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We compute the $\beta$-function for a massless Yukawa theory in a closed format the order $\mathcal{O}(1/N_f)$ in the spirit of the expansion in a largenumber of flavours $N_f$. We find an analytic expression with a finite radiusof convergence, and the first singularity occurs at the coupling value $K=5$.

The $\beta$-function for Yukawa theory at large $N_f$