arXiv subjects

Antal Jevicki

Publications and source records attributed to Antal Jevicki.

At least 19 recordsLinked to original sources

arXiv2026

Finite-$N$ Operator Algebras and the Hilbert Space of Bilocal Holography

We give an operator-algebraic and representation-theoretic description of the Hilbert spaces of finite-$N$ bilocal holography. This work is a sequel to the finite-$N$ Hilbert space construction of arXiv:2602.20788 [hep-th]. The central result is the establishment of an invariant dual-pair operator algebra: before imposing the singlet constraint the Fock space carries commuting actions of the color group and of a bilocal Lie algebra, while the projection to the singlet sector selects a single irreducible representation of the invariant Lie algebra, which we call a master algebra. The finite-$N$ trace relations, beginning with the quadratic identities studied here, are shown to become representation-theoretic identities of the selected irreducible representation. We summarize the orthogonal, symplectic and unitary cases, identify the corresponding finite-$N$ constraints, compute the singlet Casimirs, and explain how finite traces and partition functions are obtained through characters of the resulting irreducible representations. This provides a novel, previously unknown mathematical description of the singlet space.

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arXiv2026

Finite $N$ Hilbert Spaces of Bilocal Holography

For vector/AdS and dS holography we establish the structure of the emergent Hilbert space. This is done through implementation of finite $N$ trace relations on the infinite collective space. For fermionic theories a finite Hilbert space is established, while for bosonic theories a space of freely acting primaries multiplied by a finite set of secondaries emerges. The Hilbert space of states obey finite $N$ cut off bounds, implying finiteness of traces and entropy.

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arXiv2025

Collective Theory at Finite-$N$: Reduction of the Emergent Hilbert Space

Continuing the formulation of finite $N$ Hilbert spaces in emergent theories we study in this work $S_{N}$ symmetric collective models. For the case of $N$ bosons in $d$ dimensions, which map to matrix models with commuting matrices, we describe a complete algorithm and give a detailed case study reproducing the expected primaries and determining secondary invariants at each bidegree (a Hironaka decomposition). The method is based on null spaces (of the full collective theory) which are seen to yield all the independent trace relations, reducing the construction to linear algebra. As a stringent check, of our algorithm, we have verified that the system of invariants generates a subset of gauge invariant operators with no redundancies. This results in a reduction of the Hilbert space, in particular the gauge invariant secondary invariants realize an emergent Fock space with finite-$N$ occupation-numbers.

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arXiv2025

Hilbert Space of Finite $N$ Multi-matrix Models

We study the Hilbert space structure of gauge-invariant operators emergent in large-$N$ multi-matrix quantum mechanics. Building on the framework of \cite{deMelloKoch:2025ngs}, we identify a class of light single-trace operators that behave like free creation operators at low energy but saturate beyond a critical excitation level, ceasing to generate new states. This $q$-reducibility is a direct consequence of finite N trace identities and leads to a dramatic truncation of the high-energy spectrum of the emergent theory. The resulting number of independent degrees of freedom is far smaller than naïve semiclassical expectations, providing a concrete mechanism for how nonperturbative constraints shape the ultraviolet behaviour of emergent theories.

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arXiv2025

Structure of Loop Space at Finite $N$

The space of invariants for a single matrix is generated by traces containing at most $N$ matrices per trace. We extend this analysis to multi-matrix models at finite $N$. Using the Molien-Weyl formula, we compute partition functions for various multi-matrix models at different $N$ and interpret them through trace relations. This allows us to identify a complete set of invariants, naturally divided into two distinct classes: primary and secondary. The full invariant ring of the multi-matrix model is reconstructed via the Hironaka decomposition, where primary invariants act freely, while secondary invariants satisfy quadratic relations. Significantly, while traces with at most $N$ matrices are always present, we also find invariants involving more than $N$ matrices per trace. The primary invariants correspond to perturbative degrees of freedom, whereas the secondary invariants emerge as non-trivial background structures. The growth of secondary invariants aligns with expectations from black hole entropy, suggesting deep structural connections to gravitational systems.

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arXiv2025

Thermofield Theory of Large $N$ Matrix Models

We develop analytical and numerical methods for the matrix thermofield in the large $N$ limit. Through the double collective representation on the Schwinger-Keldysh contour, it provides thermodynamical properties and finite temperature correlation functions, for large $N$ matrix quantum systems.

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arXiv2024

Operator algebra, quantum entanglement, and emergent geometry from matrix degrees of freedom

For matrix model and QFT, we discuss how dual gravitational geometry emerges from matrix degrees of freedom (specifically, adjoint scalars in super Yang-Mills theory) and how operator algebra that describes an arbitrary region of the bulk geometry can be constructed. We pay attention to the subtle difference between the notions of wave packets that describe low-energy excitations: QFT wave packet associated with the spatial dimensions of QFT, matrix wave packet associated with the emergent dimensions from matrix degrees of freedom, and bulk wave packet which is a combination of QFT and matrix wave packets. In QFT, there is an intriguing interplay between QFT wave packet and matrix wave packet that connects quantum entanglement and emergent geometry. We propose that the bulk wave packet is the physical object in QFT that describes the emergent geometry from entanglement. This proposal sets a unified view on two seemingly different mechanisms of holographic emergent geometry: one based on matrix eigenvalues and the other based on quantum entanglement. Further intuition comes from the similarity to a traversable wormhole discussed as the dual description of the coupled SYK model by Maldacena and Qi: the bulk can be seen as an eternal traversable wormhole connecting boundary regions.

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arXiv2024

A model of randomly-coupled Pauli spins

We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Majorana fermions in the SYK model with spin operators. Equivalently, we replace fermions with hard-core bosons. We study this model numerically and compare the properties with those of the SYK model. We observe a striking quantitative coincidence between the spin model and the SYK model, which suggests that this spin model is strongly chaotic and, perhaps, can play some role in holography. We also discuss the path-integral approach with multi-local fields and the possibility of quantum simulations. This model may be an interesting target for quantum simulations because Pauli spins are easier to implement than fermions on qubit-based quantum devices.

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arXiv2024

Emergent factorization of Hilbert space at large $N$ and black hole

We investigate the emergent factorization of Hilbert space in the low-energy description of matrix models, addressing key aspects of the black hole information paradox. We examine the collective description for the low-energy sector of $SU(N)$ matrix model, characterized by a factorized Hilbert space composed of a finite number of boxes and anti-boxes. This factorization leads us to examine the emergence of thermofield dynamics (TFD) state in the low energy sector from a fine-tuned state. In addition, we study the collective Hamiltonian of the $U(N)$ matrix model for the semi-classical description of "particle-hole" fluctuations around a background Young tableau. Our investigation of these matrix models elucidates a concrete mechanism for constructing the truncated algebra of accessible observables, thereby facilitating an understanding of black hole complementarity. In the context of the black hole information paradox, we discuss the origin of the island appearing inside the black hole and provide a reinterpretation of the recent proposal -- the holography of information.

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arXiv2023

Symmetries and the Hilbert Space of Large $N$ Extended States

We discuss the large $N$ expansion in backgrounds of extended states with focus on implementation of Goldstone symmetries and the construction of the associated Hilbert space. The formulation is given in the general framework of collective field theory. Case of translational symmetry is described first, as the basic example. The large $N$ thermofield represents the main topics, with the emergent dynamics of Left-Right bulk fields and collective symmetry coordinates. These give the basis for a $1/N$ expansion.

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arXiv2022

Finiteness of Entanglement Entropy in Collective Field Theory

We explore the question of finiteness of the entanglement entropy in gravitational theories whose emergent space is the target space of a holographic dual. In the well studied duality of two-dimensional non-critical string theory and $c=1$ matrix model, this question has been studied earlier using fermionic many-body theory in the space of eigenvalues. The entanglement entropy of a subregion of the eigenvalue space, which is the target space entanglement in the matrix model, is finite, with the scale being provided by the local Fermi momentum. The Fermi momentum is, however, a position-dependent string coupling, as is clear in the collective field theory formulation. This suggests that the finiteness is a non-perturbative effect. We provide evidence for this expectation by an explicit calculation in the collective field theory of matrix quantum mechanics with vanishing potential. The leading term in the cumulant expansion of the entanglement entropy is calculated using exact eigenstates and eigenvalues of the collective Hamiltonian, yielding a finite result, in precise agreement with the fermion answer. Treating the theory perturbatively, we show that each term in the perturbation expansion is UV divergent. However the series can be resummed, yielding the exact finite result. Our results indicate that the finiteness of the entanglement entropy for higher dimensional string theories is non-perturbative as well, with the scale provided by the Newton constant.

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arXiv2022

Matrix Entanglement

In gauge/gravity duality, matrix degrees of freedom on the gauge theory side play important roles for the emergent geometry. In this paper, we discuss how the entanglement on the gravity side can be described as the entanglement between matrix degrees of freedom. Our approach, which we call 'matrix entanglement', is different from 'target-space entanglement' proposed and discussed recently by several groups. We consider several classes of quantum states to which our approach can play important roles. When applied to fuzzy sphere, matrix entanglement can be used to define the usual spatial entanglement in two-brane or five-brane world-volume theory nonperturbatively in a regularized setup. Another application is to a small black hole in AdS5*S5 that can evaporate without being attached to a heat bath, for which our approach suggests a gauge theory origin of the Page curve. The confined degrees of freedom in the partially-deconfined states play the important roles.

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arXiv2022

Dynamical Symmetry and the Thermofield State at Large $N$

We discus Thermofield Double QFT at real time, in the large $N$ limit. First, we establish a (dynamical) symmetry which we argue holds in general on the real time portion of the Schwinger-Kelydish contour. At large $N$ this symmetry is seen to generate a one parameter degeneracy of stationary collective solutions. The construction is explicitly worked out on the example of $O(N)$ vector QFT. As a nontrivial application we describe construction of the corresponding (large $N$) Thermofield Double State in real time collective formalism.

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arXiv2022

Large N Optimization for multi-matrix systems

In this work we revisit the problem of solving multi-matrix systems through numerical large $N$ methods. The framework is a collective, loop space representation which provides a constrained optimization problem, addressed through master-field minimization. This scheme applies both to multi-matrix integrals ($c=0$ systems) and multi-matrix quantum mechanics ($c=1$). The complete fluctuation spectrum is also computable in the above scheme, and is of immediate physical relevance in the later case. The complexity (and the growth of degrees of freedom) at large $N$ have stymied earlier attempts and in the present work we present significant improvements in this regard. The (constrained) minimization and spectrum calculations are easily achieved with close to $10^4$ variables, giving solution to Migdal-Makeenko, and collective field equations. Considering the large number of dynamical (loop) variables and the extreme nonlinearity of the problem, high precision is obtained when confronted with solvable cases. Through numerical results presented, we prove that our scheme solves, by numerical loop space methods, the general two matrix model problem.

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arXiv2021

Entanglement and Confinement in Coupled Quantum Systems

We study some general properties of coupled quantum systems. We consider simple interactions between two copies of identical Hamiltonians such as the SYK model, Pauli spin chains with random magnetic field and harmonic oscillators. Such couplings make the ground states close to the thermofield double states of the uncoupled Hamiltonians. For the coupled SYK model, we push the numerical computation further towards the thermodynamic limit so that an extrapolation in the size of the system is possible. We find good agreement between the extrapolated numerical result and the analytic result in the large-$q$ limit. We also consider the coupled gauged matrix model and vector model, and argue that the deconfinement is associated with the loss of the entanglement, similarly to the previous observation for the coupled SYK model. The understanding of the microscopic mechanism of the confinement/deconfinement transition enables us to estimate the quantum entanglement precisely, and backs up the dual gravity interpretation which relates the deconfinement to the disappearance of the wormhole. Our results demonstrate the importance of the entanglement between the color degrees of freedom in the emergence of the bulk geometry from quantum field theory via holography.

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arXiv2020

Near Conformal Perturbation Theory in SYK Type Models

We present a systematic procedure to extract the dynamics of the low energy soft mode in SYK type models with a single energy scale $J$ and emergent reparametrization symmetry in the IR. This is given in the framework of the perturbation theory scheme of arXiv:1608.07567 based on specific (off-shell) breaking of conformal invariance in the UV, adjusted to yield the exact large-$N$ saddle point. While this breaking formally vanishes on-shell, it has a non-trivial effect on correlation functions and the effective action. In particular, it leads to the Schwarzian action with a specific coupling to bi-local matter. The method is applied to the evaluation of $O(1)$ corrections to the correlation function of bi-locals. As a byproduct we confirm precise agreement with the explicit, symmetry breaking procedure. We provide a verification in the large $q$ limit (Liouville theory), where the correlators can be calculated exactly at all length scales. In this case, our scheme illuminates how the enhanced $O(J)$ and the subleading $O(1)$ contributions originate from the Schwarzian dynamics of the soft mode and its interaction with $h=2$ (bi-local) matter.

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arXiv2019

Anatomy of Deconfinement

In the weak coupling limit of ${\rm SU}(N)$ Yang-Mills theory and the ${\rm O}(N)$ vector model, explicit state counting allows us to demonstrate the existence of a partially deconfined phase: $M$ of $N$ colors deconfine, and $\frac{M}{N}$ gradually grows from zero (confinement) to one (complete deconfinement). We point out that the mechanism admits a simple interpretation in the form of spontaneous breaking of gauge symmetry. In terms of the dual gravity theory, such breaking occurs during the formation of a black hole. We speculate whether the breaking and restoration of gauge symmetry can serve as an alternative definition of the deconfinement transition in theories without center symmetry, such as QCD. We also discuss the role of the color degrees of freedom in the emergence of the bulk geometry in holographic duality.

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arXiv2018

AdS Maps and Diagrams of Bi-local Holography

We present in detail the basic ingredients contained in bi-local holography, representing a constructive scheme for reconstructing AdS bulk theories in Vectorial/AdS duality. Explicit Mapping to bulk AdS and higher spin fields is seen to be given by a double Fourier transform. All order interactions are explicitly specified through the collective action. This generates bulk Feynman (Witten) diagrams (at tree and loop level). We give details of the four-point case evaluation. It is noted that the bi-local construction goes beyond the assumptions in various discussions of non-locality.

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