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

Thomas A. Ryttov, Robert Shrock

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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.