Replica-nondiagonal solutions in the SYK model (part 2)

The talk is devoted to the discussion of the SYK model of randomly interacting fermions beyond the replica-diagonal approximation. In the second part of the talk the exact replica-nondiagonal saddle points will be discussed. At finite replica number the analytic exact solutions in the quadratic version of the model and numerical replica-nondiagonal solutions in the quartic interacting version of the model are constructed. It will be shown that the families of replica-nondiagonal solutions in quadratic and quartic SYK models are in the one-to-one correspondence. Also the contributions from these saddle points to the replica partition function and other quantities will be discussed.