A generalization of Sachdev-Ye-Kitaev

By D. Gross, V. Rosenhaus. 2016

313 citations recorded by the source corpus.

A bstractThe SYK model: fermions with a q-body, Gaussian-random, all-to-all interaction, is the first of a fascinating new class of solvable large N models. We generalize SYK to include f flavors of fermions, each occupying Na sites and appearing with a qa order in the interaction. Like SYK, this entire class of models generically has an infrared fixed point. We compute the infrared dimensions of the fermions, and the spectrum of singlet bilinear operators. We show that there is always a dimension-two operator in the spectrum, which implies that, like in SYK, there is breaking of conformal invariance and maximal chaos in the infrared four-point function of the generalized model. After a disorder average, the generalized model has a global O(N1) × O(N2) × … × O(Nf) symmetry: a subgroup of the O(N) symmetry of SYK; thereby giving a richer spectrum. We also elucidate aspects of the large q limit and the OPE, and solve q = 2 SYK at finite N.

Subfields: Astronomy and Astrophysics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/21c11303b13a549e508e9c2d9f32be6fc12a2b5f

How researchers see this paper

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

In Astronomy and Astrophysics

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

In Mathematical Physics

1. D. Gaiotto
2. I. Klebanov
3. E. Witten
4. H. Verlinde
5. J. Polchinski
6. G. Turiaci
7. M. Berkooz
8. G. Tarnopolsky

In Nuclear and High Energy Physics

1. D. Stanford
2. E. Witten
3. V. Rosenhaus
4. J. Maldacena
5. Phil Saad
6. Jordan S. Cotler
7. G. Turiaci
8. S. Shenker

Citations in the corpus

• Towards a 2d QFT analog of the SYK model (2017, methodology): “(2)Proposals for 2D generalizations of SYK with a discretized spatial dimension are given in [15, 16, 17].”
• Translationally Invariant Non-Fermi-Liquid Metals with Critical Fermi Surfaces: Solvable Models (2018, methodology): “The model is therefore a translationally invariant generalization of the SYKq model [73] with uniform hoppings.”
• Three dimensional view of the SYK/AdS duality (2017, unknown): “Related models have been studied [13, 14] with extensions [15{25] and generalizations in the form of tensor type models [26{32] .”
• Black holes and random matrices (2016, methodology): “A multiflavor version has been constructed in [26].”
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual (2017, methodology): “Variants of the SYK model have been studied in [29, 30, 31, 32, 33, 34, 35].”
• The bulk dual of SYK: cubic couplings (2017, background): “For instance, one can add flavor to SYK [10], leading to more refined symmetry groups and more parameters.”
• Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models (2016, methodology): “21), we find [33,35] g(h) = − 3 4π l3 2 −h, 1 2 l− 1−h, 1 2 = −(3) 2 tan( 2 (h− 1 2 )) h− 1/2 .”
• An introduction to the SYK model (2018, background): “hese, is to consider a model which contains f avors of fermions, with Na fermions of avor a, each appearing qa times in the interaction, so that the Hamiltonian couples q = Pf a=1 qafermions together [28], L= 1 2 Xf a=1 XNa i=1 ˜a i@˝˜ a i + (i) q 2 Qf a=1 qa! X I JI(˜ 1 i1 ˜ 1 iq 1 ) (˜f j1 ˜f jq f”
• Higher dimensional generalizations of the SYK model (2016, methodology): “tline of our paper is as follows. In section 2 we introduce the model of interacting 2In [22], a 1+1 translationally invariant model (on average), and higher dimensional extensions, were proposed. In [23], the authors propose a generalization by introducing an extra avour index for fermions and cons”
• Fermionic localization of the schwarzian theory (2017, background): “@ ˝g)2]. The partition function for such a particle was already known to be one-loop exact [27]. One expects this theory to be relevant at low-energies for generalizations of SYK with global symmetry [28, 29, 30, 31]. 3.3 Super-Virasoro We can get an interesting generalization by considering super-V”
• All point correlation functions in SYK (2017, methodology): “Figure 5: A pictorial representation of the four-point function, split into a product of two threepoint functions 〈χχO〉, see [11], using the shadow formalism.”