All point correlation functions in SYK

Abstract

Large $N$ melonic theories are characterized by two-point function Feynman diagrams built exclusively out of melons. This leads to conformal invariance at strong coupling, four-point function diagrams that are exclusively ladders, and higher-point functions that are built out of four-point functions joined together. We uncover an incredibly useful property of these theories: the six-point function, or equivalently, the three-point 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 Feynman-like rules. The result is applicable to any theory, not necessarily melonic, in which higher-point correlators are built out of four-point functions. We explicitly calculate the bilinear three-point function for $q$-body SYK, at any $q$. This leads to the bilinear four-point function, as well as all higher-point functions, expressed in terms of higher-point 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.

67 pages, v2

References in corpus (12)

• Holography from Conformal Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• A Generalization of Sachdev-Ye-Kitaev
• Spinning AdS Propagators
• More on Supersymmetric and 2d Analogs of the SYK Model
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Three Dimensional View of the SYK/AdS Duality
• A line of CFTs: from generalized free fields to SYK
• A note on the SYK model with complex fermions
• On Large $N$ Limit of Symmetric Traceless Tensor Models
• In search of conformal theories

Cited by in corpus (7)

• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• Phases Of Melonic Quantum Mechanics
• Line of fixed points in a bosonic tensor model
• The Cosmological OTOC: Formulating new cosmological micro-canonical correlation functions for random chaotic fluctuations in Out-of-Equilibrium Quantum Statistical Field Theory
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
• Generalized cut operation associated with higher order variation in tensor models