All point correlation functions in SYK
Abstract
Large N melonic theories are characterized by twopoint function Feynman diagrams built exclusively out of melons. This leads to conformal invariance at strong coupling, fourpoint function diagrams that are exclusively ladders, and higherpoint functions that are built out of fourpoint functions joined together. We uncover an incredibly useful property of these theories: the sixpoint function, or equivalently, the threepoint function of the primary O( N ) invariant bilinears, regarded as an analytic function of the operator dimensions, fully determines all correlation functions, to leading nontrivial order in 1/ N , through simple Feynmanlike rules. The result is applicable to any theory, not necessarily melonic, in which higherpoint correlators are built out of fourpoint functions. We explicitly calculate the bilinear threepoint function for qbody SYK, at any q. This leads to the bilinear fourpoint function, as well as all higherpoint functions, expressed in terms of higherpoint conformal blocks, which we discuss. We find universality of correlators of operators of large dimension, which we simplify through a saddle point analysis. We comment on the implications for the AdS dual of SYK.
 Publication:

Journal of High Energy Physics
 Pub Date:
 December 2017
 DOI:
 10.1007/JHEP12(2017)148
 arXiv:
 arXiv:1710.08113
 Bibcode:
 2017JHEP...12..148G
 Keywords:

 1/N Expansion;
 AdSCFT Correspondence;
 Conformal Field Theory;
 Integrable Field Theories;
 High Energy Physics  Theory;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 67 pages, v2