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Intersection Numbers, Polynomial Division and Relative Cohomology

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arxiv 2401.01897 v1 pith:LJFQIYSC submitted 2023-11-06 hep-th

classification hep-th
keywords intersectionnumbersalgorithmappliedcohomologydelta-formsderivedivision
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abstract

We present a simplification of the recursive algorithm for the evaluation of intersection numbers for differential $n$-forms, by combining the advantages emerging from the choice of delta-forms as generators of relative twisted cohomology groups and the polynomial division technique, recently proposed in the literature. We show that delta-forms capture the leading behaviour of the intersection numbers in presence of evanescent analytic regulators, whose use is, therefore, bypassed. This simplified algorithm is applied to derive the complete decomposition of two-loop planar and non-planar Feynman integrals in terms of a master integral basis. More generally, it can be applied to derive relations among twisted period integrals, relevant for physics and mathematical studies.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Tame multi-leg Feynman integrals beyond one loop

    hep-ph 2024-12 reject novelty 7.0 of 10

    A 'branch' reformulation of Feynman integrals claims to reduce multi-loop integrals to one-loop-like low-dimensional integrals, but the advertised parameter bound is wrong and the numerical validation is not shown.

  2. Intersection matrices associated to geometric-ordered bases of Feynman integrals

    hep-th 2026-08 conditional novelty 6.0 of 10

    Intersection matrices of geometric-ordered Feynman integral bases are Laurent polynomials or, after a power-of-epsilon factor, integers, which enables systematic elimination of redundant auxiliary functions on the max...

  3. Kira 3: integral reduction with efficient seeding and optimized equation selection

    hep-ph 2025-05 conditional novelty 6.0 of 10

    Kira 3 cuts Feynman-integral reduction cost by up to two orders of magnitude using smarter seeding and equation selection.

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