A note on scaling arguments in the effective average action formalism

TL;DR

This paper explores the scaling behavior of the effective average action (EAA) in quantum field theory, deriving an equation analogous to the Callan-Symanzik equation to understand its dependence on an auxiliary scale.

Contribution

It introduces a new equation controlling the $mu$-dependence of the EAA, analogous to the Callan-Symanzik equation, and discusses implications for composite operators.

Findings

Derived an equation for $mu$-dependence of EAA similar to Callan-Symanzik

Analyzed simple solutions for composite operators within the local potential approximation

Provided insights into the scaling behavior of the effective average action

Abstract

The effective average action (EAA) is a scale dependent effective action where a scale $k$ is introduced via an infrared regulator. The $k-$dependence of the EAA is governed by an exact flow equation to which one associates a boundary condition at a scale $\mu$. We show that the $\mu-$dependence of the EAA is controlled by an equation fully analogous to the Callan-Symanzik equation which allows to define scaling quantities straightforwardly. Particular attention is paid to composite operators which are introduced along with new sources. We discuss some simple solutions to the flow equation for composite operators and comment their implications in the case of a local potential approximation.