Perturbative unitarity bounds from momentum-space entanglement
Abstract Physical theories have a limited regime of validity and hence must be accompanied by a breakdown diagnostic to establish when they cease to be valid as parameters are varied. For perturbative theories, estimates of the first neglected order offer valuable guidance, but one is often interest...
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2025-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2025)047 |
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| author | Carlos Duaso Pueyo Harry Goodhew Ciaran McCulloch Enrico Pajer |
| author_facet | Carlos Duaso Pueyo Harry Goodhew Ciaran McCulloch Enrico Pajer |
| author_sort | Carlos Duaso Pueyo |
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| description | Abstract Physical theories have a limited regime of validity and hence must be accompanied by a breakdown diagnostic to establish when they cease to be valid as parameters are varied. For perturbative theories, estimates of the first neglected order offer valuable guidance, but one is often interested in sharp bounds beyond which perturbation theory necessarily fails. In particle physics, it is common to employ the bounds on partial waves imposed by unitarity as such a diagnostic. Unfortunately, these bounds don’t extend to curved spacetime, where scattering experiments are challenging to define. Here, we propose to use the growth of entanglement in momentum space as a breakdown diagnostic for perturbation theory in general field theories. This diagnostic can be readily used in cosmological spacetimes and does not require any flat spacetime limit. More in detail, we consider the so-called purity of the reduced density operator constructed by tracing out all but one of the Fourier modes in an effective theory and we present a diagrammatic technique to compute it perturbatively. Constraints on the regime of validity of perturbation theory are then derived when the perturbative purity violates its unitarity bounds. In flat spacetime, we compare these purity bounds to those from partial waves. We find general qualitative agreement but with remarkable differences: purity bounds can be sometimes weaker, but other times they exist when no partial wave bounds exist. We then derive purity bounds for scalar field theories in de Sitter spacetime for a variety of interactions that appear in inflationary models. Importantly, our bounds make no reference to time evolution and in de Sitter they depend exclusively on scale-invariant ratios of the physical kinematics. |
| format | Article |
| id | doaj-art-43f407482a9e403ea6c3f2511af5ea49 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-43f407482a9e403ea6c3f2511af5ea492025-08-20T03:42:26ZengSpringerOpenJournal of High Energy Physics1029-84792025-08-012025815710.1007/JHEP08(2025)047Perturbative unitarity bounds from momentum-space entanglementCarlos Duaso Pueyo0Harry Goodhew1Ciaran McCulloch2Enrico Pajer3Department of Applied Mathematics and Theoretical Physics, University of CambridgeDepartment of Applied Mathematics and Theoretical Physics, University of CambridgeDepartment of Applied Mathematics and Theoretical Physics, University of CambridgeDepartment of Applied Mathematics and Theoretical Physics, University of CambridgeAbstract Physical theories have a limited regime of validity and hence must be accompanied by a breakdown diagnostic to establish when they cease to be valid as parameters are varied. For perturbative theories, estimates of the first neglected order offer valuable guidance, but one is often interested in sharp bounds beyond which perturbation theory necessarily fails. In particle physics, it is common to employ the bounds on partial waves imposed by unitarity as such a diagnostic. Unfortunately, these bounds don’t extend to curved spacetime, where scattering experiments are challenging to define. Here, we propose to use the growth of entanglement in momentum space as a breakdown diagnostic for perturbation theory in general field theories. This diagnostic can be readily used in cosmological spacetimes and does not require any flat spacetime limit. More in detail, we consider the so-called purity of the reduced density operator constructed by tracing out all but one of the Fourier modes in an effective theory and we present a diagrammatic technique to compute it perturbatively. Constraints on the regime of validity of perturbation theory are then derived when the perturbative purity violates its unitarity bounds. In flat spacetime, we compare these purity bounds to those from partial waves. We find general qualitative agreement but with remarkable differences: purity bounds can be sometimes weaker, but other times they exist when no partial wave bounds exist. We then derive purity bounds for scalar field theories in de Sitter spacetime for a variety of interactions that appear in inflationary models. Importantly, our bounds make no reference to time evolution and in de Sitter they depend exclusively on scale-invariant ratios of the physical kinematics.https://doi.org/10.1007/JHEP08(2025)047Effective Field Theoriesde Sitter spaceRenormalization GroupEarly Universe Particle Physics |
| spellingShingle | Carlos Duaso Pueyo Harry Goodhew Ciaran McCulloch Enrico Pajer Perturbative unitarity bounds from momentum-space entanglement Journal of High Energy Physics Effective Field Theories de Sitter space Renormalization Group Early Universe Particle Physics |
| title | Perturbative unitarity bounds from momentum-space entanglement |
| title_full | Perturbative unitarity bounds from momentum-space entanglement |
| title_fullStr | Perturbative unitarity bounds from momentum-space entanglement |
| title_full_unstemmed | Perturbative unitarity bounds from momentum-space entanglement |
| title_short | Perturbative unitarity bounds from momentum-space entanglement |
| title_sort | perturbative unitarity bounds from momentum space entanglement |
| topic | Effective Field Theories de Sitter space Renormalization Group Early Universe Particle Physics |
| url | https://doi.org/10.1007/JHEP08(2025)047 |
| work_keys_str_mv | AT carlosduasopueyo perturbativeunitarityboundsfrommomentumspaceentanglement AT harrygoodhew perturbativeunitarityboundsfrommomentumspaceentanglement AT ciaranmcculloch perturbativeunitarityboundsfrommomentumspaceentanglement AT enricopajer perturbativeunitarityboundsfrommomentumspaceentanglement |