Anomalous dimensions of Composite Correlators in "Fishnet" CFT

The only universally accepted method of calculating physical quantities in quantum field theory is perturbation theory. Nevertheless, the presence of additional symmetries in the theory occasionally permits one to proceed beyond the scope of perturbative calculations, even to the extent of calculating certain quantities with absolute precision. An illustrative example of such a symmetry is conformal invariance in two-dimensional models of QFT and statistical mechanics. Constructing interacting theories with conformal symmetry at the quantum level is a challenging endeavor. Nevertheless, there are known examples of precisely solvable models in an arbitrary number of dimensions. The primary distinguishing feature of local observables is the anomalous dimension. The objective of this paper is to compute the leading contribution to the anomalous dimension of some composite operators of the conformal Fishnet model in an arbitrary number of dimensions. A formula for the leading contribution to the anomalous dimension of the «BMN − Vacuum» is presented. Furthermore, we perform a renormalization of the model, calculate its renormalization group characteristics, critical points, and some correlation functions.