Proper-time functional renormalization in $O(N)$ scalar models coupled to gravity

TL;DR

This paper applies the proper time functional Wilsonian renormalization group to O(N) scalar models coupled to gravity, comparing results with previous methods to verify critical properties and scaling solutions.

Contribution

It demonstrates the consistency of the proper time RG framework with prior effective average action results for scalar-gravity systems.

Findings

Qualitative and quantitative agreement with previous studies on scaling solutions.

Identification of small differences at finite and large N depending on scheme choices.

Confirmation of critical exponents and phase structure across frameworks.

Abstract

We focus on the use of the functional Wilsonian renormalization group framework characterized by a proper time regulator and test its use in the search of the scaling solutions and the critical properties of an O(N)-invariant scalar field multiplet coupled to gravity in d=4 and d=3 dimensions. We employ the same background-fluctuation splitting and gauge fixing procedure, already adopted in a previous study based, instead, on the effective average action framework and a similar truncation of the effective action. Our main goal is to compare the results for the scaling solutions and some of the associated critical exponents. In this analysis, performed in a different framework, most of the picture previously uncovered is confirmed both at qualitative and quantitative level. There are, neverthelss, few differences both at finite N and in its large value limit, depending also on the schemes which in both frameworks are called 'improved'