Ising model as a window on quantum gravity with matter

Abstract

We argue that the Ising model conformal field theory (CFT) can be used to obtain some clear insights into three-dimensional (3D) (quantum) gravity with matter. We review arguments for the existence of its holographic description, and concentrate on the time dependence of perturbations of the theory at high temperature, which would correspond to throwing matter into a black hole in the dual picture. Apart from an expected quasi-normal-mode-like exponential damping, we observe a plateau, a burst, and a subsequent reemergence of the whole signal, the latter being apparently at odds with a black hole interpretation. We provide an explanation of this phenomenon in terms of the properties of bulk matter fields interacting with the Banados-Teitelboim-Zanelli black hole and the fact that the geometry/metric is not fundamental but a derived quantity in the Chern-Simons formulation of 3D gravity. This allows for evading the black hole information paradox in the present context. Published by the American Physical Society 2025