Exact four point function for large $q$ SYK from Regge theory

TL;DR

This paper derives a closed-form expression for the fermion four-point function in the large q SYK model, valid across temperature regimes, using Regge theory, and confirms previous results with an alternative approach.

Contribution

It provides a novel, exact analytical formula for the four-point function in the large q SYK model applicable at all temperatures, connecting chaos and conformal regimes.

Findings

The four-point function is expressed as a sum of three Regge poles.

The Lyapunov exponent interpolates between zero and the maximal value with temperature.

Results agree with previous independent calculations.

Abstract

Motivated by the goal of understanding quantum systems away from maximal chaos, in this note we derive a simple closed form expression for the fermion four point function of the large $q$ SYK model valid at arbitrary temperatures and to leading order in $1/N$. The result captures both the large temperature, weakly coupled regime, and the low temperature, nearly conformal, maximally chaotic regime of the model. The derivation proceeds by the Sommerfeld-Watson resummation of an infinite series that recasts the four point function as a sum of three Regge poles. The location of these poles determines the Lyapunov exponent that interpolates between zero and the maximal value as the temperature is decreased. Our results are in complete agreement with the ones by Streicher arxiv:1911.10171 obtained using a different method.