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

TL;DR

This paper derives an analytic expression for the beta function of a massless Yukawa theory in the large N_f limit, revealing a finite radius of convergence and a singularity at a specific coupling value.

Contribution

It provides the first closed-form beta function for Yukawa theory at order 1/N_f, with insights into its convergence and singularity structure.

Findings

Beta function expressed in closed form at order 1/N_f.

Finite radius of convergence with a singularity at K=5.

Analytic insights into Yukawa theory behavior 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 $K=5$.