Empirical Determinations of Feynman Integrals Using Integer Relation Algorithms

Acres, Kevin; Broadhurst, David J.

doi:10.1007/978-3-030-80219-6_3

Cited by 9 publications

(18 citation statements)

References 22 publications

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“…To find the small resolutions HV and HΛ of the singular manifolds related to the polytopes discussed above, we use the toric geometry methods pioneered by Batyrev and Borisov [7,8,12]. We briefly review this approach 6 .…”

Section: The Methods Of Batyrev and Borisovmentioning

confidence: 99%

“…where B i (ζ) is either K 0 (ζ) or iπI 0 (ζ). Naïvely there are 2 6 = 64 integrals of this type, but it turns out that at a generic point in the moduli space there are exactly 32 such integrals that are convergent. The analytic continuation of each integral outside of its domain of convergence is a linear combination of integrals of the form (1.13) that converge in the new region.…”

Section: Periods Of the Five-parameter Familymentioning

confidence: 99%

“…. , ϕ 20 ) where the periods satisfy the Picard-Fuchs equation L (6) f = 0, with the operator L (6) given by (3.7). The Bessel function integrals near a i = 0 that satisfy this equation are given by…”

Section: Determining Closed Form Expressions For All Periodsmentioning

confidence: 99%

“…On the line, the discriminant locus ∆ = 0 has singularities at five points: The region |ϕ| > 89.7214 lies in the region U {1} , which contains the large complex structure point at a 0 = a 2 = a 3 = a 4 = a 5 = 0. By symmetry, we can deduce that the Bessel function integrals giving a basis of solutions to the Picard-Fuchs equation L (6) f = 0 are…”

Section: Determining Closed Form Expressions For All Periodsmentioning

confidence: 99%

“…By integrating the Picard-Fuchs operator L (6) numerically, we can find the continuation of the period vector π 0 to the region |ϕ| > 89.7214, giving the following relation between the vectors π 0 and π 1 :…”

Section: Determining Closed Form Expressions For All Periodsmentioning

confidence: 99%

See 4 more Smart Citations

Mirror Symmetry for Five-Parameter Hulek-Verrill Manifolds

Candelas¹,

Ossa²,

Kuusela³

et al. 2021

Preprint

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We study the mirrors of five-parameter Calabi-Yau threefolds first studied by Hulek and Verrill in the context of observed modular behaviour of the zeta functions for Calabi-Yau manifolds. Toric geometry allows for a simple explicit construction of these mirrors, which turn out to be familiar manifolds. These are elliptically fibred in multiple ways. By studying the singular fibres, we are able to identify the rational curves of low degree on the mirror manifolds. This verifies the mirror symmetry prediction obtained by studying the mirror map near large complex structure points. We undertake also an extensive study of the periods of the Hulek-Verrill manifolds and their monodromies. We anticipate that our results will see use in the study of modular Calabi-Yau manifolds and the theory of certain QFT scattering amplitudes.

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Section: The Methods Of Batyrev and Borisovmentioning

confidence: 99%

Section: Periods Of the Five-parameter Familymentioning

confidence: 99%

Section: Determining Closed Form Expressions For All Periodsmentioning

confidence: 99%

Section: Determining Closed Form Expressions For All Periodsmentioning

confidence: 99%

Section: Determining Closed Form Expressions For All Periodsmentioning

confidence: 99%

See 3 more Smart Citations

Mirror Symmetry for Five-Parameter Hulek-Verrill Manifolds

Candelas¹,

Ossa²,

Kuusela³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

D-brane Masses at Special Fibres of Hypergeometric Families of Calabi–Yau Threefolds, Modular Forms, and Periods

Bönisch,

Klemm,

Scheidegger

et al. 2024

Commun. Math. Phys.

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The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integrals

Blümlein

Schneider

2022

J. Phys. A: Math. Theor.

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The analytic integration and simplification of multi-loop Feynman integrals to special functions and constants plays an important role to perform higher order perturbative calculations in the Standard Model of elementary particles. In this survey article the most recent and relevant computer algebra and special function algorithms are presented that are currently used or that may play an important role to perform such challenging precision calculations in the future. They are discussed in the context of analytic zero, single and double scale calculations in the Quantum Field Theories of the Standard Model and effective field theories, also with classical applications. These calculations play a central role in the analysis of precision measurements at present and future colliders to obtain ultimate information for fundamental physics.

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Empirical Determinations of Feynman Integrals Using Integer Relation Algorithms

Cited by 9 publications

References 22 publications

Mirror Symmetry for Five-Parameter Hulek-Verrill Manifolds

Mirror Symmetry for Five-Parameter Hulek-Verrill Manifolds

D-brane Masses at Special Fibres of Hypergeometric Families of Calabi–Yau Threefolds, Modular Forms, and Periods

The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integrals

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