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

Abstract

We study properties of asymptotically free vectorial gauge theories with gauge groups $G=\mathrm{SO}(N_c)$ and $G=\mathrm{Sp}(N_c)$ 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 ${\beta }_{IR}^{\prime }$, 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.