Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark.
Phys Rev Lett. 2019 Jan 25;122(3):031601. doi: 10.1103/PhysRevLett.122.031601.
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 φ^{4} theory that saturate our predicted bound in rigidity at all loop orders.
我们将费曼积分的刚性定义为其非多对数的最小维度。我们证明，在 L 圈的情况下，在（偶数）维数 D 中具有 (L+1)D/2 个传播子的我们称之为边缘的那种情况下，在没有质量的四维度中费曼积分具有由 2(L-1) 限定的刚性。我们表明，在 D 维中边缘费曼积分通常涉及 Calabi-Yau 几何，并且我们给出了在所有环阶上都使我们预测的刚性界限饱和的无质量φ^4 理论中的有限四维费曼积分的例子。
