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

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