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arXiv · 2508.00807

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

Alfio M. Bonanno·Emiliano M. Glaviano·Gian Paolo Vacca
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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'

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Alfio M. Bonanno, Emiliano M. Glaviano, Gian Paolo Vacca. 2026-05-11. Proper-time functional renormalization in $O(N)$ scalar models coupled to gravity. https://arxiv.org/abs/2508.00807

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