Wrońskian algebra and Broadhurst-Roberts quadratic relations

Abstract

Through algebraic manipulations on Wrońskian matrices whose entries are reducible to Bessel moments, we present a new analytic proof of the quadratic relations conjectured by Broadhurst and Roberts, along with some generalizations. In the Wrońskian framework, we reinterpret the de Rham intersection pairing through polynomial coefficients in Vanhove's differential operators, and compute the Betti intersection pairing via linear sum rules for on-shell and off-shell Feynman diagrams at threshold momenta. From the ideal generated by Broadhurst--Roberts quadratic relations, we derive new non-linear sum rules for on-shell Feynman diagrams, including an infinite family of determinant identities that are compatible with Deligne's conjectures for critical values of motivic $L$-functions.

(v1) i+59 pages. Continuation of arXiv:1711.01829v2, reinterpretation and generalization of Fresán-Sabbah-Yu (arXiv:2005.11525v2, arXiv:2006.02702v1). (v2) i+55 pages. Notations upgraded and ancillary file updated. (v3) i+55 pages. For the penultimate paragraph in Sect. 4.2, there are minor notational changes and related updates in the ancillary file WronskianAlgebra_v3.nb

Cited by in corpus (2)

• Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives
• Quadratic relations between Bessel moments