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arXiv · 1809.00021

On operator mixing in fermionic CFTs in non-integer dimensions

Yao Ji·Alexander N. Manashov
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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.

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Yao Ji, Alexander N. Manashov. 2018-11-02. On operator mixing in fermionic CFTs in non-integer dimensions. https://doi.org/10.1103/physrevd.98.105001

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