Pith. sign in

REVIEW 2 cited by

Algorithm for differential equations for Feynman integrals in general dimensions

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2401.09908 v2 pith:YWGUGWQY submitted 2024-01-18 hep-th hep-phmath-phmath.MP

classification hep-thhep-phmath-phmath.MP
keywords differentialalgorithmcaseequationsregularisationanalyticdimensionalfeynman
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We present an algorithm for determining the minimal order differential equations associated to a given Feynman integral in dimensional or analytic regularisation. The algorithm is an extension of the Griffiths-Dwork pole reduction adapted to the case of twisted differential forms. In dimensional regularisation, we demonstrate the applicability of this algorithm by explicitly providing the inhomogeneous differential equations for the multiloop two-point sunset integrals: up to 20 loops for the equal mass case, the generic mass case at two- and three-loop orders. Additionally, we derive the differential operators for various infrared-divergent two-loop graphs. In the analytic regularisation case, we apply our algorithm for deriving a system of partial differential equations for regulated Witten diagrams, which arise in the evaluation of cosmological correlators of conformally coupled $\phi^4$ theory in four-dimensional de Sitter space.

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

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

  1. The multiloop sunset to all orders

    hep-th 2026-03 conditional novelty 8.0 of 10

    Multiloop sunset integrals in D=2 are expressed as convergent sums of symmetric polynomials in logarithms of mass ratios, with a dimension-raising operator that propagates the result to D=4-2ε.

  2. Differential Space of Feynman Integrals: Annihilators and $\mathcal{D}$-module

    hep-th 2025-06 conditional novelty 6.0 of 10

    A Griffiths-Dwork based algorithm builds annihilators and D-modules for Feynman-like integrals, and in all tested cases the holonomic rank matches the twisted de Rham cohomology dimension.

Pith tools