Large p SYK from chord diagrams
Baur Mukhametzhanov
Abstract
A bstract 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 ≪ p ≪ N and “double-scaled” SYK N , p → ∞ 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 2 n -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 $$ {\mathcal{U}}_q\left( su\left(1,1\right)\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>U</mml:mi> <mml:mi>q</mml:mi> </mml:msub> <mml:mfenced> <mml:mrow> <mml:mi>su</mml:mi> <mml:mfenced> <mml:mn>1</mml:mn> <mml:mn>1</mml:mn> </mml:mfenced> </mml:mrow> </mml:mfenced> </mml:math> 6j-symbol.