Revealing Nonperturbative Effects in the SYK Model

Aref’eva, I. Ya.; Волович, И. В.; Khramtsov, Mikhail

doi:10.1134/s0040577919110059

Cited by 5 publications

(9 citation statements)

References 57 publications

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“…The subleading solutions with higher Reã acquire extra extrema compared to the leading solutions, as shown on the plots (e) and (f). This is similar to subleading saddle points in the Euclidean SYK partition function at finite q [10,49,52].…”

Section: Early-time Solutionmentioning

confidence: 61%

“…• We see that the slope region has a discrete set of subleading saddle points parametrized by integer numbers, analogous to the subleading saddles in finite q SYK [10,49,52].…”

Section: Jhep03(2021)031 6 Discussion and Outlookmentioning

confidence: 90%

“…• Spontaneously broken time translations. The replica-diagonal solutions (4.29)- (4.30) break time translations in both replicas as U(1) × U(1) → U(1), as is commonplace for such solutions [13,49,52]. In the obtained solutions, the parameter σ plays the role of the time translation zero mode.…”

Section: Jhep03(2021)031mentioning

confidence: 84%

“…However, we have also found that on the slope regime there are subleading saddles. There are no such saddles on the ramp, but there are replicanondiagonal analogues at finite q for the Euclidean replica partition function [49,52]. This provides a new constraint on the question of importance of the subleading SYK saddles in the gravity description.…”

Section: Jhep03(2021)031mentioning

confidence: 98%

“…The work [13] also showed that some of this universality can be described neatly in terms of the semiclassical formulation as a nontrivial large N saddle point. Meanwhile, in the work [49,52] we have demonstrated that there are other nontrivial large N saddle points in the Euclidean partition function, and it is not clear what is their physical meaning. Some of these saddle points are the replica-nondiagonal solutions, which exist for integer number of SYK copies (replicas), even if they do not interact.…”

Section: Jhep03(2021)031mentioning

confidence: 99%

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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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Section: Early-time Solutionmentioning

confidence: 61%

“…• We see that the slope region has a discrete set of subleading saddle points parametrized by integer numbers, analogous to the subleading saddles in finite q SYK [10,49,52].…”

Section: Jhep03(2021)031 6 Discussion and Outlookmentioning

confidence: 90%

Section: Jhep03(2021)031mentioning

confidence: 84%

Section: Jhep03(2021)031mentioning

confidence: 98%

Section: Jhep03(2021)031mentioning

confidence: 99%

See 3 more Smart Citations

Spectral form factor in the double-scaled SYK model

Khramtsov

Lanina

2021

J. High Energ. Phys.

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From minimal strings towards Jackiw–Teitelboim gravity: on their resurgence, resonance, and black holes

Gregori,

Schiappa

2024

Class. Quantum Grav.

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Two remarkable facts about Jackiw-Teitelboim two-dimensional dilaton-gravity have been recently uncovered: this theory is dual to an ensemble of quantum mechanical theories; and such ensembles are described by a random matrix model which itself may be regarded as a special (large matter-central-charge) limit of minimal string theory. This work addresses this limit, putting it in its broader matrix-model context; comparing results between multicritical models and minimal strings (i.e., changing in-between multicritical and conformal backgrounds); and in both cases making the limit of large matter-central-charge precise (as such limit can also be defined for the multicritical series). These analyses are first done via spectral geometry, at both perturbative and nonperturbative levels, addressing the resurgent large-order growth of perturbation theory, alongside a calculation of nonperturbative instanton-actions and corresponding Stokes data. This calculation requires an algorithm to reach large-order, which is valid for arbitrary two-dimensional topological gravity. String equations---as derived from the Gel'fand-Dikii construction of the resolvent---are analyzed in both multicritical and minimal string theoretic contexts, and studied both perturbatively and nonperturbatively (always matching against the earlier spectral-geometry computations). The resulting solutions, as described by resurgent transseries, are shown to be resonant. The large matter-central-charge limit is addressed---in the string-equation context---and, in particular, the string equation for Jackiw-Teitelboim gravity is obtained to next derivative-orders, beyond the known genus-zero case (its possible exact-form is also discussed). Finally, a discussion of gravitational perturbations to Schwarzschild-like black hole solutions in these minimal-string models, regarded as deformations of Jackiw-Teitelboim gravity, is included---alongside a brief discussion of quasinormal modes.

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