Matching partition functions of deformed JT gravity and the cSYK model

Abstract

Motivated by recent analogies between the large-$q$ cSYK model and charged black holes, we aim to find a concrete gravitation theory with a matching partition function. Our main focus is to match the thermodynamics of the $(0+1)$-dimensional cSYK model, with that of a $(1+1)$-dimensional gravitational model. We focus on a model of deformed JT gravity, characterized by some unknown dilaton potential function and unknown dilaton-to-Maxwell field coupling. By finding the general solutions, we are able to find the Lagrangian which produces the same partition function and equation of state as that of the considered SYK model. We go beyond showing that the thermodynamics overlaps, by also showing that the Lyapunov exponents, characterizing the degree of chaos, overlap close to the second order phase transition. In the low temperature rescaled regime, there remains open questions about the Lyapunov exponents, given that our analysis ignores the black hole back action which can be large in this regime.

14 pages, 3 figures

References in corpus (7)

• Viscosity, Black Holes, and Quantum Field Theory
• Universality in Chaos of Particle Motion near Black Hole Horizon
• Circular Motion of Charged Particles near Charged Black Hole
• Phases Of Melonic Quantum Mechanics
• Constructing AdS_2 flow geometries
• Thermalization of many many-body interacting SYK models
• The shared universality of charged black holes and the many many-body SYK model

Cited by in corpus (5)

• Pole-skipping in two-dimensional de Sitter spacetime and double-scaled SYK model
• Excitation Transmission through a non-Hermitian traversable wormhole
• Thermodynamic and Real-time Dynamic Properties of Complex Sachdev-Ye-Kitaev Model
• Thermodynamics and dynamics of coupled complex SYK models
• Unveiling Novel Insights in Quantum Dynamics through Extended Sachdev-Ye-Kitaev Model