Standard Running, "Physical Running", Cosmological Constant and Newton Coupling

TL;DR

This paper clarifies the correct way to analyze the running of coupling constants like the cosmological constant and Newton's coupling in curved spacetime, correcting misconceptions from previous assumptions.

Contribution

It demonstrates that choosing an appropriate renormalization scale resolves issues with the beta function and discusses the running of fundamental constants in curved spacetime.

Findings

Proper renormalization scale choice is crucial for correct running of couplings.

The cosmological constant and Newton coupling can run when considering curved spacetime.

Incorrect assumptions about scale lead to misconceptions about coupling behavior.

Abstract

Recently it is asserted that the standard beta function does not describe the correct running of the coupling constant in some theories. We show that the problem arises from the assumption $\mu=p$ ($\mu$ is a renormalization point) and that a suitable choice of $\mu$ gives the correct running. It is also claimed that neither the cosmological constant nor Newton coupling run. We argue that running can be discussed when we consider the curved spacetime.