FZZT branes and non-singlets of matrix quantum mechanics

Betzios, Panagiotis; Papadoulaki, Olga

doi:10.1007/jhep07(2020)157

Cited by 15 publications

(98 citation statements)

References 91 publications

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“…The plateau behaviour arises due to the repulsion among neighboring energy eigenvalues. On the other hand, the ramp behaviour arises due to the repulsion among eigenvalues that are far apart 27 [8]. The difference between our case and the one in [10] is not surprising, since in our case the genus zero part is obtained in the limit µ → ∞ where effects involving eigenvalues that are far apart are suppressed.…”

Section: Spectral Form Factor Due To Connected Geometriescontrasting

confidence: 45%

Liouville theory and matrix models: a Wheeler DeWitt perspective

Betzios

Papadoulaki

2020

J. High Energ. Phys.

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We analyse the connections between the Wheeler DeWitt approach for two dimensional quantum gravity and holography, focusing mainly in the case of Liouville theory coupled to c = 1 matter. Our motivation is to understand whether some form of averaging is essential for the boundary theory, if we wish to describe the bulk quantum gravity path integral of this two dimensional example. The analysis hence, is in a spirit similar to the recent studies of Jackiw-Teitelboim (JT)-gravity. Macroscopic loop operators define the asymptotic region on which the holographic boundary dual resides. Matrix quantum mechanics (MQM) and the associated double scaled fermionic field theory on the contrary, is providing an explicit “unitary in superspace” description of the complete dynamics of such two dimensional universes with matter, including the effects of topology change. If we try to associate a Hilbert space to a single boundary dual, it seems that it cannot contain all the information present in the non-perturbative bulk quantum gravity path integral and MQM.

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Section: Spectral Form Factor Due To Connected Geometriescontrasting

confidence: 45%

Liouville theory and matrix models: a Wheeler DeWitt perspective

Betzios

Papadoulaki

2020

J. High Energ. Phys.

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“…dictated by the gauge field zero mode on each boundary. If the MQM model is Gaussian (as for c = 1 MQM), one can integrate M 1,2 out and derive an explicit result for the twisted thermal partition function that is [61,43,47]…”

Section: The Partition Functionmentioning

confidence: 99%

“…In addition, in a large representation limit that we describe in sections 2.3 and 2.4, one can show the presence of competing saddles, some of which could correspond to connected and others to disconnected bulk geometries (each individual singlet MQM with an inverted oscillator potential is known to describe c = 1-Liouville string theory on a linear dilaton background) 10 . Unfortunately, not much is known about the geometric interpretation of the non-singlet sector of MQM (see though [45,46,48,47] for some preliminary steps in this direction) and hence we cannot completely settle this question in the affirmative at the moment. In section 2.5 we analyse some simple two-and four-point cross-correlators and demonstrate their expected properties.…”

Section: Introductionmentioning

confidence: 99%

Interacting systems and wormholes

Betzios,

Kiritsis,

Papadoulaki

2021

Preprint

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We consider a class of tripartite systems for which two d-dimensional QFTs are cross-coupled via a third d + 1-dimensional "messenger" QFT. We analyse in detail the example of a pair of one-dimensional matrix quantum mechanics, coupled via a two-dimensional theory of the BF-type and compute its partition function and simple correlators. This construction is extendible in higher dimensions, using a Chern-Simons "messenger" theory. In all such examples, the exact partition function acquires a form, speculated to correspond to systems dual to Euclidean wormholes and the cross correlators are sufficiently soft and consistent with analogous gravitational calculations. Another variant of the tripartite system is studied, where the messenger theory is described by a non-self-interacting (matrix)-field, reaching similar conclusions. While the Euclidean theories we consider are perfectly consistent, the two possible analytic continuations into Lorentzian signature (messenger vs. boundary QFT directions) of the tripartite models, reveal physical features and "pathologies" resembling those of the expected Lorentzian gravitational backgrounds.

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“…Large N multi-matrix problems are at the center of many theories of current interest, involving membranes [1], reduced super Yang-Mills theories [2][3][4][5][6], field theory of critical and noncritical strings [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], phase transitions and black holes [23][24][25][26][27][28][29][30][31], and M-atrix theory [32]. At the same time, apart from very special cases, these systems are not solvable due to the fact that they are highly nonlinear.…”

Section: Introductionmentioning

confidence: 99%

Large N optimization for multi-matrix systems

Koch

Jevicki²,

Liu³

et al. 2022

J. High Energ. Phys.

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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 systems). 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 104 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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FZZT branes and non-singlets of matrix quantum mechanics

Cited by 15 publications

References 91 publications

Liouville theory and matrix models: a Wheeler DeWitt perspective

Liouville theory and matrix models: a Wheeler DeWitt perspective

Interacting systems and wormholes

Large N optimization for multi-matrix systems

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