The interplay between black hole interior dynamics and quantum chaos provides a crucial framework for probing quantum effects in quantum gravity. In this work, we investigate non-perturbative overlaps in Jackiw-Teitelboim (JT) gravity to uncover universal signatures of quantum chaos and quantum complexity. Taking advantage of universal spectral correlators from random matrix theory, we compute the overlaps between the thermofield double (TFD) state and two distinct classes of states: fixed-length states, which encode maximal volume slices, and time-shifted TFD states. The squared overlaps naturally define probability distributions that quantify the expectation values of gravitational observables. Central to our results is the introduction of generating functions for quantum complexity measures, such as 〈$\textit{e}$ 〉. The time evolution of these generating functions exhibits the universal slope-ramp-plateau structure, mirroring the behavior of the spectral form factor (SFF). Using generating functions, we further demonstrate that the universal time evolution of complexity for chaotic systems, which is characterized by a linear growth followed by a late-time plateau, arises from the disappearance of the linear ramp as the regularization parameter $\textit{α}$ decreases. With regard to the time-shifted TFD state, we derive a surprising result: the expectation value of the time shift, which classically grows linearly, vanishes when non-perturbative quantum corrections are incorporated. This cancellation highlights a fundamental distinction between semiclassical and quantum gravitational descriptions of the black hole interior. All our findings establish generating functions as powerful probes of quantum complexity and chaos in gravitational and quantum systems.

Japan

Masamichi Miyaji

China

Belgium

Shan-Ming Ruan

Shono Shibuya

Kazuyoshi Yano

Non-perturbative overlaps in JT gravity: from spectral form factor to generating functions of complexity

This paper investigates the challenges and resolutions in computing the entanglement entropy for the quantum field theory coupled to de Sitter (dS) gravity along a timelike boundary. The conventional island formula, originally designed to calculate the fine-grained entropy for a non-gravitational system coupled to anti-de Sitter (AdS) gravity, encounters difficulties in de Sitter gravitational spacetime, failing to provide a physically plausible extremal island. To overcome these problems, we introduce a doubly holographic model by embedding a dS braneworld in an AdS bulk spacetime. This approach facilitates the computation of entanglement entropy through holographic correlation functions, effectively circumventing the constraints of the island formula. We demonstrate that the correct recipe for calculating entanglement entropy with dS gravity involves the non-extremal island, whose boundary is instead defined at the edge of the dS gravitational region. Our findings indicate that, during the island phase, the entanglement wedge of the non-gravitational bath includes the entire dS gravitational space. Using the second variation formula, we further show that the existence of a locally minimal surface anchored on the gravitational brane is intrinsically linked to the extrinsic curvature of the brane.

Peng-Xiang Hao

Taishi Kawamoto

Tadashi Takayanagi

Non-extremal island in de Sitter gravity

We employ double holography to examine a system of two entangled gravitating universes that live on two codimension-one branes in an asymptotically AdS3 spacetime with two disjoint conformal boundaries. There are distinct brane configurations depending on the temperature of the thermofield double (TFD) state between the left and right systems. The topology transition between two branes is naturally identified with the emergence of an Einstein-Rosen bridge connecting the two entangled universes. This doubly holographic construction offers a holographic perspective on gravitational collapse and black hole formation in brane universes. Through this holographic framework, we analyze the quantum information structure of the two gravitating universes. Specifically, we calculate the mutual information between defects present in the boundary theories on the left and right sides. Furthermore, we investigate the decoupling process in the Hayden-Preskill protocol applied to the two copies of the defect field theory and discuss the interpretation of the Yoshida-Kitaev decoding protocol.

Canada

Robert Myers

Tomonori Ugajin

Double holography of entangled universes

A long-standing and intriguing question is: does the holographic principle apply to cosmologies like de Sitter spacetime? In this work, we consider a half dS spacetime wherein a timelike boundary encloses the bulk spacetime, presenting a version of de Sitter holography. By analyzing the holographic entanglement entropy in this space and comparing it with that in AdS/CFT, we argue that gravity on a half dS d+1 is dual to a highly non-local field theory residing on dS d  boundary. This non-locality induces a breach in the subadditivity of holographic entanglement entropy. Remarkably, this observation can be linked to another argument that time slices in global de Sitter space overestimate the degrees of freedom by redundantly counting the same Hilbert space multiple times.

Yu-ki Suzuki

A half de Sitter holography

We investigate how the complexity=anything observables proposed by [1, 2] can be used to investigate the interior geometry of AdS black holes. In particular, we illustrate how the flexibility of the complexity=anything approach allows us to systematically probe the geometric properties of black hole singularities. We contrast our results for the AdS Schwarzschild and AdS Reissner-Nordström geometries, i.e., for uncharged and charged black holes, respectively. In the latter case, the holographic complexity observables can only probe the interior up to the inner horizon.

Eivind Jørstad

Complexity=anything: singularity probes

In this paper, we investigate gluing together two Anti-de Sitter (AdS) geometries along a timelike brane, which corresponds to coupling two brane field theories (BFTs) through gravitational interactions in the dual holographic perspective. By exploring the general conditions for this gluing process, we show that the energy stress tensors of the BFTs backreact on the dynamical metric in a manner reminiscent of the TTbar deformation. In particular, we present explicit solutions for the three-dimensional case with chiral excitations and further construct perturbative solutions with non-chiral excitations.

Gluing AdS/CFT

We expand on our results in [1] to present a broad new class of gravitational observables in asymptotically Anti-de Sitter space living on general codimension-zero regions of the bulk spacetime. By taking distinct limits, these observables can reduce to well-studied holographic complexity proposals, e.g., the volume of the maximal slice and the action or spacetime volume of the Wheeler-DeWitt patch. As with the codimension-one family found in [1], these new observables display two key universal features for the thermofield double state: they grow linearly in time at late times and reproduce the switchback effect. Hence we argue that any member of this new class of observables is an equally viable candidate as a gravitational dual of complexity. Moreover, using the Peierls construction, we show that variations of the codimension-zero and codimension-one observables are encoded in the gravitational symplectic form on the semi-classical phase-space, which can then be mapped to the CFT.

Switzerland

CERN

Italy

Alexandre Belin

Gábor Sárosi

United States

Antony Speranza

Complexity equals anything II

We systematically study moving mirror models in two-dimensional conformal field theory (CFT). By focusing on their late-time behavior, we separate the mirror profiles into four classes, named type A (timelike) mirrors, type B (escaping) mirrors, type C (chasing) mirrors, and type D (terminated) mirrors. We analytically explore the characteristic features of the energy flux and entanglement entropy for each type and work out their physical interpretation. Moreover, we construct their gravity duals for which end-of-the-world (EOW) branes play a crucial role. Depending on the mirror type, the profiles of the EOW branes show distinct behaviors. In addition, we also provide a criterion that decides whether the replica method in CFTs computes entanglement entropy or pseudo entropy in moving mirror models.

Ibrahim Akal

Zixia Wei

Zoo of holographic moving mirrors

The black hole singularity plays a crucial role in formulating Hawking’s information paradox. The global spacetime analysis may be reconciled with unitarity by imposing a final state boundary condition on the spacelike singularity. Motivated by the final state proposal, we explore the effect of final state projection in two dimensional conformal field theories. We calculate the time evolution under postselection by employing the real part of pseudoentropy to estimate the amount of quantum entanglement averaged over histories between the initial and final states. We find that this quantity possesses a Page-curve-like behavior.

Page curve under final state projection

We study the CV, CA, and CV2.0 approaches to holographic complexity in (d + 1)-dimensional de Sitter spacetime. We find that holographic complexity and corresponding growth rate presents universal behaviour for all three approaches. In particular, the holographic complexity exhibits ‘hyperfast’ growth [1] and appears to diverge with a universal power law at a (finite) critical time. We introduce a cutoff surface to regulate this divergence, and the subsequent growth of the holographic complexity is linear in time.