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

Understand

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.