Complete random matrix classification of SYK models with N = 0, 1 and 2 supersymmetry

• Published in: The journal of high energy physics Vol. 2017; no. 9; p. 1
• Main Authors: Kanazawa, Takuya, Wettig, Tilo
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 13.09.2017; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Classification; Elementary Particles; Energy levels; High energy physics; Image classification; Mathematical models; Matrix theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetry; Symmetry; AdS-CFT Correspondence; Random Systems; Supersymmetry Breaking; Matrix Models
• DOI: 10.1007/JHEP09(2017)050

A bstract We present a complete symmetry classification of the Sachdev-Ye-Kitaev (SYK) model with N = 0, 1 and 2 supersymmetry (SUSY) on the basis of the Altland-Zirnbauer scheme in random matrix theory (RMT). For N = 0 and 1 we consider generic q -body interactions in the Hamiltonian and find RMT classes that were not present in earlier classifications of the same model with q = 4. We numerically establish quantitative agreement between the distributions of the smallest energy levels in the N = 1 SYK model and RMT. Furthermore, we delineate the distinctive structure of the N = 2 SYK model and provide its complete symmetry classification based on RMT for all eigenspaces of the fermion number operator. We corroborate our classification by detailed numerical comparisons with RMT and thus establish the presence of quantum chaotic dynamics in the N =2 SYK model. We also introduce a new SYK-like model without SUSY that exhibits hybrid properties of the N = 1 and N = 2 SYK models and uncover its rich structure both analytically and numerically.