Bounded Collection of Feynman Integral Calabi-Yau Geometries

TY - JOUR

T1 - Bounded Collection of Feynman Integral Calabi-Yau Geometries

AU - Bourjaily, Jacob L.

AU - McLeod, Andrew J.

AU - Von Hippel, Matt

AU - Wilhelm, Matthias

PY - 2019/1/24

Y1 - 2019/1/24

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevLett.122.031601

DO - 10.1103/PhysRevLett.122.031601

M3 - Journal article

C2 - 30735423

AN - SCOPUS:85060643237

SN - 0031-9007

VL - 122

JO - Physical Review Letters

JF - Physical Review Letters

IS - 3

M1 - 031601

ER -