Eur. Phys. J. C (2020) 80: 249
https://doi.org/10.1140/epjc/s10052-020-7798-9

Regular Article - Theoretical Physics

On exact proper time Wilsonian RG flows

¹ INAF, Osservatorio Astrofisico di Catania, via S.Sofia 78, 9 5123, Catania, Italy
² INFN, Sezione di Catania, via S. Sofia 64, 95123, Catania, Italy
³ Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120, Heidelberg, Germany
⁴ SISSA, via Bonomea 265, 34136, Trieste, Italy
⁵ INFN, Sezione di Trieste, Trieste, Italy
⁶ INFN, Sezione di Bologna, via Irnerio 46, 40126, Bologna, Italy

^* e-mail: percacci@sissa.it

Received: 2 February 2020
Accepted: 1 March 2020
Published online: 18 March 2020

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.