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Main Author: LeClair, André
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2504.09327
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author LeClair, André
author_facet LeClair, André
contents We define a model of 2 coupled SU(2) doublets of scalar fields in $4$ spacetime dimensions which have a rich structure of renormalization group (RG) flows to 1-loop when the SU(2) is broken to U(1). The model is pseudo-hermitian, $H^\dagger = {\cal K} H {\cal K}^\dagger$ with ${\cal K} ^\dagger {\cal K} = {\cal K}^2 =1$, which makes it non-unitary, however in a very specific manner with some desirable properties. We compute the beta functions to 3 loops from the operator product expansion and show that the 1-loop structure of flows persists to higher orders. For $SU(2)$ broken to $U(1)$, we conjecture a beta function to all orders. The flows can be extended to large coupling using a strong-weak coupling symmetry $g \to 1/g$ of the beta functions. One finds a line of fixed points which are non-unitary conformal field theories in 4 spacetime dimensions that were previously unknown. We also find massless flows between 2 non-trivial fixed points, and a regime with a cyclic RG flow, which is allowed since the model is non-unitary. For the flows between fixed points on the critical line, we compute the anomalous dimensions of the perturbations in the UV and IR, and identify some special points where anomalous dimensions are rational numbers.
format Preprint
id arxiv_https___arxiv_org_abs_2504_09327
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Non-perturbative renormalization group for pseudo-hermitian scalar fields in 4D
LeClair, André
High Energy Physics - Theory
High Energy Physics - Phenomenology
We define a model of 2 coupled SU(2) doublets of scalar fields in $4$ spacetime dimensions which have a rich structure of renormalization group (RG) flows to 1-loop when the SU(2) is broken to U(1). The model is pseudo-hermitian, $H^\dagger = {\cal K} H {\cal K}^\dagger$ with ${\cal K} ^\dagger {\cal K} = {\cal K}^2 =1$, which makes it non-unitary, however in a very specific manner with some desirable properties. We compute the beta functions to 3 loops from the operator product expansion and show that the 1-loop structure of flows persists to higher orders. For $SU(2)$ broken to $U(1)$, we conjecture a beta function to all orders. The flows can be extended to large coupling using a strong-weak coupling symmetry $g \to 1/g$ of the beta functions. One finds a line of fixed points which are non-unitary conformal field theories in 4 spacetime dimensions that were previously unknown. We also find massless flows between 2 non-trivial fixed points, and a regime with a cyclic RG flow, which is allowed since the model is non-unitary. For the flows between fixed points on the critical line, we compute the anomalous dimensions of the perturbations in the UV and IR, and identify some special points where anomalous dimensions are rational numbers.
title Non-perturbative renormalization group for pseudo-hermitian scalar fields in 4D
topic High Energy Physics - Theory
High Energy Physics - Phenomenology
url https://arxiv.org/abs/2504.09327