Spontaneous symmetry breaking in fermionic random matrix model

Aref’eva, I. Ya.; Волович, И. В.

doi:10.1007/jhep10(2019)114

Cited by 9 publications

(7 citation statements)

References 39 publications

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“…The holographic boundary dual of the JT gravity in spacetime with M boundaries is the M-replica SYK model in the low energy limit [65][66][67][68]. The studies of [61,[69][70][71][72][73] show that the nonperturbative completion of SYK involves nontrivial replica-nondiagonal saddle points. The replica-nondiagonal structures in SYK with replica interaction [73][74][75][76] demonstrate nontrivial phase structures and symmetry breaking patterns.…”

Section: Discussionmentioning

confidence: 99%

Gas of Baby Universes in JT Gravity and Matrix Models

Aref’eva

Волович

2020

Symmetry

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It has been shown recently by Saad, Shenker and Stanford that the genus expansion of a certain matrix integral generates partition functions of Jackiw-Teitelboim (JT) quantum gravity on Riemann surfaces of arbitrary genus with any fixed number of boundaries. We use an extension of this integral for studying gas of baby universes or wormholes in JT gravity. To investigate the gas nonperturbatively we explore the generating functional of baby universes in the matrix model. The simple particular case when the matrix integral includes the exponential potential is discussed in some detail. We argue that there is a phase transition in the gas of baby universes.

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Section: Discussionmentioning

confidence: 99%

Gas of Baby Universes in JT Gravity and Matrix Models

Aref’eva

Волович

2020

Symmetry

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“…The interplay between the ensemble averaging and semiclassical nature of the large N expansion raises questions about its structure, in particular about the replica trick and the difference between quenched and annealed averaging [48][49][50][51]. The disorder averaging was shown to be of great benefit for studies of fine-grained quantum chaos in SYK [10,13,21,23,24,29,34], because it provides a mechanism to emphasize the universal RMT behavior which is built into the theory.…”

Section: Jhep03(2021)031mentioning

confidence: 99%

Spectral form factor in the double-scaled SYK model

Khramtsov

Lanina

2021

J. High Energ. Phys.

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In this note we study the spectral form factor in the SYK model in large q limit at infinite temperature. We construct analytic solutions for the saddle point equations that describe the slope and the ramp regions of the spectral form factor time dependence. These saddle points are obtained by taking different approaches to the large q limit: the slope region is described by a replica-diagonal solution and the ramp region is described by a replica-nondiagonal solution. We find that the onset of the ramp behavior happens at the Thouless time of order q log q. We also evaluate the one-loop corrections to the slope and ramp solutions for late times, and study the transition from the slope to the ramp. We show this transition is accompanied by the breakdown of the perturbative 1/q expansion, and that the Thouless time is defined by the consistency of extrapolation of this expansion to late times.

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“…The more suitable quantity for probing the replica-nondiagonal structure is the Bogolyubov quasi-average [34,40]. In our case we define it as follows:…”

Section: Quasi-averagingmentioning

confidence: 99%

“…In particular, it was shown that the replica-nondiagonal saddle points of the replica field path integral are related to the ramp behavior of the spectral form-factor [14]. Replica-nondiagonal structures of saddle points of SYK-like models were also studied in [24,[29][30][31][32][33][34], in particular in relation to the issue of spin glasses and replica symmetry breaking. From the gravity point of view, the nonperturbative effects arising from the subleading saddle points are related to the topologies of higher genus [15,18,35], and they probe discrete spectrum of black hole microstates and are important for the recovery of lost information [13][14][15].…”

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confidence: 99%

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Revealing Nonperturbative Effects in the SYK Model

2019

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We study the large N saddle points of two SYK chains coupled by an interaction that is nonlocal in Euclidean time. We start from analytic treatment of the free case with q = 2 and perform the numerical study of the interacting case q = 4. We show that in both cases there is a nontrivial phase structure with infinite number of phases. Every phase correspond to a saddle point in the non-interacting two-replica SYK. The nontrivial saddle points have non-zero value of the replica-nondiagonal correlator in the sense of quasi-averaging, when the coupling between replicas is turned off. Thus, the nonlocal interaction between replicas provides a protocol for turning the nonperturbatively subleading effects in SYK into non-equilibrium configurations which dominate at large N . For comparison we also study two SYK chains with local interaction for q = 2 and q = 4. We show that the q = 2 model also has a similar phase structure, whereas in the q = 4 model, dual to the traversable wormhole, the phase structure is different. arXiv:1905.04203v1 [hep-th]

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Spontaneous symmetry breaking in fermionic random matrix model

Cited by 9 publications

References 39 publications

Gas of Baby Universes in JT Gravity and Matrix Models

Gas of Baby Universes in JT Gravity and Matrix Models

Spectral form factor in the double-scaled SYK model

Revealing Nonperturbative Effects in the SYK Model

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