The abelian gauge-Yukawa $\beta$-functions at large $N_f$

TL;DR

This paper analyzes the influence of Yukawa interactions on abelian gauge theories in the large-$N_f$ limit by deriving coupled $eta$-functions at order $1/N_f$, providing insights into their renormalization behavior.

Contribution

It presents a novel calculation of coupled $eta$-functions for abelian gauge-Yukawa systems at large $N_f$ in a closed form, advancing understanding of their quantum corrections.

Findings

Derived coupled $eta$-functions at $ ext{O}(1/N_f)$

Provided a closed-form expression for the $eta$-functions

Enhanced understanding of Yukawa effects in abelian gauge theories

Abstract

We study the impact of the Yukawa interaction in the large-$N_f$ limit to the abelian gauge theory. We compute the coupled $\beta$-functions for the system in a closed form at $\mathcal{O}(1/N_f)$.