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We use lattice simulations and the continuous renormalization-group method,based on the gradient flow, to calculate the $\beta$ function and anomalousdimensions of the SU(3) gauge theory with $N_f=10$ flavors of fermions in thefundamental representation. We employ several improvements to extend the rangeof available renormalized couplings, including the addition of heavyPauli-Villars bosons to reduce cutoff effects and the combination of a range ofgradient flow transformations. While in the weak coupling regime our result isconsistent with those of earlier studies, our techniques allow us to study thesystem at much stronger couplings than previously possible. We find that therenormalization group $\beta$ function develops a zero, corresponding to aninfrared-stable fixed point, at gradient-flow coupling $g^2=15.0(5)$. We alsodetermine the mass and tensor anomalous dimensions: At the fixed point we find$\gamma_m\simeq0.6$, suggesting that this system might be deep inside theconformal window.

Infrared fixed point of the SU(3) gauge theory with $N_f = 10$ flavors