Large p SYK from chord diagrams

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 $N,p\to \mathrm{\infty }$ with $\lambda =2p^2\mathrm{/}N$ 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.