Scheme-Independent Calculations in Conformal Field Theories

Preprint number: CP3-Origins-2018-17 DNRF90
Authors: John A. Gracey (Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool), Thomas A. Ryttov (CP3-Origins & DIAS), and Robert Shrock (YITP Stony Brook University)
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We present analytic scheme-independent series calculations of anomalous dimensions of several types of baryon operators at an infrared fixed point (IRFP) in an asymptotically free SU(3) gauge theory with $N_f$ fermions. Separately, for an asymptotically free gauge theory with a gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, we consider physical quantities at an IRFP, including the anomalous dimension of gauge-invariant fermion bilinears and the derivative of the beta function. These quantities have been calculated in series expansions whose coefficients have been proved to be scheme-independent at each order. We illustrate the scheme independence using a variety of schemes, including the RI$^prime$ scheme and several types of momentum subtraction (MOM) schemes.