Wrońskian algebra and Broadhurst–Roberts quadratic relations

Zhou, Yajun

doi:10.4310/cntp.2021.v15.n4.a1

Cited by 7 publications

(3 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, refs. [206][207][208][209] considered quadratic relations between moments of Bessel functions, which are closely related to banana integrals and their cuts. Quadratic relations for maximal cuts for l = 2 and l = 3 were also studied in ref.…”

Section: Bilinear Relations Among Maximal Cuts From Griffiths Transve...mentioning

confidence: 99%

Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives

Bönisch¹,

Duhr²,

Fischbach³

et al. 2021

Preprint

View full text Add to dashboard Cite

We provide a comprehensive summary of concepts from Calabi-Yau motives relevant to the computation of multi-loop Feynman integrals. From this we derive several consequences for multi-loop integrals in general, and we illustrate them on the example of multi-loop banana integrals. For example, we show how Griffiths transversality, known from the theory of variation of mixed Hodge structures, leads quite generically to a set of quadratic relations among maximal cut integrals associated to Calabi-Yau motives. These quadratic relations then naturally lead to a compact expression for l-loop banana integrals in D = 2 dimensions in terms of an integral over a period of a Calabi-Yau (l − 1)-fold. This new integral representation generalizes in a natural way the known representations for l ≤ 3 involving logarithms with square root arguments and iterated integrals of Eisenstein series. In a second part, we show how the results obtained by some of the authors in earlier work can be extended to dimensional regularization. We present a method to obtain the differential equations for banana integrals with an arbitrary number of loops in dimensional regularization without the need to solve integration-by-parts relations. We also present a compact formula for the leading asymptotics of banana integrals with an arbitrary number of loops in the large momentum limit. This generalizes the novel Γ-class introduced by some of the authors to dimensional regularization and provides a convenient boundary condition to solve the differential equations for the banana integrals. As an application, we present for the first time numerical results for equal-mass banana integrals with up to four loops and up to second order in the dimensional regulator.

show abstract

Section: Bilinear Relations Among Maximal Cuts From Griffiths Transve...mentioning

confidence: 99%

Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives

Bönisch¹,

Duhr²,

Fischbach³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…These are entirely avoided by our uniform formula (52). Yajun Zhou [31] has given an illuminating classical proof, with generalizations.…”

Section: Quadratic Relationsmentioning

confidence: 99%

Empirical determinations of Feynman integrals using integer relation algorithms

Acres¹,

Broadhurst²

2021

Preprint

View full text Add to dashboard Cite

Integer relation algorithms can convert numerical results for Feynman integrals to exact evaluations, when one has reason to suspect the existence of reductions to linear combinations of a basis, with rational or algebraic coefficients. Once a tentative reduction is obtained, confidence in its validity is greatly increased by computing more decimal digits of the terms and verifying the stability of the result. Here we give examples of how the PSLQ and LLL algorithms have yielded remarkable reductions of Feynman integrals to multiple polylogarithms and to the periods and quasi-periods of modular forms. Moreover, these algorithms have revealed quadratic relations between Feynman integrals. A recent application concerning black holes involves quadratic relations between combinations of Feynman integrals with algebraic coefficients.

show abstract

“…Strong biases. Chebyshev's bias was studied in various settings and for various sets, e.g., [Ng 2000;Moree 2004;Fiorilli 2014a;2014b;Devin 2020;2021;Bailleul 2021], in particular for products of a fixed number of primes [Dummit et al 2016;Ford and Sneed 2010;Meng 2018;Devin and Meng 2021].…”

mentioning

confidence: 99%

Untitled

2023

Alg. Number Th.

View full text Add to dashboard Cite

show abstract

Wrońskian algebra and Broadhurst–Roberts quadratic relations

Cited by 7 publications

References 43 publications

Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives

Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives

Empirical determinations of Feynman integrals using integer relation algorithms

Untitled

Contact Info

Product

Resources

About