The spectrum in the Sachdev-Ye-Kitaev model

By J. Polchinski, V. Rosenhaus. 2016

692 citations recorded by the source corpus.

A bstractThe SYK model consists of N ≫ 1 fermions in 0 + 1 dimensions with a random, all-to-all quartic interaction. Recently, Kitaev has found that the SYK model is maximally chaotic and has proposed it as a model of holography. We solve the SchwingerDyson equation and compute the spectrum of two-particle states in SYK, finding both a continuous and discrete tower. The four-point function is expressed as a sum over the spectrum. The sum over the discrete tower is evaluated.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/94a97319c5146409ba008bbe5a7c78399c0655f0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

1. D. Stanford
2. J. Maldacena
3. Phil Saad
4. V. Rosenhaus
5. D. Harlow
6. E. Witten
7. S. Shenker
8. Tom Mertens

Citations in the corpus

• All point correlation functions in SYK (2017, background): “While SYK appears conformally invariant at the level of the two-point function, the conformal invariance is broken at the level of the four-point function [5, 7, 8], resulting in SYK being “nearly” conformally invariant in the infrared.”
• Supersymmetric Sachdev-Ye-Kitaev models (2017, methodology): “As in [7,12,17] these dimensions are computed by using conformal symmetry to diagonalize the ladder kernel in terms of a basis of functions of two variables with definite conformal casimir specified by a conformal dimension h.”
• Holographic Quantum Matter (2016, background): “These models, and their holographic duals, allow a systematic study of 1/N corrections [26; 244; 272; 536; 537; 609], and the locally critical scaling holds down to the smallest values of (total energy)/N .”
• The Black Hole Information Problem (2016, background): “And, a recent two-dimensional chaotic model [67, 69, 70] provised a very interesting model”
• Solving the Schwarzian via the conformal bootstrap (2017, background): “The SYK model is a soluble many body quantum system with a well-controlled large N limit that exhibits maximal chaos and other characteristics that indicate it has a holographic dual given by a 2D gravity theory on AdS2 [2, 6, 7, 8, 9, 10, 11].”
• A generalization of Sachdev-Ye-Kitaev (2016, background): “, as well as h = 1/2 + is where s > 0 [38,13,14].”
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual (2017, background): “Polchinski and Rosenhaus [19] studied the conformal four-point function, which is complementary to the soft mode.”
• The Schwarzian theory — origins (2018, background): “Sachdev-Ye-Kitaev (SYK) models of N Majorana fermions with random all-to-all interactions have received a host of attention in the past few years [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], mainly due to the appearance of maximally chaotic behavior [13, 14, 15, 16, 17], suggesting a 2d holographic dual”
• Three dimensional view of the SYK/AdS duality (2017, neutral): “To understand the implications of this, consider the bi-local propagator, first evaluated in [8].”
• The complete 1/N expansion of a SYK–like tensor model (2016, methodology): “ leading order two and four point functions. The full 1/Nexpansion of arbitrary correlations can be obtained by similar methods. 1 Introduction A tensor model version [1] of the SYK model [3, 4] (see [5, 6] for recent reviews) has been recently proposed by Witten. The model is constructed starting f”
• The bulk dual of SYK: cubic couplings (2017, background): “The SYK four-point function to order 1/N , studied in [2, 5, 4], is given by,”