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

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.