On operator mixing in fermionic CFTs 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.

9 pages; typos are fixed; Journal reference is given

References in corpus (5)

• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
• Fixed point stability and decay of correlations
• Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion
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Cited by in corpus (4)

• 3d Abelian Gauge Theories at the Boundary
• Conformal symmetry of QCD in $d$-dimensions
• Disturbing news about the $d=2+\epsilon$ expansion
• Correction exponents in the chiral Heisenberg model at $1/N^2$: singular contributions and operator mixing