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

Abstract

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

15 pages, 2 figures. v3 error in the computation of the n-loop scalar self-energy corrected. The first singularity occurs at $K=5$, qualitatively the analysis is unchanged

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• Towards a fundamental safe theory of composite Higgs and Dark Matter
• An asymptotically safe guide to quantum gravity and matter
• $a$-theorem at large $N_f$
• Trans-series from condensates
• Background field method in the large $N_f$ expansion of scalar QED