Exact Correlation Functions in Conformal Fishnet Theory

TL;DR

This paper provides an exact computation of 4-point correlation functions in the fishnet conformal field theory, revealing detailed conformal data and behavior at weak and strong coupling regimes.

Contribution

It presents the first exact expressions for correlation functions, scaling dimensions, and structure constants in the fishnet CFT, including analysis at weak and strong coupling.

Findings

Exact 4-point correlation functions computed

Conformal data of key operators determined

Correlation functions exhibit semiclassical scaling at strong coupling

Abstract

We compute exactly various 4-point correlation functions of shortest scalar operators in bi-scalar planar four-dimensional "fishnet" CFT. We apply the OPE to extract from these functions the exact expressions for the scaling dimensions and the structure constants of all exchanged operators with an arbitrary Lorentz spin. In particular, we determine the conformal data of the simplest unprotected two-magnon operator analogous to the Konishi operator, as well as of the one-magnon operator. We show that at weak coupling 4-point correlation functions can be systematically expanded in terms of harmonic polylogarithm functions and verify our results by explicit calculation of Feynman graphs at a few orders in the coupling. At strong coupling we obtain that the correlation functions exhibit the scaling behaviour typical for semiclassical description hinting at the existence of the holographic dual.