On operator mixing in fermionic CFTs in non-integer dimensions

Understand

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.