A note on scaling arguments in the effective average action formalism

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.

30 pages, 1 figure

References in corpus (12)

• Exact evolution equation for the effective potential
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Ising exponents from the functional renormalisation group
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Scaling Solutions in Continuous Dimension
• Scale invariance implies conformal invariance for the three-dimensional Ising model
• Scaling and superscaling solutions from the functional renormalization group
• Functional Renormalization Group approach to the Kraichnan model
• General Computations Without Fixing the Gauge
• Construction of the Energy-Momentum Tensor for Wilson Actions
• On the relation between RG and ERG
• Momenta fields and the derivative expansion

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