Replica-nondiagonal solutions in the SYK model

We study the Sachdev-Ye-Kitaev (SYK) model in the large N limit beyond the replica-diagonal approximation. We obtain the exact replica-nondiagonal solutions in the quadratic version of the model, and the numerical solutions in the quartic interacting model. The defining feature of these solutions in both quadratic and quartic interaction cases is singular behavior in the limit of zero replica number. We also study replica-nondiagonal solutions of the SYK model in the strong coupling limit. We construct them analytically using the Parisi ansatz for arbitrary replica number. Based on paper by I. Aref'eva, M. Khramtsov, M. Tikhanovskaya and I. Volovich, "Replica-nondiagonal solutions in the SYK model".