Confinement/deconfinement transition in the D0-brane matrix model — A signature of M-theory?

Bergner, Georg; Bodendorfer, Norbert; Hanada, Masanori; Pateloudis, Stratos; Rinaldi, Enrico; Schäfer, Andreas; Vranas, Pavlos; Watanabe, Hiromasa

doi:10.1007/jhep05(2022)096

Cited by 13 publications

(42 citation statements)

References 74 publications

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“…where M is the truncation parameter. To reduce the computational cost of exact diagonalization, we further use the discrete parity symmetry of the Hamiltonians ( 4) and ( 6) to represent the matrices (10) and (12) in block diagonal form. We then perform numerical diagonalization of the matrices (10) and (12).…”

Section: Methodsmentioning

confidence: 99%

“…To reduce the computational cost of exact diagonalization, we further use the discrete parity symmetry of the Hamiltonians ( 4) and ( 6) to represent the matrices (10) and (12) in block diagonal form. We then perform numerical diagonalization of the matrices (10) and (12). For not very large M 100 we use the QR algorithm as implemented in the LAPACK routine dsyev, finding all eigenvectors and eigenvalues of the matrices (10) and (12).…”

Section: Methodsmentioning

confidence: 99%

“…We then perform numerical diagonalization of the matrices (10) and (12). For not very large M 100 we use the QR algorithm as implemented in the LAPACK routine dsyev, finding all eigenvectors and eigenvalues of the matrices (10) and (12). For larger values of M we use the Arnoldi algorithm as implemented in the ARPACKPP library to find n M 2 lowest eigenvalues, with n taking values between 10 2 and 10 3 .…”

Section: Methodsmentioning

confidence: 99%

“…6. For the truncation parameter M = 100, we show all eigenvalues of the Hamiltonian matrices (10) and (12). For M ≥ 500, we use between 200 and 800 smallest eigenvalues of the Hamiltonian matrices ( 10) and ( 12) obtained using the Arnoldi algorithm.…”

Section: Eigenstates Of the Supersymmetric Hamiltonianmentioning

confidence: 99%

“…The progress was mostly limited to conformal field theory, quantum circuits and simple spin chain models [6][7][8], often with quenched disorder [9,10]. For example, so far it was not possible to explicitly demonstrate the saturation of the MSS bound (3) in the BFSS matrix model [11], which has a well-established holographic description in terms of black D0-branes in type IIA superstring theory and is in the black brane regime at all temperatures [12,13]. Even in the SYK model, the equality λ = 2πT can only be demonstrated using a model-specific diagrammatic technique [3,4,14], while generally applicable techniques such as exact diagonalization so far could not reach the relevant low-temperature, large-system regime [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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Quantum chaos in supersymmetric quantum mechanics: an exact diagonalization study

Buividovich¹

2022

Preprint

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We use exact diagonalization to study energy level statistics and out-of-time-order correlators (OTOCs) for the simplest supersymmetric extension of the bosonic Hamiltonian ĤB = p21 +p 2 2 +x 2 1 x2 2 . For a long time, this bosonic Hamiltonian was considered as the simplest system which exhibits dynamical chaos both classically and quantum-mechanically. Its structure closely resembles that of spatially compactified pure Yang-Mills theory. Correspondingly, the structure of our supersymmetric Hamiltonian is similar to that of spatially compactified supersymmetric Yang-Mills theory, also known as the Banks-Fischler-Shenker-Susskind (BFSS) model. We present numerical evidence that a continuous energy spectrum of the supersymmetric model leads to monotonous growth of OTOCs down to the lowest temperatures, a property that is also expected for the BFSS model from holographic duality. We find that this growth is saturated by low-lying energy eigenstates with effectively one-dimensional wave functions and a completely non-chaotic energy level distribution. Our data suggests, although with a limited confidence, that the OTOC growth might be exponential over a finite range of time, with the corresponding Lyapunov exponent scaling linearly with temperature. In contrast, the gapped low-energy spectrum of the bosonic Hamiltonian leads to oscillating OTOCs at low temperatures without any signatures of exponential growth. We also find that the OTOCs for the bosonic Hamiltonian is never sufficiently close to the classical Lyapunov distance. On the other hand, the OTOCs for the supersymmetric system agree with the classical limit reasonably well over a finite range of temperatures and evolution times.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Eigenstates Of the Supersymmetric Hamiltonianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum chaos in supersymmetric quantum mechanics: an exact diagonalization study

Buividovich¹

2022

Preprint

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Matrix entanglement

Gautam

Hanada

Jevicki

et al. 2023

J. High Energ. Phys.

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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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Precision test of gauge/gravity duality in D0-brane matrix model at low temperature

Pateloudis

Bergner²,

Hanada

et al. 2023

J. High Energ. Phys.

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We test the gauge/gravity duality between the matrix model and type IIA string theory at low temperatures with unprecedented accuracy. To this end, we perform lattice Monte Carlo simulations of the Berenstein-Maldacena-Nastase (BMN) matrix model, which is the one-parameter deformation of the Banks-Fischler-Shenker-Susskind (BFSS) matrix model, taking both the large N and continuum limits. We leverage the fact that sufficiently small flux parameters in the BMN matrix model have a negligible impact on the energy of the system while stabilizing the flat directions so that simulations at smaller N than in the BFSS matrix model are possible. Hence, we can perform a precision measurement of the large N continuum energy at the lowest temperatures to date. The energy is in perfect agreement with supergravity predictions including estimations of α′-corrections from previous simulations. At the lowest temperature where we can simulate efficiently (T = 0.25λ1/3, where λ is the ’t Hooft coupling), the difference in energy to the pure supergravity prediction is less than 10%. Furthermore, we can extract the coefficient of the 1/N4 corrections at a fixed temperature with good accuracy, which was previously unknown.

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Confinement/deconfinement transition in the D0-brane matrix model — A signature of M-theory?

Cited by 13 publications

References 74 publications

Quantum chaos in supersymmetric quantum mechanics: an exact diagonalization study

Quantum chaos in supersymmetric quantum mechanics: an exact diagonalization study

Matrix entanglement

Precision test of gauge/gravity duality in D0-brane matrix model at low temperature

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