Bounded Collection of Feynman Integral Calabi-Yau Geometries

Jacob L. Bourjaily, Andrew J. McLeod, Matt Von Hippel, Matthias Wilhelm

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71 Scopus citations


We define the rigidity of a Feynman integral to be the smallest dimension over which it is nonpolylogarithmic. We prove that massless Feynman integrals in four dimensions have a rigidity bounded by 2(L-1) at L loops provided they are in the class that we call marginal: those with (L+1)D/2 propagators in (even) D dimensions. We show that marginal Feynman integrals in D dimensions generically involve Calabi-Yau geometries, and we give examples of finite four-dimensional Feynman integrals in massless φ4 theory that saturate our predicted bound in rigidity at all loop orders.

Original languageEnglish (US)
Article number031601
JournalPhysical review letters
Issue number3
StatePublished - Jan 24 2019

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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