Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark.
School of Physics, NanKai University, Tianjin, 300071, P.R. China.
Phys Rev Lett. 2018 Aug 17;121(7):071603. doi: 10.1103/PhysRevLett.121.071603.
We describe a family of finite, four-dimensional, L-loop Feynman integrals that involve weight-(L+1) hyperlogarithms integrated over (L-1)-dimensional elliptically fibered varieties we conjecture to be Calabi-Yau manifolds. At three loops, we identify the relevant K3 explicitly and we provide strong evidence that the four-loop integral involves a Calabi-Yau threefold. These integrals are necessary for the representation of amplitudes in many theories-from massless φ^{4} theory to integrable theories including maximally supersymmetric Yang-Mills theory in the planar limit-a fact we demonstrate.
我们描述了一族有限的、四维的 L 圈费曼积分，它们涉及到在我们猜想是卡拉比-丘流形的（L-1）维椭圆纤维化族上积分的权-(L+1)超对数。在三圈，我们明确地识别出了相关的 K3，并且我们提供了强有力的证据表明四圈积分涉及到一个卡拉比-丘三维流形。这些积分对于许多理论中的振幅表示是必要的——从无质量 φ^{4}理论到可积理论，包括在平面极限下的最大超对称杨-米尔斯理论——我们证明了这一点。
