Large p SYK from chord diagrams

TL;DR

This work connects two finite-temperature solvable limits of the p-body SYK model by deriving large-p observables as the $\lambda\to0$ limit of double-scaled SYK results. Using chord diagrams and the asymptotics of the $U_q(su(1,1))$ 6j-symbol, it provides explicit expressions for the density of states, partition function, Euclidean $2n$-point functions, and the OTOC at long times, uncovering a submaximal chaos regime with a temperature- and energy-dependent Lyapunov exponent $\lambda_L={2\pi\over\beta}\left(1-{2\over\pi}\lambda s\right)$. It also demonstrates that Euclidean correlators factorize into Wick contractions at leading order and that the 6j-symbol can be approximated by a delta-function to recover generalized free-field behavior, while the Askey–Wilson framework offers a controlled route to stringy corrections to JT gravity. Overall, the paper bridges large-$p$ and double-scaled solvable regimes, clarifying how stringy corrections modify chaotic growth and holographic interpretations in finite-temperature SYK.

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 $λ= 2 p^2/N$ 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.