Fixed point merger in the SU(N) gauge beta functions

TL;DR

This paper investigates the behavior of SU(N) gauge beta functions in QCD with many flavors, revealing the existence and merging of IR and UV fixed points within the conformal window using non-perturbative methods.

Contribution

It demonstrates the presence of both IR and UV fixed points in the gauge beta functions and analyzes their merger at the conformal window edge using an approximation scheme.

Findings

Existence of IR and UV fixed points in the gauge beta function.

Fixed points merge and disappear at the conformal window boundary.

Scaling dimensions of quark mass operator at fixed points are provided.

Abstract

We discuss qualitative behavior of the SU(N) gauge beta functions in QCD with many massless flavors. Non-perturbative beta functions can be obtained by extracting the renormalized trajectories in the exact renormalization group framework. We examine the renormalization group equations for the general four-fermi couplings as well as the gauge coupling obtained in a simple approximation scheme. It is shown that the gauge beta function possesses not only an IR but also a UV fixed point in the conformal window. These fixed points merge with each other and disappear at the edge of the conformal window. The scaling dimensions of the quark mass operator at the fixed points are also shown.