Bounded Collection of Feynman Integral Calabi-Yau Geometries

Bourjaily, Jacob L. (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark) ; McLeod, Andrew J. (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark) ; von Hippel, Matt (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark) ; Wilhelm, Matthias (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark)

25 January 2019

Abstract: 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(L1) 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.


Published in: Physical Review Letters 122 (2019)
Published by: APS
DOI: 10.1103/PhysRevLett.122.031601
arXiv: 1810.07689
License: CC-BY-4.0



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