Preprint number: CP3-Origins-2017-5 DNRF90

Authors:

External link: arXiv.org

We consider an asymptotically free vectorial SU($N_c$) gauge theory with

$N_f$ massless fermions in a representation $R$, having an infrared fixed

point (IRFP) of the renormalization group at $alpha_{IR}$ in the conformal

non-Abelian Coulomb phase. The cases with $R$ equal to the fundamental,

adjoint, and symmetric rank-2 tensor representation are considered. We

present scheme-independent calculations of the anomalous dimension

$gamma_{barpsipsi,IR}$ to $O(Delta_f^4)$ and $beta’_{IR}$ to

$O(Delta_f^5)$ at this IRFP, where $Delta_f$ is an $N_f$-dependent

expansion parameter. Comparisons are made with conventional $n$-loop

calculations and lattice measurements. As a test of the accuracy of the

$Delta_f$ expansion, we calculate $gamma_{barpsipsi,IR}$ to

$O(Delta_f^3)$ in ${cal N}=1$ SU($N_c$) supersymmetric quantum

chromodynamics and find complete agreement, to this order, with the exactly

known expression. The $Delta_f$ expansion also avoids a problem in which

an IRFP may not be manifest as an IR zero of a higher $n$-loop beta

function.