New Massive JT Multi-Gravity and N-Replica of SYK Models

TL;DR

This paper explores new multi-gravity extensions of the JT model, connecting them with multi-SYK models and quantum mechanics, and discusses their quantization and potential applications in condensed matter physics.

Contribution

It introduces novel multi-gravity models related to SYK and Schwarzian theories, providing a $BF$-like formulation and quantization methods, with implications for condensed matter systems.

Findings

Established correspondences among multi-gravity, multi-SYK, and Schwarzian models.

Developed a $BF$-like formulation for the models.

Discussed quantization approaches and potential condensed matter applications.

Abstract

We study a series of powerful correspondences among new multi-gravity extensions of the Jackiw-Teitelboim model, multi-SYK models and multi-Schwarzian quantum mechanics, in the $\rm{(A)dS_{2}/CFT}$ arena. Deploying a $BF$-like formulation of the model, we discuss the counting of the degrees of freedom for some specific classes of multi-gravity potentials, and unveil connections among a variety of apparently different models. Quantization of multi-gravity models can be then achieved from both the Hartle-Hawking no-boundary proposal, the SYK partition function and the spin-foam approaches. We comment on the SYK quantization procedure, and deepen in the appendix the quantization scheme naturally achieved in the $BF$ framework. The new multi-gravity theory hence recovered presents intriguing applications for analogue gravitational models developed for condensed matter physics, including graphene, endowed with defects and high intensity magnetic fields.