Outer automorphisms are sufficient conditions for RG fixed points

Fuente: arXiv
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Main Authors: de Boer, Thede, Trautner, Andreas
Format: Preprint
Published: 2026
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_version_ 1866911509501706240
author de Boer, Thede
Trautner, Andreas
author_facet de Boer, Thede
Trautner, Andreas
contents We point out that the existence of an outer automorphism (Out) is a sufficient condition for the existence of a fixed hyperplane (fixed point, separatrix) in the renormalization group (RG) flow of a Quantum Field Theory (QFT). The corresponding RG fixed hyperplane is determined by a symmetry argument and can be computed without resorting to perturbation theory. This provides the mathematical underpinning of 't Hooft's technical naturalness argument, and results in a systematic way to derive non-perturbative all-order constraints on the RG beta functions. If an Out exists, the symmetry of the fully coupled system of beta functions is larger than the symmetry of the action. We also stress the importance of including goofy transformations in these considerations.
format Preprint
id arxiv_https___arxiv_org_abs_2603_12318
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Outer automorphisms are sufficient conditions for RG fixed points
de Boer, Thede
Trautner, Andreas
High Energy Physics - Theory
Statistical Mechanics
High Energy Physics - Phenomenology
We point out that the existence of an outer automorphism (Out) is a sufficient condition for the existence of a fixed hyperplane (fixed point, separatrix) in the renormalization group (RG) flow of a Quantum Field Theory (QFT). The corresponding RG fixed hyperplane is determined by a symmetry argument and can be computed without resorting to perturbation theory. This provides the mathematical underpinning of 't Hooft's technical naturalness argument, and results in a systematic way to derive non-perturbative all-order constraints on the RG beta functions. If an Out exists, the symmetry of the fully coupled system of beta functions is larger than the symmetry of the action. We also stress the importance of including goofy transformations in these considerations.
title Outer automorphisms are sufficient conditions for RG fixed points
topic High Energy Physics - Theory
Statistical Mechanics
High Energy Physics - Phenomenology
url https://arxiv.org/abs/2603.12318