On Exact Proper Time Wilsonian RG Flows

TL;DR

This paper explores the formulation of exact Wilsonian RG flow equations using proper time regulators, analyzing their relation to field redefinitions and applying the approach to the 3D Ising universality class.

Contribution

It introduces a framework for defining exact RG equations with proper time regulators and examines their connection to field redefinitions and coarse-graining procedures.

Findings

Derived a functional mapping linking RG schemes to field redefinitions.

Applied the formalism to the 3D Ising model within a second order derivative expansion.

Provided insights into the structure of RG flows with proper time regulators.

Abstract

We discuss the possibility to define exact RG equations for a UV regulated Wilsonian action based on a proper time (PT) regulator function. We start from a functional mapping which shows how each particular flow equation (and RG scheme) is associated to infinitely many scale dependent field redefinitions, which are related to specific coarse-graining procedures. On specializing to a sub-family of one parameter PT regulators we briefly analyze few results for the Ising Universality class in three dimensions, obtained within a second order truncation in the derivative expansion of the Wilsonian action.