Anomalous Dimensions at an Infrared Fixed Point in an SU($N_c$) Gauge Theory with Fermions in the Fundamental and Antisymmetric Tensor Representations

TL;DR

This paper calculates scheme-independent anomalous dimensions at an infrared fixed point in an SU(Nc) gauge theory with fermions in fundamental and antisymmetric tensor representations, and confirms results with lattice simulations.

Contribution

It provides novel scheme-independent calculations of anomalous dimensions for specific fermion representations in SU(Nc) gauge theories, validated by lattice data.

Findings

Calculated anomalous dimensions for fermion bilinear operators at IR fixed point.

Results agree with recent lattice simulation data for specific parameters.

Demonstrated scheme independence of the computed anomalous dimensions.

Abstract

We present scheme-independent calculations of the anomalous dimensions $\gamma_{\bar\psi\psi,IR}$ and $\gamma_{\bar\chi\chi,IR}$ of fermion bilinear operators $\bar\psi\psi$ and $\bar\chi\chi$ at an infrared fixed point in an asymptotically free SU($N_c$) gauge theory with massless Dirac fermion content consisting of $N_F$ fermions $\psi^a_i$ in the fundamental representation and $N_{A_2}$ fermions $\chi^{ab}_j$ in the antisymmetric rank-2 tensor representation, where $i,j$ are flavor indices. For the case $N_c=4$, $N_F=4$, and $N_{A_2}=4$, we compare our results with values of these anomalous dimensions measured in a recent lattice simulation and find agreement.