Large p SYK from chord diagrams

TL;DR

This paper investigates the large p SYK model, deriving observables and correlators in different limits, and clarifies the relationship between the large p and double-scaled regimes, revealing stringy corrections to dual gravity.

Contribution

It provides an exact analysis of the p-body SYK model in large p and double-scaled limits, connecting the two and computing key correlators and asymptotics.

Findings

Derived observables in the large p limit from double-scaled results.

Computed Euclidean 2n-point and out-of-time-order correlators.

Identified asymptotics of the U_q(su(1,1)) 6j-symbol for correlator calculations.

Abstract

The p-body SYK model at finite temperature exhibits submaximal chaos and contains stringy-like corrections to the dual JT gravity. It can be solved exactly in two different limits: "large p" SYK $1 \ll p \ll N$ and "double-scaled" SYK $N,p \to \infty$ with $\lambda = 2 p^2/N$ fixed. We clarify the relation between the two. Starting from the exact results in the double-scaled limit, we derive several observables in the large p limit. We compute euclidean $2n$-point correlators and out-of-time-order four-point function at long lorentzian times. To compute the correlators we find the relevant asymptototics of the $U_{q}(su(1,1))$ 6j-symbol.