arXiv subjects

Ricardo Espíndola

Publications and source records attributed to Ricardo Espíndola.

14 recordsLinked to original sources

arXiv2026

Full Eigenstate Thermalization in Quantum Field Theory and Gravitational Scrambling

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arXiv2026

Full Eigenstate Thermalization in Quantum Field Theory: Free Cumulants and Gravitational Scrambling

Using thermal analyticity, we derive directional large-frequency bounds on the smooth functions entering full eigenstate thermalization in continuum quantum field theory. The strongest directions reproduce the scales previously identified for lattice systems, while the complete analyticity domain reveals a broader asymmetric multifrequency structure. In thermal two-dimensional conformal field theory, exact two- and three-point functions saturate the corresponding bounds. At fourth order, where genuine dynamical information first appears, we show that the holographic CFTs studied here saturate the strongest full-ETH bounds. These results establish a direct connection between full ETH, free cumulants, and gravitational scrambling, and are consistent with the emergence of asymptotic freeness realized by the gravitational scrambling algebra.

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arXiv2026

The mini-Page Curve in Cosmology

The black hole information paradox has motivated extensive study of how and when information escapes from evaporating black holes. Here we address the analogous question for cosmological horizons: when does an individual Hawking pair begin to carry information out of a de Sitter horizon? We study this problem in a class of two-dimensional flow geometries that interpolate smoothly between an asymptotic AdS$ _2 $ boundary and a dS$ _2 $ static patch. Modeling the emission of a Hawking pair via a probe state constructed from local operators and their modular conjugates, we promote the centaur algebra of observables to a Type II$ _\infty $ factor through the crossed-product construction. This allows us to compute the entropy difference between the thermofield-double reference state and the Hawking-pair state. We find that this difference traces a characteristic mini-Page curve for the cosmological horizon: it starts near zero, reaches a minimum near $ τ\approx β/8 $ before increasing again. We interpret the location of the minimum as the time at which quantum information begins to escape the cosmological horizon. Extending the analysis to the microcanonical ensemble, we show that the algebraic entropy coincides with the generalized entropy of an entanglement wedge cut that tracks the emitted particle along the horizon. Furthermore, the relative modular flow generated between the two states yields a Lyapunov exponent $λ=2π/β$, identifying the scrambling time as the scale at which the information carried by the pair becomes accessible to a static-patch observer.

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arXiv2026

Flow-geometry microstates

We construct geometric microstates for a class of two-dimensional flow geometries$-$spacetimes that interpolate from an asymptotic AdS$_2$ boundary to a dS$_2$ static patch in the interior$-$by inserting particles behind the horizon. We show that this mechanism produces dS microstates with an Einstein-Rosen bridge of infinite length behind the horizon. The state-counting of these microstates, including wormhole contributions, reproduces the Gibbons-Hawking entropy, $S_{\rm dS}=A^{\rm dS}_{\rm horizon}/4G$. Furthermore, we extend the microstate-counting method to the case of a finite-length Einstein-Rosen bridge. As a result, the Hilbert space of the dS horizon in the flow geometry can be spanned by states with a purely dS Einstein-Rosen bridge, containing no AdS portion on the time-symmetric slice. This provides a concrete realization of dS microstates within a controlled holographic framework.

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arXiv2026

Spectral Admissibility of Real Observers in Euclidean de Sitter Gravity

The Euclidean de Sitter path integral contains the familiar phase associated with conformal negative modes. Maldacena's construction shows that a suitably included real observer can reorganize the refined state-counting problem. This paper does not rederive that cancellation. It addresses the prior semiclassical admissibility question: which observer sectors couple to the de Sitter saddle as genuine metric observers without becoming spectators or producing infrared-singular backreaction? On $S^D$, after gauge fixing and zero-mode projection, the observer's quadratic influence is governed by a Schur complement. We formulate a form-domain criterion: if the observer kernel is positive and the mixed metric-observer source is bounded after applying $Δ_{ΦΦ}^{-1/2}$, the induced metric correction is a bounded quadratic-form perturbation on the chosen channel. In the gapped case, $Δ_{ΦΦ}\geq m_*^2\mathbf{1}$ gives $\|K^\dagger Δ_{ΦΦ}^{-1} K\|_{\rm op} \leq \|K\|_{\rm op}^2/m_*^2$; metric-coupled soft modes produce corrections growing as $1/\varepsilon$. We prove a sufficiency theorem: on any stable channel with coercive form $Q_{gg}^P \geq δ_P \|h\|^2$, the Gaussian saddle remains controlled whenever $\|Δ_{ΦΦ}^{-1/2} \mathfrak{j}_P\|_{\rm op}^2 < δ_P$. We construct a localized gapped clock-detector with internal oscillators on a smeared worldline that satisfies the criterion with a computable bound and gives explicit $S^4$ benchmark versus the round-sphere TT scale. The conformal channel is treated only as an indefinite or contour-defined sector; boundedness does not imply positivity. The criterion identifies the semiclassically admissible observer class. Phase cancellation follows only when this class overlaps the relevant conformal or negative-mode sector and is combined with an independent contour or state-counting prescription.

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arXiv2025

Islands and traversable wormholes

We study information recovery in black hole evaporation using traversable wormhole protocols in AdS$_2$ Jackiw-Teitelboim gravity with matter fields coupled to an external bath. By introducing a simple non-local interaction between left and right radiation regions, we generate negative-energy shockwaves that render the wormhole traversable. We compute the resulting shifts in Kruskal coordinates, changes in the stress tensor, and backreaction effects on quantum extremal surfaces, finding a consistent decrease of the generalized entropy that aligns with the flat Page curve. Finally, we analyze the impact of negative-energy shocks on boundary two-point functions, providing a microscopic probe of island/radiation duality and discussing possible implications for experimental realizations in analog quantum-mechanical models.

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arXiv2025

A teleportation protocol in Schwarzschild-de Sitter space

We propose a new information transfer protocol for de Sitter space, using black holes as energy reservoirs. We consider antipodal observers in pure de Sitter space in the Bunch-Davis state. They can store Hawking modes from the cosmological horizon in a box. Alternatively, due to thermal fluctuations in de Sitter space, black holes formed through a pair-creation {process can be used} as energy reservoirs. We focus on the Nariai black hole case, which corresponds to an equilibrium state. Once the black hole is produced, energy pulses can be released into its interior, opening a traversable wormhole. We provide bounds for the amount of information that can be transferred. Specializing in (1+1)-dimensions, we explore how the teleportation protocol leads to an explicit geometric description of the information transmitted through an island region. The protocol uncovers quantum information aspects of de Sitter space, independently of any particular realization of de Sitter space holography.

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arXiv2024

The centaur-algebra of observables

This letter explores a transition in the type of von Neumann algebra for asymptotically AdS spacetimes from the implementations of the different gravitational constraints. We denote it as the \emph{centaur-algebra} of observables. In the first part of the letter, we employ a class of flow geometries interpolating between AdS$_2$ and dS$_2$ spaces, the centaur geometries. We study the type II$_\infty$ crossed product algebra describing the semiclassical gravitational theory, and we explore the algebra of bounded sub-regions in the bulk theory following $T\overline{T}$ deformations of the geometry and study the gravitational constraints with respect to the quasi-local Brown-York energy of the system at a finite cutoff. In the second part, we study arbitrary asymptotically AdS spacetimes, where we implement the boundary protocol of an infalling observer modeled as a probe black hole proposed by arXiv:2211.16512 to study modifications in the algebra. In both situations, we show how incorporating the constraints requires a type II$_1$ description.

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arXiv2023

Changing states in holography: From modular Berry curvature to the bulk symplectic form

We present a new perspective on bulk reconstruction using Berry phases in the boundary CFT. Our parallel transport of modular Hamiltonians is associated to a trajectory in the space of states, which we obtain from the insertion of a source in the Euclidean path integral. Using a modular version of the extrapolate dictionary and the equivalence between modular flow in the boundary and the bulk, we show that the expectation value of the modular Berry curvature on the boundary agrees with an appropriately defined bulk symplectic form associated to the entanglement wedge. In addition, we derive a quantum information metric on the space of density matrices from the Berry curvature, which is related to the canonical energy in the bulk. We also explore the case where a state change reduces to a shape change, uncovering the coadjoint orbit structure of kinematic space in higher dimensions.

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arXiv2022

Virasoro Entanglement Berry Phases

We study the parallel transport of modular Hamiltonians encoding entanglement properties of a state. In the case of 2d CFT, we consider a change of state through action with a suitable diffeomorphism on the circle: one that diagonalizes the adjoint action of the modular Hamiltonian. These vector fields exhibit kinks at the interval boundary, thus together with their central extension they differ from usual elements of the Virasoro algebra. The Berry curvature associated to state-changing parallel transport is the Kirillov-Kostant symplectic form on an associated coadjoint orbit, one which differs appreciably from known Virasoro orbits. We find that the boundary parallel transport process computes a bulk symplectic form for a Euclidean geometry obtained from the backreaction of a cosmic brane, with Dirichlet boundary conditions at the location of the brane. We propose that this gives a reasonable definition for the symplectic form on an entanglement wedge.

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arXiv2022

How to Make Traversable Wormholes: Eternal AdS$_4$ Wormholes from Coupled CFT's

We construct an eternal traversable wormhole connecting two asymptotically $\text{AdS}_4$ regions. The wormhole is dual to the ground state of a system of two identical holographic CFT's coupled via a single low-dimension operator. The coupling between the two CFT's leads to negative null energy in the bulk, which supports a static traversable wormhole. As the ground state of a simple Hamiltonian, it may be possible to make these wormholes in the lab or on a quantum computer.

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arXiv2022

Islands in FRW Cosmologies

We search for candidate island regions in FRW cosmologies supported by radiation, cosmological constant $Λ$, and non-zero spatial curvature. The radiation is assumed to be in a thermal state. We apply the necessary conditions introduced in [arXiv:2008.01022]. Both for the open and closed universes with $Λ<0$, the Friedmann equation admits recollapsing solutions with a time-symmetric slice. In the case of closed universes, there is always an island that is the whole Cauchy slice. However, for $Λ<0$, we also find another finite-sized candidate island region, in the middle of the spacetime, at the turnaround time. In the case of the open universes, we only find a candidate island region for $Λ<0$, that appears at the turnaround time. It starts from a finite value of the radial coordinate and extends to infinity. Looking at both open and closed universes, we conclude that the key ingredient that allows the existence of islands is the negative cosmological constant. We provide analytic results along the time-symmetric slices and support our results with numerics in the whole spacetime.

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arXiv2018

Entanglement Wedge Reconstruction and Entanglement of Purification

In the holographic correspondence, subregion duality posits that knowledge of the mixed state of a finite spacelike region of the boundary theory allows full reconstruction of a specific region of the bulk, known as the entanglement wedge. This statement has been proven for local bulk operators. In this paper, specializing first for simplicity to a Rindler wedge of AdS$_3$, we find that generic curves within the wedge are in fact not fully reconstructible with entanglement entropies in the corresponding boundary region, even after using the most general variant of hole-ography, which was recently shown to suffice for reconstruction of arbitrary spacelike curves in the Poincare patch. This limitation is an analog of the familiar phenomenon of entanglement shadows, which we call 'entanglement shade'. We overcome it by showing that the information about the nonreconstructible curve segments is encoded in a slight generalization of the concept of entanglement of purification, whose holographic dual has been discussed very recently. We introduce the notion of 'differential purification', and demonstrate that, in combination with differential entropy, it enables the complete reconstruction of all spacelike curves within an arbitrary entanglement wedge in any 3-dimensional bulk geometry.

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arXiv2018

What's the Point? Hole-ography in Poincare AdS

In the context of the AdS/CFT correspondence, we study bulk reconstruction of the Poincare wedge of AdS$_3$ via hole-ography, i.e., in terms of differential entropy of the dual CFT$_2$. Previous work had considered the reconstruction of closed or open spacelike curves in global AdS, and of infinitely extended spacelike curves in Poincare AdS that are subject to a periodicity condition at infinity. Working first at constant time, we find that a closed curve in Poincare is described in the CFT by a family of intervals that covers the spatial axis at least twice. We also show how to reconstruct open curves, points and distances, and obtain a CFT action whose extremization leads to bulk points. We then generalize all of these results to the case of curves that vary in time, and discover that generic curves have segments that cannot be reconstructed using the standard hole-ographic construction. This happens because, for the nonreconstructible segments, the tangent geodesics fail to be fully contained within the Poincare wedge. We show that a previously discovered variant of the hole-ographic method allows us to overcome this challenge, by reorienting the geodesics touching the bulk curve to ensure that they all remain within the wedge. Our conclusion is that all spacelike curves in Poincare AdS can be completely reconstructed with CFT data, and each curve has in fact an infinite number of representations within the CFT.

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