Exactly solvable single-trace four point correlators in $\chi$CFT$_4$

TL;DR

This paper provides an exact solution for a broad class of four-point correlators in a special conformal field theory, using integrable spin chain models to compute complex Feynman integrals at any loop order.

Contribution

It introduces a novel method to solve Feynman integrals in $ ext{chiCFT}_4$ via an exactly solvable spin chain with $SO(1,5)$ symmetry, extending previous conjectures.

Findings

Derived a general formula for Feynman integrals using separated variables.

Reproduced the fishnet integral conjecture for scalar fields.

Provided a detailed solution of the associated spin chain model.

Abstract

In this paper we study a wide class of planar single-trace four point correlators in the chiral conformal field theory ($\chi$CFT$_4$) arising as a double scaling limit of the $\gamma$-deformed $\mathcal{N}=4$ SYM theory. In the planar (t'Hooft) limit, each of such correlators is described by a single Feynman integral having the bulk topology of a square lattice "fishnet" and/or of an honeycomb lattice of Yukawa vertices. The computation of this class of Feynmann integrals at any loop is achieved by means of an exactly-solvable spin chain magnet with $SO(1,5)$ symmetry. In this paper we explain in detail the solution of the magnet model as presented in our recent letter and we obtain a general formula for the representation of the Feynman integrals over the spectrum of the separated variables of the magnet, for any number of scalar and fermionic fields in the corresponding correlator. For the particular choice of scalar fields only, our formula reproduces the conjecture of B. Basso and L. Dixon for the fishnet integrals.