Intersection Numbers from Companion Tensor Algebra
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915456030343168 |
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| author | Brunello, Giacomo Chestnov, Vsevolod Mastrolia, Pierpaolo |
| author_facet | Brunello, Giacomo Chestnov, Vsevolod Mastrolia, Pierpaolo |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intersection Numbers from Companion Tensor Algebra Brunello, Giacomo Chestnov, Vsevolod Mastrolia, Pierpaolo High Energy Physics - Theory Mathematical Physics 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. |
| title | Intersection Numbers from Companion Tensor Algebra |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2408.16668 |