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arXiv:2604.05815 · Physical review. D/Physical review. D.

Probing the Factorized Island Branch with the Capacity of Entanglement in JT Gravity

Raúl Arias, Agustín Tamis

hep-thgr-qcquant-phSubmitted Apr 7, 2026• Announced Apr 8, 2026• 0 citations
arXivHTMLPDF

Abstract

Black hole islands are usually diagnosed through the von Neumann entropy, but the full replica saddle contains more information than survives in the limit $n \to 1$. In this paper we show that the capacity of entanglement can detect that extra structure already within the controlled factorized island branch of JT gravity coupled to a large-$c$ bath. In the late-time high-temperature regime, the entropy plateau remains unchanged at the first nontrivial order, while the capacity acquires a definite correction. This provides a sharp semiclassical example in which nearby replica data are physically meaningful even when the entropy itself appears rigid. Our result shows that the factorized island saddle already carries finite-$n$ information beyond the entropy, and that the capacity is a natural observable for exposing it. More broadly, it highlights that the physics of island saddles is not exhausted by the $n=1$ limit: the surrounding replica geometry can contain additional, and observable, information about how the semiclassical saddle is assembled.

DOI
10.1103/rw5x-4t3d
Comments
25 pages, 4 figures

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Black hole islands are usually diagnosed through the von Neumann entropy, but the full replica saddle contains more information than survives in the limit n→1n \to 1n→1. In this paper we show that the capacity of entanglement can detect that extra structure already within the controlled factorized island branch of JT gravity coupled to a large-ccc bath. In the late-time high-temperature regime, the entropy plateau remains unchanged at the first nontrivial order, while the capacity acquires a definite correction. This provides a sharp semiclassical example in which nearby replica data are physically meaningful even when the entropy itself appears rigid. Our result shows that the factorized island saddle already carries finite-nnn information beyond the entropy, and that the capacity is a natural observable for exposing it. More broadly, it highlights that the physics of island saddles is not exhausted by the n=1n=1n=1 limit: the surrounding replica geometry can contain additional, and observable, information about how the semiclassical saddle is assembled.
We compute the capacity of entanglement in two dimensional dilaton gravity in a setting where Hawking radiation, backreaction, and islands can be treated analytically. Our focus is the eternal black hole of the Russo Susskind Thorlacius model coupled to N conformal matter fields. Unlike previous gravitational computations, which were mostly carried out in JT gravity, the RST model forces one to deal with a genuinely dynamical conformal factor and with the global constraints of the replica construction. The main technical step is therefore to solve the replica deformation on the orbifold globally at first order near n=1, including the homogeneous sector fixed by single valuedness and by the requirement of a fixed microcanonical state. For a single interval we obtain a time independent generalized capacity, parallel to the generalized entropy. For two intervals, even in the late time factorization regime, the global solution generates an interaction term between replica fixed points; after Lorentzian continuation this produces a time dependent capacity on the two QES saddle, despite the corresponding entropy plateau. We discuss the regime of validity of the resulting expressions and explain how the large size of the two QES capacity implies a highly non uniform saddle competition near n=1, providing a concrete mechanism for sharp features of the capacity at the Page transition.
We study thermodynamic properties and the entanglement island of a black hole in asymptotically safe quantum gravity, analyzing key thermodynamic quantities such as the Hawking temperature, heat capacity, and entropy, as well as the mass-horizon radius relation. Unlike Schwarzschild black holes, the temperature decreases with mass near the evaporation endpoint, signaling a phase transition and possible stable remnant. The entanglement entropy of Hawking radiation is obtained both with and without island contributions. Without islands, the radiation entropy grows linearly indefinitely, leading to the information paradox. By including island contributions and extremizing the generalized entropy functional, we resolve this paradox. At late times, the radiation entropy saturates at the Bekenstein-Hawking entropy, confirming unitary evolution. From this, we derive the Page time and scrambling time by equating early- and late-time entanglement entropies. The result of this study establishes the finiteness of the radiation entropy and consistency with quantum mechanics.
We study how mixed-state correlations reorganize across island transitions in Jackiw-Teitelboim gravity coupled to a non-gravitating bath. Using the partial-dimensional-reduction realization of double holography, we compute reflected entropy for adjacent and disjoint radiation regions in the vacuum and in the thermofield-double state of an eternal black hole. Reflected entropy probes the internal partition of the entanglement wedge and therefore resolves structure that is invisible to the ordinary Page curve: its dominant saddle can change even when the entropy saddle of the union remains fixed, and it vanishes at leading order when the entanglement wedge disconnects. We show that the lower-dimensional reflected-island description agrees, to leading order in the dynamical brane fluctuation, with the higher-dimensional defect-extremal-surface picture. The finite-angle comparison further suggests a projection-covariant identification of island and brane endpoints at linear order. The resulting Page-like curves and Markov gaps provide a geometric probe of the reorganization of the purification and of non-Markovian, multipartite correlation structure during island transitions.
Abstract The black hole interior is a mysterious region of spacetime where non-perturbative effects are sometimes important. These non-perturbative effects are believed to be highly theory-dependent. We sharpen these statements by considering a setup where the state of the black hole is in a superposition of states corresponding to boundary theories with different couplings, entangled with a reference which keeps track of those couplings. The entanglement wedge of the reference can then be interpreted as the bulk region most sensitive to the values of the couplings. In simple bulk models, e.g., JT gravity + a matter BCFT, the QES formula implies that the reference contains the black hole interior at late times. We also analyze the Renyi-2 entropy tr ρ2 of the reference, which can be viewed as a diagnostic of chaos via the Loschmidt echo. We find explicitly the replica wormhole that diagnoses the island and restores unitarity. Numerical and analytical evidence of these statements in the SYK model is presented. Similar considerations are expected to apply in higher dimensional AdS/CFT, for marginal and even irrelevant couplings.
This thesis explores entanglement entropy, the black hole information paradox, and applications of physics-informed deep learning, with the Anti-de Sitter/conformal field theory (AdS/CFT) correspondence serving as a central framework. The first part examines entanglement islands as a possible resolution to the information paradox. Islands are surfaces in spacetime that contribute to purifying Hawking radiation in semi-classical gravity. We derive the entanglement entropy for annular entangling regions on d-dimensional AdS black hole backgrounds, and show that islands are highly sensitive to the underlying field theory modeling radiation - not only in details but in their very existence. Furthermore, we show how inhomogeneous transformations of entanglement entropy, via the replica trick, encode details about island formation, reflected in the stress tensor on both replica and base manifolds. We also introduce a framework for computing replica corrections to the thermal stress tensor, with intrinsic interest. To make contact with islands in positively curved spacetimes, we construct a multiverse model using T2-deformed dS wedge holography with dS Jackiw–Teitelboim gravity on infrared end-of-the-world branes, where finite-cutoff observers recover Page curves via islands. The second part investigates physics-informed neural networks (PINNs), which embed physical laws into the loss function. Motivated by the challenge of evaluating holographic entanglement entropy with sparse boundary data, we apply Bayesian PINNs (B-PINNs) to solve the corresponding nonlinear PDEs. The latter exemplifies high-energy theory complexities, extending PINNs beyond traditional engineering uses. We examine overconfidence in these models, attributing it to physical priors in the loss rather than miscalibration, and introduce diagnostic tools to assess this effect. Further, Hessian decomposition reveals how constraints hierarchically influence network behavior and shape the solution space, in a non-trivial way when varying with loss weight adjustments.
Recent work has demonstrated the need to include contributions from entanglement islands when computing the entanglement entropy in quantum field theory states coupled to regions of semiclassical gravity. We propose a new formula for the reflected entropy that includes additional contributions from such islands. We derive this formula from the gravitational path integral by finding additional saddles that include generalized replica wormholes. We also demonstrate that our covariant formula satisfies all the inequalities required of the reflected entropy. We use this formula in various examples that demonstrate its relevance in illustrating the structure of multipartite entanglement that are invisible to the entropies.