Abstract
We compute the exact, all energy scale, 4-point function of the large N doublescaled SYK model, by using only combinatorial tools and relating the correlation functions to sums over chord diagrams. We apply the result to obtain corrections to the maximal Lyapunov exponent at low temperatures. We present the rules for the non-perturbative diagrammatic description of correlation functions of the entire model. The latter indicate that the model can be solved by a reduction of a quantum deformation of SL(2), that generalizes the Schwarzian to the complete range of energies.
Highlights
Introduction and summary of resultsThe Sachdev-Ye-Kitaev (SYK) model [1,2,3,4,5] is a quantum-mechanical model in 0 + 1 dimensions, constructed out of N Majorana fermions with all-to-all interactions, and random couplings
We present the rules for the non-perturbative diagrammatic description of correlation functions of the entire model
The division of 1, · · ·, k into pairs can be represented by a map π : {1, · · ·, k} → {1, · · ·, k/2} such that |π−1(j)| = 2, and each intersection is a pair 1 ≤ r, s ≤ k/2 such that there exist 1 ≤ a < b < c < d ≤ k with π(a) = π(c) = r and π(b) = π(d) = s. 4The computations can be adapted for non-random operators as well. 5It does not matter if we introduce additional constants J (A) for these operators, as the dependence on them in a given correlation function is trivial
Summary
The Sachdev-Ye-Kitaev (SYK) model [1,2,3,4,5] is a quantum-mechanical model in 0 + 1 dimensions, constructed out of N Majorana fermions with all-to-all interactions, and random (disordered) couplings. The random couplings α are again independent, have zero mean, uniformly bounded moments, and variance αa21,··· ,ap,(i1,··· ,ip) The analysis of this model is completely analogous to that of (1.1) in the double-scaling limit (1.2); the results are the same when expressed in terms of λ or q, with the only difference being that λ=. One of the applications of having the 4-point function is the ability to compute the chaos (Lyapunov) exponent in double-scaled SYK Analogously to the Schwarzian case relating the R-matrix to the 6j-symbol of SU(1, 1), the R-matrix in doublescaled SYK is closely related to the 6j-symbol of Uq1/2(su(1, 1)) It suggests that the entire model can be solved by considering symmetry with respect to this quantum group.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
