Chaos in AdS 2 Holography

155

200

The SYK model, a quantum mechanical model of N 1 Majorana fermions χ i , with a q-body, random interaction, is a novel realization of holography. It is known that the AdS 2 dual contains a tower of massive particles, yet there is at present no proposal for the bulk theory. As SYK is solvable in the 1/N expansion, one can systematically derive the bulk. We initiate such a program, by analyzing the fermion two, four and six-point functions, from which we extract the tower of singlet, large N dominant, operators, their dimensions, and their three-point correlation functions. These determine the masses of the bulk fields and their cubic couplings. We present these couplings, analyze their structure and discuss the simplifications that arise for large q.

“…However, the dilaton is not constant and has a nontrivial action, of the type studied in [3]. It was recognized in [38,39] (see also [40][41][42][43]) that this…”

Section: Fermion Four-point Functionmentioning

confidence: 99%

The bulk dual of SYK: cubic couplings

Gross

Rosenhaus

2017

155

200

“…SYK model [6][7][8][9][10] is a microscopic quantum hamiltonian with random Gaussian non-local couplings among majonara fermions. As is maximally chaotic and nearly conformal, this model could be treated as a holographic dual of quantum black hole with AdS 2 horizon through the (near) AdS/CFT correspondence [11][12][13][14][15][16][17][18][19][20]. In the recent research people have also discussed several generalizations of the SYK model [21][22][23][24], such as higher dimensional generalizations and supersymmetric constraints.…”

Section: Jhep06(2017)111mentioning

confidence: 99%

Supersymmetric SYK model and random matrix theory

Liu

Yuan

et al. 2017

131

147

In this paper, we investigate the effect of supersymmetry on the symmetry classification of random matrix theory ensembles. We mainly consider the random matrix behaviors in the N = 1 supersymmetric generalization of Sachdev-Ye-Kitaev (SYK) model, a toy model for two-dimensional quantum black hole with supersymmetric constraint. Some analytical arguments and numerical results are given to show that the statistics of the supersymmetric SYK model could be interpreted as random matrix theory ensembles, with a different eight-fold classification from the original SYK model and some new features. The time-dependent evolution of the spectral form factor is also investigated, where predictions from random matrix theory are governing the late time behavior of the chaotic hamiltonian with supersymmetry.

“…It is a simple model with solvable aspects which exhibits interesting connections to quantum chaos [9][10][11][12][13], black hole physics and quantum gravity in 1+1 dimensions [14][15][16][17][18][19][20]. Understanding these relations better in this model, and potential extensions of it, is an active and exciting research direction that promises to improve our knowledge of holography.…”

Section: Introduction and Conclusionmentioning

confidence: 99%

Higher dimensional generalizations of the SYK model

Berkooz

Narayan

Rozali

et al. 2017

143

127

We discuss a 1+1 dimensional generalization of the Sachdev-Ye-Kitaev model. The model contains N Majorana fermions at each lattice site with a nearest-neighbour hopping term. The SYK random interaction is restricted to low momentum fermions of definite chirality within each lattice site. This gives rise to an ordinary 1+1 field theory above some energy scale and a low energy SYK-like behavior. We exhibit a class of low-pass filters which give rise to a rich variety of hyperscaling behaviour in the IR. We also discuss another set of generalizations which describes probing an SYK system with an external fermion, together with the new scaling behavior they exhibit in the IR.