Infrared Fixed Point Physics in ${\rm SO}(N_c)$ and ${\rm Sp}(N_c)$ Gauge Theories

TL;DR

This paper investigates the infrared behavior of certain gauge theories with SO(Nc) and Sp(Nc) groups, calculating anomalous dimensions and beta function derivatives to understand phase boundaries and properties of these theories.

Contribution

It provides scheme-independent calculations of anomalous dimensions and beta function derivatives for SO(Nc) and Sp(Nc) gauge theories, extending understanding of their non-Abelian Coulomb phase.

Findings

Anomalous dimensions increase monotonically with decreasing Nf.

All calculated coefficients are positive, indicating consistent phase behavior.

New estimates for the lower end of the non-Abelian Coulomb phase.

Abstract

We study properties of asymptotically free vectorial gauge theories with gauge groups $G={\rm SO}(N_c)$ and $G={\rm Sp}(N_c)$ and $N_f$ fermions in a representation $R$ of $G$, at an infrared (IR) zero of the beta function, $\alpha_{IR}$, in the non-Abelian Coulomb phase. The fundamental, adjoint, and rank-2 symmetric and antisymmetric tensor fermion representations are considered. We present scheme-independent calculations of the anomalous dimensions of (gauge-invariant) fermion bilinear operators $\gamma_{\bar\psi\psi,IR}$ to $O(\Delta_f^4)$ and of the derivative of the beta function at $\alpha_{IR}$, denoted $\beta'_{IR}$, to $O(\Delta_f^5)$, where $\Delta_f$ is an $N_f$-dependent expansion variable. It is shown that all coefficients in the expansion of $\gamma_{\bar\psi\psi,IR}$ that we calculate are positive for all representations considered, so that to $O(\Delta_f^4)$, $\gamma_{\bar\psi\psi,IR}$ increases monotonically with decreasing $N_f$ in the non-Abelian Coulomb phase. Using this property, we give a new estimate of the lower end of this phase for some specific realizations of these theories.