is to understand what kind of quantum circuits each holographic spacetime corresponds to, drawing on recent developments in quantum complexity theories and studying concrete examples of holography in string theory. Next, we should extend the concept of holography to general spacetimes, e.g., those spacetimes which appear in realistic cosmologies, by utilizing the connections between quantum information and holography. To address the fundamental question of how time emerges, I will propose the concepts of pseudoentropy and timelike entanglement as a useful tool in our exploration. Part of a series of Essays in Physical Review Letters which concisely present author visions for the future of their field.

Essay: Emergent Holographic Spacetime from Quantum Information

Using recent developments in expressing one-loop partition functions in Euclidean $\textit{AdS}$ space-times in terms of character integrals, we relate the one-loop effective action for a free field theory in $\textit{AdS}$ (comprised of a massless scalar field and a massless Majorana fermion field) to the partition function of the de Alfaro-Fubini-Furlan (DFF) conformal quantum mechanics (CQM) models on the two global $\textit{AdS}$ boundaries. The equal number of bosonic and fermionic degrees in the field theory guarantee that the one-loop calculation is free of all UV divergences except a logarithmic one consistent with the expected entanglement entropy behaviour in a CQM. Via a thermofield double representation, we compute the entanglement entropy between two copies of the $\textit{CFT}$ (CQM), each living near one of the two boundaries of global $\textit{AdS}$ , in a state at global time $\textit{τ}$ → – ∞. This entanglement entropy is expressed in terms of the logarithm of the regularised length of a closed particle trajectory infinitesimally near the rim of the Euclidean $\textit{AdS}$ disc. We view this relation between boundary quantum entanglement and a bulk geometrical quantity as the $\textit{AdS}$ /$\textit{CFT}$ version of the Ryu-Takayanagi conjecture in our setup. The boundary entanglement entropy is equal to 4 times the thermodynamic entropy read off from the regularised one-loop effective action in $\textit{AdS}$ . Further, we compute the bulk entanglement entropy associated with black hole horizons in Lorentzian $\textit{AdS}$ and show that it precisely matches the boundary entanglement entropy.

Portugal

Gabriel Cardoso

Bernardo Martins

Suresh Nampuri

Bulk-boundary entanglement correspondence and the Ryu-Takayanagi conjecture in an $\textit{AdS}$

We study (i) Janus deformations and (ii) non-local double trace deformations of a pair of CFTs, as two different ways to construct CFT duals of traversable AdS wormholes. First we construct a simple model of traversable wormholes by gluing two Poincaré AdS geometries and BTZ black holes and compute holographic two point functions and (pseudo) entanglement entropy. We point out that a Janus gravity solution describes a traversable wormhole when the deformation parameter takes imaginary values. On the other hand, we show that double trace deformations between two decoupled CFTs can reproduce two point functions of traversable AdS wormholes. By considering the case where the double trace deformation is given by a non-local $$ T\overline{T} $$ deformation, we analyze the dual gravity which implies emergence of wormholes. We present toy model of these deformed CFTs by using free scalars and obtain qualitative behaviors expected for them. We argue that the crucial difference between the two constructions is that a global time slice of wormhole is described by a pure state for Janus deformations, while it is a mixed state for the double trace deformations.

Taishi Kawamoto

Ryota Maeda

Nanami Nakamura

Traversable AdS wormhole via non-local double trace or Janus deformation

In this paper, we study the time-dependent dynamics of an end-of-the-world (EOW) brane in AdS with a scalar field localized on the brane. We mainly studied several aspects of holography and cosmology. Standard requirements in the AdS +1 /CFT lead to a constraint on the conformal dimension in the dS /CFT −1 . We also prove a time-like analog of g-theorem using the null energy condition in the context of AdS /BCFT . In the cosmological interpretation, we rewrite the equation of motion of the brane as a Friedman-like equation, which enables us to consider its dynamics in analogy with the ordinal cosmology. And then we classify all possible solutions of the brane when the potential takes a constant value. We find that our brane cosmology model can describe a process of creating a universe via a big-bang. Additionally, we show that when the brane is close to a hyperplane, its effective action is given by a Liouville gravity with a scalar field matter. Finally, we also obtain brane solutions with boost symmetry, which are obtained by analytical continuation of Euclidean branes with a torus topology.