Bounded Collection of Feynman Integral Calabi-Yau Geometries

被引：82
|
作者：
Bourjaily, Jacob L. [1 ,2 ]
McLeod, Andrew J. [1 ,2 ]
von Hippel, Matt [1 ,2 ]
Wilhelm, Matthias [1 ,2 ]
机构：
[1] Univ Copenhagen, Niels Bohr Int Acad, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark
[2] Univ Copenhagen, Niels Bohr Inst, Discovery Ctr, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark
来源：
PHYSICAL REVIEW LETTERS | 2019年 / 122卷 / 03期
基金：
欧洲研究理事会;
关键词：
HODGE STRUCTURE; DIAGRAMS; SERIES; HYPERSURFACES; SPACE; GRAPH;
D O I：
10.1103/PhysRevLett.122.031601
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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 phi(4) theory that saturate our predicted bound in rigidity at all loop orders.
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页数：7
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