On operator mixing in fermionic CFTs in non-integer dimensions

TL;DR

This paper analyzes the complex mixing of four-fermion operators in non-integer dimensional fermionic conformal field theories, providing analytic solutions for anomalous dimensions and revealing their spectral properties.

Contribution

It introduces a method to solve the infinite operator mixing problem via recurrence relations, advancing understanding of operator spectra in non-integer dimensional CFTs.

Findings

Analytic solutions for recurrence relations of operator mixing

Determination of anomalous dimension spectrum

Insights into operator mixing in non-integer dimensions

Abstract

We consider renormalization of four-fermion operators in the critical QED and $SU(N_c)$ version of Gross--Neveu--Yukawa model in non-integer dimensions. Since the number of mixing operators is infinite, the diagonalization of an anomalous dimension matrix becomes a nontrivial problem. At leading order, construction of eigen-operators is equivalent to solving certain three-term recurrence relations. We find analytic solutions of these recurrence relations that allows to determine the spectrum of anomalous dimensions and study their properties.