Feynman integrals, elliptic integrals and two-parameter K3 surfaces
Abstract The three-loop banana integral with three equal masses and the conformal two-loop five-point traintrack integral in two dimensions are related to a two-parameter family of K3 surfaces. We compute the corresponding periods and the mirror map, and we show that they can be expressed in terms o...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-06-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP06(2025)250 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849387811448291328 |
|---|---|
| author | Claude Duhr Sara Maggio |
| author_facet | Claude Duhr Sara Maggio |
| author_sort | Claude Duhr |
| collection | DOAJ |
| description | Abstract The three-loop banana integral with three equal masses and the conformal two-loop five-point traintrack integral in two dimensions are related to a two-parameter family of K3 surfaces. We compute the corresponding periods and the mirror map, and we show that they can be expressed in terms of ordinary modular forms and functions. In particular, we find that the maximal cuts of the three-loop banana integral with three equal masses can be written as a product of two copies of the maximal cuts of the two-loop equal-mass sunrise integral. Our computation reveals a hidden symmetry of the banana integral not manifest from the Feynman integral representation, which corresponds to exchanging the two copies of the sunrise elliptic curve. |
| format | Article |
| id | doaj-art-e2f37ca7aa844d46b44443cf2d6598c5 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-e2f37ca7aa844d46b44443cf2d6598c52025-08-20T03:42:29ZengSpringerOpenJournal of High Energy Physics1029-84792025-06-012025612410.1007/JHEP06(2025)250Feynman integrals, elliptic integrals and two-parameter K3 surfacesClaude Duhr0Sara Maggio1Bethe Center for Theoretical Physics, Universität BonnBethe Center for Theoretical Physics, Universität BonnAbstract The three-loop banana integral with three equal masses and the conformal two-loop five-point traintrack integral in two dimensions are related to a two-parameter family of K3 surfaces. We compute the corresponding periods and the mirror map, and we show that they can be expressed in terms of ordinary modular forms and functions. In particular, we find that the maximal cuts of the three-loop banana integral with three equal masses can be written as a product of two copies of the maximal cuts of the two-loop equal-mass sunrise integral. Our computation reveals a hidden symmetry of the banana integral not manifest from the Feynman integral representation, which corresponds to exchanging the two copies of the sunrise elliptic curve.https://doi.org/10.1007/JHEP06(2025)250Scattering AmplitudesDifferential and Algebraic Geometry |
| spellingShingle | Claude Duhr Sara Maggio Feynman integrals, elliptic integrals and two-parameter K3 surfaces Journal of High Energy Physics Scattering Amplitudes Differential and Algebraic Geometry |
| title | Feynman integrals, elliptic integrals and two-parameter K3 surfaces |
| title_full | Feynman integrals, elliptic integrals and two-parameter K3 surfaces |
| title_fullStr | Feynman integrals, elliptic integrals and two-parameter K3 surfaces |
| title_full_unstemmed | Feynman integrals, elliptic integrals and two-parameter K3 surfaces |
| title_short | Feynman integrals, elliptic integrals and two-parameter K3 surfaces |
| title_sort | feynman integrals elliptic integrals and two parameter k3 surfaces |
| topic | Scattering Amplitudes Differential and Algebraic Geometry |
| url | https://doi.org/10.1007/JHEP06(2025)250 |
| work_keys_str_mv | AT claudeduhr feynmanintegralsellipticintegralsandtwoparameterk3surfaces AT saramaggio feynmanintegralsellipticintegralsandtwoparameterk3surfaces |