Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space
Abstract It has recently been demonstrated that Feynman integrals relevant to a wide range of perturbative quantum field theories involve periods of Calabi-Yau manifolds of arbitrarily large dimension. While the number of Calabi-Yau manifolds of dimension three or higher is considerable (if not infi...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-01-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2020)078 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832586111581421568 |
|---|---|
| author | Jacob L. Bourjaily Andrew J. McLeod Cristian Vergu Matthias Volk Matt von Hippel Matthias Wilhelm |
| author_facet | Jacob L. Bourjaily Andrew J. McLeod Cristian Vergu Matthias Volk Matt von Hippel Matthias Wilhelm |
| author_sort | Jacob L. Bourjaily |
| collection | DOAJ |
| description | Abstract It has recently been demonstrated that Feynman integrals relevant to a wide range of perturbative quantum field theories involve periods of Calabi-Yau manifolds of arbitrarily large dimension. While the number of Calabi-Yau manifolds of dimension three or higher is considerable (if not infinite), those relevant to most known examples come from a very simple class: degree-2k hypersurfaces in k-dimensional weighted projective space WP1,...,1,k . In this work, we describe some of the basic properties of these spaces and identify additional examples of Feynman integrals that give rise to hypersurfaces of this type. Details of these examples at three loops and of illustrations of open questions at four loops are included as supplementary material to this work. |
| format | Article |
| id | doaj-art-255bbbf9365b49e6b49a9cb3d590ff71 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-255bbbf9365b49e6b49a9cb3d590ff712025-01-26T12:11:34ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020114010.1007/JHEP01(2020)078Embedding Feynman integral (Calabi-Yau) geometries in weighted projective spaceJacob L. Bourjaily0Andrew J. McLeod1Cristian Vergu2Matthias Volk3Matt von Hippel4Matthias Wilhelm5Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of CopenhagenNiels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of CopenhagenNiels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of CopenhagenNiels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of CopenhagenNiels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of CopenhagenNiels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of CopenhagenAbstract It has recently been demonstrated that Feynman integrals relevant to a wide range of perturbative quantum field theories involve periods of Calabi-Yau manifolds of arbitrarily large dimension. While the number of Calabi-Yau manifolds of dimension three or higher is considerable (if not infinite), those relevant to most known examples come from a very simple class: degree-2k hypersurfaces in k-dimensional weighted projective space WP1,...,1,k . In this work, we describe some of the basic properties of these spaces and identify additional examples of Feynman integrals that give rise to hypersurfaces of this type. Details of these examples at three loops and of illustrations of open questions at four loops are included as supplementary material to this work.https://doi.org/10.1007/JHEP01(2020)078Differential and Algebraic GeometryScattering Amplitudes |
| spellingShingle | Jacob L. Bourjaily Andrew J. McLeod Cristian Vergu Matthias Volk Matt von Hippel Matthias Wilhelm Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space Journal of High Energy Physics Differential and Algebraic Geometry Scattering Amplitudes |
| title | Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space |
| title_full | Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space |
| title_fullStr | Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space |
| title_full_unstemmed | Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space |
| title_short | Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space |
| title_sort | embedding feynman integral calabi yau geometries in weighted projective space |
| topic | Differential and Algebraic Geometry Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP01(2020)078 |
| work_keys_str_mv | AT jacoblbourjaily embeddingfeynmanintegralcalabiyaugeometriesinweightedprojectivespace AT andrewjmcleod embeddingfeynmanintegralcalabiyaugeometriesinweightedprojectivespace AT cristianvergu embeddingfeynmanintegralcalabiyaugeometriesinweightedprojectivespace AT matthiasvolk embeddingfeynmanintegralcalabiyaugeometriesinweightedprojectivespace AT mattvonhippel embeddingfeynmanintegralcalabiyaugeometriesinweightedprojectivespace AT matthiaswilhelm embeddingfeynmanintegralcalabiyaugeometriesinweightedprojectivespace |