arXiv subjects

Tomonori Ugajin

Publications and source records attributed to Tomonori Ugajin.

At least 19 recordsLinked to original sources

arXiv2026

Physical Predictions in Closed Quantum Gravity

Recent developments in gravitational path integrals indicate that the nonperturbative physical Hilbert space of a closed universe is one-dimensional within each superselection sector. This raises a basic puzzle: how can a unique quantum-gravity state give rise to semiclassical physics, measurement outcomes, and classical probabilities? In this paper, we develop a framework in which nontrivial and statistically stable predictions emerge despite the one-dimensionality of the fully constrained Hilbert space. The key idea is to extract physical predictions in an enlarged, unconstrained Hilbert space by conditioning on observational data. We show that partial observability -- reflecting the limited access of observers to the degrees of freedom of the universe -- suppresses ensemble fluctuations associated with microscopic structure in the gravitational path integral, thereby restoring semiclassical predictability with exponential accuracy. We formulate the construction explicitly including contributions from the Hartle--Hawking no-boundary state, define a gauge-invariant Hilbert space for observations via a density operator, and generalize the formalism to conditioning on histories, clarifying the emergence of classical probabilities and an effective arrow of time. Finally, we explore whether this framework can support a realistic cosmology and identify assumptions that the underlying theory of quantum gravity must satisfy.

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arXiv2026

Emergent Closed Universes in Symmetric Orbifold CFTs

We identify closed universe sectors in large $N$ symmetric orbifold CFTs with holographic duals. Starting from tensor product states built out of a finite dimensional low energy subspace of the seed theory, we show that the large $N$ Hilbert space decomposes into superselection sectors labeled by occupation number distributions. Before imposing the orbifold gauge constraint, these sectors have exponentially large dimensions, and the maximally entropic sector dominates the ungauged Hilbert space. We argue that this sector exhibits several characteristic features expected of a closed universe Hilbert space: pure states become indistinguishable from a mixed state at the level of simple correlation functions, and the associated operator algebra is naturally a hyperfinite type II$_1$ von Neumann algebra. We then impose the $S_N$ gauge constraint. The large gauge redundancy drastically reduces the number of independent states. In particular, in the large $N$ limit, the dimension of the physical Hilbert space grows only polynomially with $N$. Consequently, each superselection sector after imposing the constraint is one dimensional in this limit. This reproduces the qualitative behavior suggested by gravitational path integral calculations with wormholes. We then show why, in this setup, the Hartle-Hawking type semiclassical approximation for the dominant closed universe fails to reproduce the CFT results. Nevertheless, the dominant saddle point approximation for gravitational path integral calculation is reconstructed once the CFT degrees of freedom are coupled to external observer degrees of freedom.

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arXiv2026

Black Hole Interior and Quantum Error Correction with Dynamical Gravity

According to the island formula, information in the code subspace defined in the black hole interior is embedded in the Hawking radiation after the Page time. At first sight, this embedding suggests that operations acting on the Hawking radiation could modify the information in the code subspace, potentially leading to an apparent violation of causality. Indeed, in previous studies based on the PSSY model, which incorporates only the topological degrees of freedom of gravity, it was shown that when the error is sufficiently large, a violation of causality can arise, as indicated by a nonvanishing mutual information. In this paper, we investigate the situation in which dynamical gravity also acts on the Hawking radiation. In this case, operations on the Hawking radiation induce nontrivial backreaction on the bulk spacetime appearing in the gravitational path integral for the mutual information -- an effect that is absent when the Hawking radiation is non-gravitating. We find that this backreaction renders the relevant mutual information vanishing. This result implies that, in theories with dynamical gravity, the apparent violation of causality is resolved.

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arXiv2025

Nonperturbative Quantum Gravity in a Closed Lorentzian Universe

We study how meaningful physical predictions can arise in nonperturbative quantum gravity in a closed Lorentzian universe. In such settings, recent developments suggest that the quantum gravitational Hilbert space is one-dimensional and real for each $α$-sector, as induced by spacetime wormholes. This appears to obstruct the conventional quantum-mechanical prescription of assigning probabilities via projection onto a basis of states. While previous approaches have introduced external observers or augmented the theory to resolve this issue, we argue that quantum gravity itself contains all the necessary ingredients to make physical predictions. We demonstrate that the emergence of classical observables and probabilistic outcomes can be understood as a consequence of partial observability: physical observers access only a subsystem of the universe. Tracing out the inaccessible degrees of freedom yields reduced density matrices that encode classical information, with uncertainties exponentially suppressed by the environment's entropy. We develop this perspective using both the Lorentzian path integral and operator formalisms and support it with a simple microscopic model. Our results show that quantum gravity in a closed universe naturally gives rise to meaningful, robust predictions without recourse to external constructs.

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arXiv2024

Double Holography of Entangled Universes

We employ double holography to examine a system of two entangled gravitating universes that live on two codimension-one branes in an asymptotically AdS$_3$ 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.

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arXiv2023

The Petz (lite) recovery map for scrambling channel

We study properties of the Petz recovery map in chaotic systems, such as the Hayden-Preskill setup for evaporating black holes and the SYK model. Since these systems exhibit the phenomenon called scrambling, we expect that the expression of the recovery channel $\mathcal{R}$ gets simplified, given by just the adjoint $\mathcal{N}^{\dagger}$ of the original channel $\mathcal{N}$ which defines the time evolution of the states in the code subspace embedded into the physical Hilbert space. We check this phenomenon in two examples. The first one is the Hayden-Preskill setup described by Haar random unitaries. We compute the relative entropy $S(\mathcal{R}\left[\mathcal{N}[ρ]\right] ||ρ)$ and show that it vanishes when the decoupling is archived. We further show that the simplified recovery map is equivalent to the protocol proposed by Yoshida and Kitaev. The second example is the SYK model where the two dimensional code subspace is defined by an insertion of a fermionic operator, and the system is evolved by the SYK Hamiltonian. We check the recovery phenomenon by relating some matrix elements of an output density matrix $\langle T|\mathcal{R}[\mathcal{N}[ρ]]|T' \rangle$ to Rényi-two modular flowed correlators, and show that they coincide with the elements for the input density matrix with small error after twice the scrambling time.

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arXiv2023

de Sitter space is sometimes not empty

Multiple lines of evidence suggest that the Hilbert space of an isolated de Sitter universe is one dimensional but can appear larger when probed by a gravitating observer. To test this idea, we compute the von Neumann entropy of a field theory in a two-dimensional de Sitter universe which is entangled in a thermal-like state with the same field theory on a disjoint, asymptotically anti-de Sitter (AdS) black hole. Previously, it was shown that the replica trick for computing the entropy of such entangled gravitating systems requires the inclusion of a non-perturbative effect in quantum gravity -- novel wormholes connecting the two spaces. Here we show that: (a) the expected wormholes connecting de Sitter and AdS universes exist, avoiding a no-go theorem via the presence of sources on the AdS boundary; (b) the entanglement entropy vanishes if the nominal entropy of the de Sitter cosmological horizon (S_dS = A_horizon^dS / 4G_N) is less than the entropy of the AdS black hole horizon (S_BH = A_horizon^AdS / 4G_N), i.e., S_dS < S_BH; (c) the entanglement entropy is finite when S_dS > S_BH. Thus, the de Sitter Hilbert space is effectively nontrivial only when S_dS > S_BH. The AdS black hole we introduce can be regarded as an ``observer'' for de Sitter space. In this sense, our result is a non-perturbative generalization of the recent perturbative argument that the algebra of observables on the de Sitter static patch becomes nontrivial in the presence of an observer.

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arXiv2022

Entanglement between two evaporating black holes

We study a thermo-field double type entangle state on two disjoint gravitating universes, say A and B, with an eternal black hole on each. As was shown previously, its entanglement entropy of the universe A is computed by the generalized entropy on a new spacetime constructed by suitably gluing the black holes on A and B. We study such spacetime gluings when universes are asymptotically flat and AdS cases, especially when the masses of these black holes are different. We also clarify the rule to construct such a glued spacetime in more general settings from the gravitational path integral view point.

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arXiv2022

A comment on a fine-grained description of evaporating black holes with baby universes

We study a partially fine-grained description of an evaporating black hole by introducing an open baby universe with a boundary. Since the Page's calculation of the entropy of Hawking radiation involves an ensemble average over a class of states, one can formally obtain a fine-grained state by purifying this setup. For AdS black holes with a holographic dual, this purification amounts to introducing an additional boundary (i.e., baby universe) and then connecting it to the original black hole through an Einstein-Rosen bridge. We uncover several details of this setup. As applications, we briefly discuss how this baby universe modifies the semi-classical gravitational Gauss law as well as the gravitational dressing of operators behind the horizon.

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arXiv2022

Holographic Local Operator Quenches in BCFTs

We present a gravity dual of local operator quench in a two-dimensional CFT with conformal boundaries. This is given by a massive excitation in a three-dimensional AdS space with the end of the world brane (EOW brane). Due to the gravitational backreaction, the EOW brane gets deformed in a nontrivial way. We show that the energy-momentum tensor and entanglement entropy computed from the gravity dual and from the BCFT in the large $c$ limit match perfectly. Interestingly, this comparison avoids the folding of the EOW brane in an elegant way.

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arXiv2021

Factorizing Wormholes in a Partially Disorder-Averaged SYK Model

In this paper, we introduce a "partially disorder-averaged" SYK model. This model has a real parameter that smoothly interpolates between the ordinary totally disorder-averaged SYK model and the totally fixed-coupling model. For the large $N$ effective description, in addition to the usual bi-local collective fields, we also introduce a new additional set of local collective fields. These local fields can be understood as "half" of the bi-local collective fields, and in the totally fixed-coupling limit, they represent the "half-wormholes" which were found in recent studies. We find that the large $N$ saddles of these local fields vanish in the total-disorder-averaged limit, while they develop nontrivial profiles as we gradually fix the coupling constants. We argue that the bulk picture of these local collective fields represents a correlation between a spacetime brane and the asymptotic AdS boundary. This illuminates how the half-wormhole saddles emerge in the SYK model with fixed couplings.

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arXiv2021

Evaporation of black holes in flat space entangled with an auxiliary universe

We study a thermofield double type entangled state on two disjoint universes $A$ and $B$, where one of the universes is asymptotically flat containing a black hole. As we increase the entanglement temperature, this black hole receives back-reaction from the stress energy tensor of the state. This results in lengthening of the wormhole region in the black hole interior, and decreasing of its horizon area, both of which are key features of an evaporating black hole. We then compute the entanglement entropy on the universe $A$ through the island formula, and argue that it naturally follows the Page curve of an evaporating black hole in flat space. We also study the effects of local operations in the gravitating universe with the black hole. We find that they accelerate the evaporation of the black hole, therefore disrupt the entanglement between two universes. Furthermore, we observe that depending on whether the operation can be regarded as an LOCC or not, the behavior of the entanglement entropy changes. In particular, when the operation is made neither in the entanglement wedge of the radiation system or that of the black hole, the transition between the island phase and the no-island phase can happen multiple times.

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arXiv2021

Product of Random States and Spatial (Half-)Wormholes

We study how coarse-graining procedure of an underlying UV-complete quantum gravity gives rise to a connected geometry. It has been shown, quantum entanglement plays a key role in the emergence of such a geometric structure, namely a smooth Einstein-Rosen bridge. In this paper, we explore the possibility of the emergence of similar geometric structure from classical correlation, in the AdS/CFT setup. To this end, we consider a setup where we have two decoupled CFT Hilbert spaces, then choose a random typical state in one of the Hilbert spaces and the same state in the other. The total state in the fine-grained picture is of course a tensor product state, but averaging over the states sharing the same random coefficients creates a geometric connection for simple probes. Then, the apparent spatial wormhole causes a factorization puzzle. We argue that there is a spatial analog of half-wormholes, which resolves the puzzle in the similar way as the spacetime half-wormholes.

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arXiv2021

Spectrum of End of the World Branes in Holographic BCFTs

We study overlaps between two regularized boundary states in conformal field theories. Regularized boundary states are dual to end of the world branes in an AdS black hole via the AdS/BCFT. Thus they can be regarded as microstates of a single sided black hole. Owing to the open-closed duality, such an overlap between two different regularized boundary states is exponentially suppressed as $\langle ψ_{a} | ψ_{b} \rangle \sim e^{-O(h^{(min)}_{ab})}$, where $h^{(min)}_{ab}$ is the lowest energy of open strings which connect two different boundaries $a$ and $b$. Our gravity dual analysis leads to $h^{(min)}_{ab} = c/24$ for a pure AdS$_3$ gravity. This shows that a holographic boundary state is a random vector among all left-right symmetric states, whose number is given by a square root of the number of all black hole microstates. We also perform a similar computation in higher dimensions, and find that $h^{( min)}_{ab}$ depends on the tensions of the branes. In our analysis of holographic boundary states, the off diagonal elements of the inner products can be computed directly from on-shell gravity actions, as opposed to earlier calculations of inner products of microstates in two dimensional gravity.

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arXiv2021

Entanglement between two gravitating universes

We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the $n^{\text{th}}$ Rényi entropy includes a wormhole between the $n$ copies of the gravitating universe, leading to a standard "island formula" for entanglement entropy consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the path integral is now dominated by a novel wormhole with $2n$ boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by $\mathbb{Z}_n$ replica symmetry, giving a cylinder connecting the two universes. When entanglement is large, this configuration has an effective description as a "swap wormhole", a geometry in which the boundaries of the two universes are glued together by a "swaperator". This description allows precise computation of a generalized entropy-like formula for entanglement entropy. The quantum extremal surface computing the entropy lives on the Lorentzian continuation of the cylinder/swap wormhole, which has a connected Cauchy slice stretching between the universes -- a realization of the ER=EPR idea. The new wormhole restores unitarity of quantum information.

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arXiv2021

Wormholes and holographic decoherence

We study a class of decoherence process which admits a 3 dimensional holographic bulk. Starting from a thermo-field double dual to a wormhole, we prepare another thermo-field double which plays the role of environment. By allowing the energy flow between the original and environment thermo-field double, the entanglement of the original thermo-field double eventually decoheres. We model this decoherence by four-boundary wormhole geometries, and study the time-evolution of the moduli parameters to see the change of the entanglement pattern among subsystems. A notable feature of this holographic decoherence processes is that at the end point of the processes, the correlations of the original thermo-field double are lost completely both classically and also quantum mechanically. We also discuss distinguishability between thermo-field double state and thermo mixed double state, which contains only classical correlations, and construct a code subspace toy model for that.

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arXiv2020

Entanglement between two disjoint universes

We use the replica method to compute the entanglement entropy of a universe without gravity entangled in a thermofield-double-like state with a disjoint gravitating universe. Including wormholes between replicas of the latter gives an entropy functional which includes an "island" on the gravitating universe. We solve the back-reaction equations when the cosmological constant is negative to show that this island coincides with a causal shadow region that is created by the entanglement in the gravitating geometry. At high entanglement temperatures, the island contribution to the entropy functional leads to a bound on entanglement entropy, analogous to the Page behavior of evaporating black holes. We demonstrate that the entanglement wedge of the non-gravitating universe grows with the entanglement temperature until, eventually, the gravitating universe can be entirely reconstructed from the non-gravitating one.

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arXiv2020

Islands in de Sitter space

We consider black holes in 2d de Sitter JT gravity coupled to a CFT, and entangled with matter in a disjoint non-gravitating universe. Tracing out the entangling matter leaves the CFT in a density matrix whose stress tensor backreacts on the de Sitter geometry, lengthening the wormhole behind the black hole horizon. Naively, the entropy of the entangling matter increases without bound as the strength of the entanglement increases, but the monogamy property predicts that this growth must level off. We compute the entropy via the replica trick, including wormholes between the replica copies of the de Sitter geometry, and find a competition between conventional field theory entanglement entropy and the surface area of extremal "islands" in the de Sitter geometry. The black hole and cosmological horizons both play a role in generating such islands in the back-reacted geometry, and have the effect of stabilizing the entropy growth as required by monogamy. We first show this in a scenario in which the de Sitter spatial section has been decompactified to an interval. Then we consider the compact geometry, and argue for a novel interpretation of the island formula in the context of closed universes that recovers the Page curve. Finally, we comment on the application of our construction to the cosmological horizon in empty de Sitter space.

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