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

Preprint number: CP3-Origins-2017-34 DNRF90
Authors: Thomas A. Ryttov (CP3-Origins & DIAS) and Robert Shrock (C. N. Yang Institute for Theoretical Physics)

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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
$gamma_{barpsipsi,IR}$ 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 $gamma_{barpsipsi,IR}$ that we
calculate are positive for all representations considered, so that to
$O(Delta_f^4)$, $gamma_{barpsipsi,IR}$ 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.