Five-dimensional CFTs from the $\epsilon$-expansion

Abstract

We look for UV fixed points of non-abelian $SU(n_c)$ gauge theories in $4+2\epsilon$ 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 $\epsilon$. 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.

arXiv comment18 pages, 6 figures, 2 tables; v3: corrected mistake in the estimate of the non-perturbative error, final results only partially affected, figures revised

References in corpus (12)

• Five-Loop Running of the QCD coupling constant
• Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Renormalizability of gauge theories in extra dimensions
• Five-loop quark mass and field anomalous dimensions for a general gauge group
• Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators
• The $O(N)$ Model in $4<d<6$: Instantons and Complex CFTs
• Large N flavor beta-functions: a recap
• Generalized $F$-Theorem and the $\epsilon$ Expansion
• Six dimensional QCD at two loops
• Evidence for a Non-Supersymmetric 5d CFT from Deformations of 5d $SU(2)$ SYM
• Classification and one loop renormalization of dimension six and eight operators in quantum gluodynamics