Bi-scalar integrable CFT at any dimension

TL;DR

This paper introduces a D-dimensional generalization of a bi-scalar conformal field theory, extending integrability and exact correlation function computations from 4D to any dimension, revealing new connections to spin chains and QCD analogues.

Contribution

It generalizes the 4D bi-scalar CFT to arbitrary dimensions, providing exact correlation functions and operator dimensions, and links the theory to integrable spin chains across dimensions.

Findings

Exact four-point correlation functions at any coupling.

Explicit dimensions of R-charge 2 operators with arbitrary spin.

Identification of the D-dimensional fishnet graphs with integrable spin chains.

Abstract

We propose a $D$-dimensional generalization of $4D$ bi-scalar conformal quantum field theory recently introduced by G\"{u}rdogan and one of the authors as a strong-twist double scaling limit of $\gamma$-deformed $\mathcal{N}=4$ SYM theory. Similarly to the $4D$ case, this D-dimensional CFT is also dominated by "fishnet" Feynman graphs and is integrable in the planar limit. The dynamics of these graphs is described by the integrable conformal $SO(D+1,1)$ spin chain. In $2D$ it is the analogue of L. Lipatov's $SL(2,\mathbb{C})$ spin chain for the Regge limit of $QCD$, but with the spins $s=1/4$ instead of $s=0$. Generalizing recent $4D$ results of Grabner, Gromov, Korchemsky and one of the authors to any $D$ we compute exactly, at any coupling, a four point correlation function, dominated by the simplest fishnet graphs of cylindric topology, and extract from it exact dimensions of R-charge 2 operators with any spin and some of their OPE structure constants.