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 $n_f\leq 4$ and pure $SU(n_c)$ theories for $n_c\leq 4$. 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.
Highlights
Conformal Field Theories (CFTs) play a major role in theoretical physics
We report our results starting from the case of pure SU(2) gauge theory, our best example, and we generalize to different values of nc and nf
In order not to clutter the picture, the error band is shown only for the optimal approximant [2=2], which has been determined by using exact Oð1=nfÞ results for β in the large-nf limit
Summary
Conformal Field Theories (CFTs) play a major role in theoretical physics. In d > 4 the natural question is whether there exists a UV fixed point, i.e., an interacting CFT that when deformed by a relevant operator admits an effective description as a nonAbelian gauge theory. The existence of such a fixed point for Yang-Mills theories in d > 4 would be analogous to well-known lower-dimensional examples of perturbatively
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