EFT meets CFT: Multiloop renormalization of higher-dimensional operators in general $ϕ^4$ theories

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Main Authors: Henriksson, Johan, Kousvos, Stefanos R., Nepveu, Jasper Roosmale
Format: Preprint
Published: 2025
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author Henriksson, Johan
Kousvos, Stefanos R.
Nepveu, Jasper Roosmale
author_facet Henriksson, Johan
Kousvos, Stefanos R.
Nepveu, Jasper Roosmale
contents The renormalization of composite operators is a fundamental aspect of quantum field theory, relevant for the description of phase transitions and high energy phenomenology. We calculate the anomalous dimensions of a large set of operators in any scalar $ϕ^4$ theory in $d=4-\varepsilon$ dimensions, up to five loops in most cases. The results have applications in both effective field theory (EFT) and conformal field theory (CFT). As an EFT application, we extract the five-loop renormalization group (RG) equations of the Higgs sector of the Standard Model EFT at dimension six, and up to two loops at dimension eight, aligning our operator basis with custodial symmetry violation. Additionally, for CFT, by resumming the $\varepsilon$-expanded results at the fixed-point, we determine the entire low-lying spectrum (i.e. up to dimension six and Lorentz rank two) of the Ising, $O(n)$ and hypercubic scalar CFTs. Our work enables future conformal bootstrap studies for numerous theories of interest. We include introductions to EFT and CFT, and we illustrate our method and the structure in RG mixing matrices in several illuminating examples, which may also be of general interest. All results in the general theory are publicly available and we describe a systematic path towards applying them to more complicated CFTs.
format Preprint
id arxiv_https___arxiv_org_abs_2511_16740
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle EFT meets CFT: Multiloop renormalization of higher-dimensional operators in general $ϕ^4$ theories
Henriksson, Johan
Kousvos, Stefanos R.
Nepveu, Jasper Roosmale
High Energy Physics - Theory
Statistical Mechanics
High Energy Physics - Phenomenology
The renormalization of composite operators is a fundamental aspect of quantum field theory, relevant for the description of phase transitions and high energy phenomenology. We calculate the anomalous dimensions of a large set of operators in any scalar $ϕ^4$ theory in $d=4-\varepsilon$ dimensions, up to five loops in most cases. The results have applications in both effective field theory (EFT) and conformal field theory (CFT). As an EFT application, we extract the five-loop renormalization group (RG) equations of the Higgs sector of the Standard Model EFT at dimension six, and up to two loops at dimension eight, aligning our operator basis with custodial symmetry violation. Additionally, for CFT, by resumming the $\varepsilon$-expanded results at the fixed-point, we determine the entire low-lying spectrum (i.e. up to dimension six and Lorentz rank two) of the Ising, $O(n)$ and hypercubic scalar CFTs. Our work enables future conformal bootstrap studies for numerous theories of interest. We include introductions to EFT and CFT, and we illustrate our method and the structure in RG mixing matrices in several illuminating examples, which may also be of general interest. All results in the general theory are publicly available and we describe a systematic path towards applying them to more complicated CFTs.
title EFT meets CFT: Multiloop renormalization of higher-dimensional operators in general $ϕ^4$ theories
topic High Energy Physics - Theory
Statistical Mechanics
High Energy Physics - Phenomenology
url https://arxiv.org/abs/2511.16740