My talk is devoted to studies of large N saddle point structures in the SYK model beyond the commonly used approximations, in particular the replica-diagonal assumption and the conformal limit. 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 consider their properties and implications for the gravity dual, a UV completion of JT gravity.
The talk is based on papers arXiv:1811.04831, arXiv:1905.04203 and on current work in progress.