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

TL;DR

This paper investigates the existence of ultraviolet fixed points in five-dimensional non-abelian gauge theories using high-order perturbative calculations and resummation techniques, providing evidence for such fixed points in specific cases.

Contribution

It applies five-loop beta functions and advanced resummation methods to identify potential 5D UV fixed points in SU(n_c) gauge theories with fermions, a novel approach in higher-dimensional QFTs.

Findings

Evidence for 5D UV fixed points in SU(2) theories with up to 4 fermions.

Computed anomalous dimensions at the fixed points.

Demonstrated the effectiveness of Padé-Borel resummation in higher-dimensional gauge theories.

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 $\overline{{\rm MS}}$ $\beta$-function and employing Pad\'e-Borel resummation techniques and Pad\'e approximants to the series expansion in $\epsilon$. We find evidence for a $5d$ UV-fixed point for $SU(2)$ theories with $n_f\leq 4$. 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.