The Spectrum in the Sachdev-Ye-Kitaev Model

TL;DR

This paper analyzes the spectrum of two-particle states in the SYK model, revealing both continuous and discrete components, and connects these findings to the model's chaotic and holographic properties.

Contribution

It provides an exact solution to the Schwinger-Dyson equation for the SYK model's spectrum, including the discrete tower of states, advancing understanding of its spectral structure.

Findings

Identified continuous and discrete spectra in SYK model

Computed the four-point function as a sum over the spectrum

Evaluated the contribution of the discrete tower

Abstract

The SYK model consists of $N\gg 1$ 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 Schwinger-Dyson 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.