Bi-scalar integrable CFT at any dimension

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.