Strong CP as an Infrared Holonomy: The $θ$ Vacuum and Dressing in Yang-Mills Theory

Fuente: arXiv
Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Gamboa, Jorge, Arellano, Natalia A. Tapia
Format: Preprint
Veröffentlicht: 2025
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866911347372982272
author Gamboa, Jorge
Arellano, Natalia A. Tapia
author_facet Gamboa, Jorge
Arellano, Natalia A. Tapia
contents We reformulate the strong $CP$ problem from an infrared viewpoint in which the vacuum angle $θ$ is not treated as a local coupling but as a global Berry-type holonomy of the infrared-dressed state space over $\mathcal{A}/\mathcal{G}$. Infrared dressing is described as adiabatic parallel transport of physical states in configuration space, generated by an infrared connection $\mathcal{A}_{\rm IR}$. Using the Chern-Simons collective coordinate, we show that the Pontryagin index emerges as an integer infrared winding, such that the resulting holonomy phase is quantized by $Q\in\mathbb Z$ and reproduces the standard weight $e^{iθQ}$. A quantum rotor provides a controlled infrared example illustrating why broad classes of local correlators may remain insensitive to $θ$, while global response functions, such as the vacuum energy curvature and the topological susceptibility, retain a nontrivial dependence. We contrast this picture with recent claims of $θ$--independence based on the order of limits and show that it is consistent with both the rotor benchmark and the classic Witten-Veneziano perspective.
format Preprint
id arxiv_https___arxiv_org_abs_2512_24480
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Strong CP as an Infrared Holonomy: The $θ$ Vacuum and Dressing in Yang-Mills Theory
Gamboa, Jorge
Arellano, Natalia A. Tapia
High Energy Physics - Theory
We reformulate the strong $CP$ problem from an infrared viewpoint in which the vacuum angle $θ$ is not treated as a local coupling but as a global Berry-type holonomy of the infrared-dressed state space over $\mathcal{A}/\mathcal{G}$. Infrared dressing is described as adiabatic parallel transport of physical states in configuration space, generated by an infrared connection $\mathcal{A}_{\rm IR}$. Using the Chern-Simons collective coordinate, we show that the Pontryagin index emerges as an integer infrared winding, such that the resulting holonomy phase is quantized by $Q\in\mathbb Z$ and reproduces the standard weight $e^{iθQ}$. A quantum rotor provides a controlled infrared example illustrating why broad classes of local correlators may remain insensitive to $θ$, while global response functions, such as the vacuum energy curvature and the topological susceptibility, retain a nontrivial dependence. We contrast this picture with recent claims of $θ$--independence based on the order of limits and show that it is consistent with both the rotor benchmark and the classic Witten-Veneziano perspective.
title Strong CP as an Infrared Holonomy: The $θ$ Vacuum and Dressing in Yang-Mills Theory
topic High Energy Physics - Theory
url https://arxiv.org/abs/2512.24480