Proper time regulator and Renormalization Group flow

TL;DR

This paper explores the use of proper time regulators in Renormalization Group flow equations, demonstrating that a specific limit enhances the accuracy of critical exponent calculations for scalar theories.

Contribution

It introduces a method to analytically implement a limit of proper time regulators, improving the precision of RG flow analyses for scalar field theories.

Findings

Optimized results for critical exponents in 3D O(N) scalar theories.

Analytical implementation of the regulator limit enhances flow equation accuracy.

Insights into large N and perturbative features in 4D theories.

Abstract

We consider some applications of the Renormalization Group flow equations obtained by resorting to a specific class of proper time regulators. Within this class a particular limit that corresponds to a sharpening of the effective width of the regulator is investigated and a procedure to analytically implement this limit on the flow equations is shown. We focus on the critical exponents determination for the O(N) symmetric scalar theory in three dimensions. The large N limit and some perturbative features in four dimensions are also analysed. In all problems examined the results are optimized when the mentioned limit of the proper time regulator is taken.