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From elliptic curves to Feynman integrals

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Luise Adams, Ekta Chaubey, Stefan Weinzierl

High Energy Physics - Phenomenology · Submitted 10 Jul 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show with the help of an explicit example that in the set of master integrals more than one elliptic curve may occur.

how it is stated · asserted 0.70 read the record →

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arXiv ID1807.03599 (version 1)
Pith IDSUPJYUUT, Pith's permanent record of this paper and its review
CitationEkta Chaubey, Luise Adams, Stefan Weinzierl. "From elliptic curves to Feynman integrals." arXiv:1807.03599 (2018). https://pith.science/paper/SUPJYUUT
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,188 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this talk we discuss Feynman integrals which are related to elliptic curves. We show with the help of an explicit example that in the set of master integrals more than one elliptic curve may occur. The technique of maximal cuts is a useful tool to identify the elliptic curves. By a suitable transformation of the master integrals the system of differential equations for our example can be brought into a form linear in $\varepsilon$, where the $\varepsilon^0$-term is strictly lower-triangular. This system is easily solved in terms of iterated integrals.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this talk we discuss Feynman integrals which are related to elliptic curves. background 0.83 0.45 0.08 asserted 0.96
s1 We show with the help of an explicit example that in the set of master integrals more than one elliptic curve may occur. result 0.94 0.94 0.55 asserted 0.70
s2 The technique of maximal cuts is a useful tool to identify the elliptic curves. method 0.99 0.34 0.08 asserted 0.98
s3 By a suitable transformation of the master integrals the system of differential equations for our example can be brought into a form linear in $\varepsilon$, where the $\varepsilon^0$-term is strictly lower-triangular. method 0.67 0.91 0.14 asserted 1.00
s4 This system is easily solved in terms of iterated integrals. result 0.73 0.82 0.13 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.70 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this talk we discuss Feynman integrals which are related to elliptic curves. We show with the help of an explicit example that in the set of master integrals more than one elliptic curve may occur. The technique of maximal cuts is a useful tool to identify the elliptic curves. By a suitable transformation of the master integrals the system of differential equations for our example can be brought into a form linear in $\varepsilon$, where the $\varepsilon^0$-term is strictly lower-triangular. This system is easily solved in terms of iterated integrals.

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How the literature uses it

4 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 17 sentences without a confident label

Uses the method or tool of 13 papers
Cites as background 33 papers

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