The coupled SYK model at finite temperature

• Published in: The journal of high energy physics Vol. 2020; no. 5; pp. 1 - 14
• Main Authors: Qi, Xiao-Liang, Zhang, Pengfei
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2020; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: 1/N Expansion; 2D Gravity; Black holes; Classical and Quantum Gravitation; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Conformal and W Symmetry; Conformal Field Theory; Dilatons; Elementary Particles; Fermions; Geometry; High energy physics; High temperature; Low temperature; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Conformal and W Symmetry; 2D Gravity; Conformal Field Theory; 1/N Expansion
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2020)129

A bstract Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS 2 dilaton gravity. Ref. [ 1 ] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS 2 geometry. This geometry is an “eternal wormhole” because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function.