The spectrum in the Sachdev-Ye-Kitaev model

Abstract

Abstract: The SYK model consists of N ≫ 1 fermions in 0 + 1 dimensions with a random, all-to-all quartic interaction. Recently, Kitaev has found that the SYK model is maximally chaotic and has proposed it as a model of holography. We solve the SchwingerDyson equation and compute the spectrum of two-particle states in SYK, finding both a continuous and discrete tower. The four-point function is expressed as a sum over the spectrum. The sum over the discrete tower is evaluated.