Bounded Collection of Feynman Integral Calabi-Yau Geometries

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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
Article number031601
JournalPhysical Review Letters
Issue number3
Number of pages7
Publication statusPublished - 24 Jan 2019

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