Five-dimensional CFTs from the $ϵ$-expansion

Abstract

We look for UV fixed points of non-abelian $SU(n_c)$ gauge theories in $4+2ϵ$ dimensions with $n_f$ Dirac fermions in the fundamental representation, using the available five-loop $\overline{\mathrm{MS}}$ $\beta$-function and employing Padé-Borel resummation techniques and Padé approximants to the series expansion in $ϵ$. We find evidence for a $5d$ UV-fixed point for $SU(2)$ theories with $n_f\le 4$. We also compute the anomalous dimensions $\gamma$ and ${\gamma }_g$ of respectively the fermion mass bilinear and the gauge kinetic term operator at the UV fixed point.

Comments: 18 pages, 6 figures, 2 tables; v3: corrected mistake in the estimate of the non-perturbative error, final results only partially affected, figures revised