Probing nonperturbative effects in 2D gravity with SYK model

This talk is devoted to studies of the large N saddle point structures in the SYK model. We will discuss new solutions of the saddle point equations in the SYK and their role in physics of the model and in the gravity dual description. We will focus on the replica-nondiagonal exact saddle points, which introduce small nonperturbative effects in the 1/N expansion of SYK. We will discuss a deformation of the model, which allows to build a nontrivial phase structure from these saddle points. We will also consider the properties of the saddle points in regards to the holographic gravity dual, a UV completion of JT gravity.
The talk is based on papers in collaboration with I. Aref'eva, M. Tikhanovskaya and I. Volovich arXiv:1811.04831, arXiv:1905.04203 and on current work in progress.