Strong CP as an Infrared Holonomy: The $θ$ Vacuum and Dressing in Yang-Mills Theory
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arXiv
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| Format: | Preprint |
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2025
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| 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 |