Intersection numbers from companion tensor algebra
Abstract Twisted period integrals are ubiquitous in theoretical physics and mathematics, where they inhabit a finite-dimensional vector space governed by an inner product known as the intersection number. In this work, we uncover the associated tensor structures of intersection numbers and integrate...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2025)045 |
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| _version_ | 1849334098956386304 |
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| author | Giacomo Brunello Vsevolod Chestnov Pierpaolo Mastrolia |
| author_facet | Giacomo Brunello Vsevolod Chestnov Pierpaolo Mastrolia |
| author_sort | Giacomo Brunello |
| collection | DOAJ |
| description | Abstract Twisted period integrals are ubiquitous in theoretical physics and mathematics, where they inhabit a finite-dimensional vector space governed by an inner product known as the intersection number. In this work, we uncover the associated tensor structures of intersection numbers and integrate them with the fibration method to develop a novel evaluation scheme. Companion matrices allow us to cast the computation of the intersection numbers in terms of a matrix operator calculus within the ambient tensor space. For illustrative purposes, our algorithm has been successfully applied to the numerical decomposition of a sample of two-loop integrals, coming from planar five-point massless functions, representing a significant advancement for the direct projection of Feynman integrals to master integrals via intersection numbers. |
| format | Article |
| id | doaj-art-640642f33ddf4b0bb0ac20c24dbadcdf |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-640642f33ddf4b0bb0ac20c24dbadcdf2025-08-20T03:45:40ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-012025713410.1007/JHEP07(2025)045Intersection numbers from companion tensor algebraGiacomo Brunello0Vsevolod Chestnov1Pierpaolo Mastrolia2Dipartimento di Fisica e Astronomia, Università degli Studi di Padova and INFN, Sezione di PadovaDipartimento di Fisica e Astronomia, Università di Bologna and INFN, Sezione di BolognaDipartimento di Fisica e Astronomia, Università degli Studi di Padova and INFN, Sezione di PadovaAbstract Twisted period integrals are ubiquitous in theoretical physics and mathematics, where they inhabit a finite-dimensional vector space governed by an inner product known as the intersection number. In this work, we uncover the associated tensor structures of intersection numbers and integrate them with the fibration method to develop a novel evaluation scheme. Companion matrices allow us to cast the computation of the intersection numbers in terms of a matrix operator calculus within the ambient tensor space. For illustrative purposes, our algorithm has been successfully applied to the numerical decomposition of a sample of two-loop integrals, coming from planar five-point massless functions, representing a significant advancement for the direct projection of Feynman integrals to master integrals via intersection numbers.https://doi.org/10.1007/JHEP07(2025)045Differential and Algebraic GeometryHigher-Order Perturbative CalculationsScattering Amplitudes |
| spellingShingle | Giacomo Brunello Vsevolod Chestnov Pierpaolo Mastrolia Intersection numbers from companion tensor algebra Journal of High Energy Physics Differential and Algebraic Geometry Higher-Order Perturbative Calculations Scattering Amplitudes |
| title | Intersection numbers from companion tensor algebra |
| title_full | Intersection numbers from companion tensor algebra |
| title_fullStr | Intersection numbers from companion tensor algebra |
| title_full_unstemmed | Intersection numbers from companion tensor algebra |
| title_short | Intersection numbers from companion tensor algebra |
| title_sort | intersection numbers from companion tensor algebra |
| topic | Differential and Algebraic Geometry Higher-Order Perturbative Calculations Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP07(2025)045 |
| work_keys_str_mv | AT giacomobrunello intersectionnumbersfromcompaniontensoralgebra AT vsevolodchestnov intersectionnumbersfromcompaniontensoralgebra AT pierpaolomastrolia intersectionnumbersfromcompaniontensoralgebra |