Perturbative and non-perturbative aspects of the proper time renormalization group

Abstract

The renormalization group flow equation obtained by means of a proper time regulator is used to calculate the two loop beta function and anomalous dimension eta of the field for the O(N) symmetric scalar theory. The standard perturbative analysis of the flow equation does not yield the correct results for both beta and eta. We also show that it is still possible to extract the correct beta and eta from the flow equation in a particular limit of the infrared scale. A modification of the derivation of the Exact Renormalization Group flow, which involves a more general class of regulators, to recover the proper time renormalization group flow is analyzed.

arXiv comment26 pages.Latex.Version accepted for publication

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• Ising exponents from the functional renormalisation group
• Spontaneous Symmetry Breaking and Proper-Time Flow Equations
• Exact scheme independence at two loops
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Nambu Jona Lasinio model with proper time regularization in a finite volume
• The Wilson-Polchinski exact renormalization group equation
• Functional Renormalization and $\overline{\text{MS}}$
• On Exact Proper Time Wilsonian RG Flows
• Scheme Independence to all Loops
• Limit of vanishing regulator in the functional renormalization group
• Enhancement of field renormalization in scalar theories via functional renormalization group
• Renormalization group analysis of the three-dimensional Gross-Neveu model at finite temperature and density
• Physics-informed operator flows and observables