The shared universality of charged black holes and the many many-body SYK model

There are various reasons to believe that Sachdev-Ye-Kitaev (SYK) models are simple examples of condensed-matter/gravity dualities. Motivated by this, we discuss a novel thermodynamic connection between the charged many many-body SYK model and charged black holes. The first many refers to $q$-body interactions and treating $1/q$ as an expansion parameter. Taking $q o infty$ one then obtains the leading order corrections.

By varying the chemical potential or temperature, the condensed-matter system undergoes a phase transition between maximally chaotic gaseous and liquid phases. A similar transition is seen in charged AdS black holes with a small and a large event horizon phase, both also being maximally chaotic. Analytically calculating the critical exponents, we find that these models also share a universality class. At lower temperatures, the liquid phase becomes integrable while the gaseous phase remains maximally chaotic. This is reminiscent of another gravitational instability—the Hawking-Page transition between a large black hole and free thermal radiation.

This talk is based on arXiv: 2204.09629.