Pith. sign in

REVIEW 3 cited by

Logarithmic forms and differential equations for Feynman integrals

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

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 1909.04777 v2 pith:N34276AN submitted 2019-09-10 hep-th hep-ph

Logarithmic forms and differential equations for Feynman integrals

Enrico Herrmann , Julio Parra-Martinez This is my paper
classification hep-th hep-ph
keywords differentialequationsfeynmanintegralscertaincitedescribeddlog
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

We describe how a dlog representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized unitarity. For the examples we study, the alphabet of the differential equation is related to special points in kinematic space, described by certain cut equations which encode the geometry of the Feynman integral. At one loop, we reproduce the motivic formulae described by Goncharov \cite{Goncharov:1996tate} that reappeared in the context of Feynman parameter integrals in \cite{Spradlin:2011wp,Arkani-Hamed:2017ahv}. The dlog representation allows us to generalize the differential equations to higher loops and motivates the study of certain mixed-dimension integrals.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 3 Pith papers

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

  1. Kinematics, cluster algebras and Feynman integrals

    hep-th 2021-12 unverdicted novelty 7.0

    Cluster algebras for planar conformal kinematics are identified as G(4,n) subalgebras and used to bootstrap the symbol of an 8-point three-loop wheel integral via D3 and new algebraic letters.

  2. Notes on the bootstrap of four-point conformal integrals

    hep-th 2026-07 accept novelty 6.0

    A leading-singularity bootstrap with single-valued polylog ansätze and region-expansion boundaries evaluates previously intractable four-loop conformal integrals, including non-planar sectors.

  3. Notes on the bootstrap of four-point conformal integrals

    hep-th 2026-07 conditional novelty 6.0

    A leading-singularity bootstrap workflow yields new analytic expressions for four-loop conformal integrals, including previously intractable non-planar sectors.