论文标题
Amplituhedron的签名翻转三角形
Sign Flip Triangulations of the Amplituhedron
论文作者
论文摘要
我们提出了$ m = 4 $ amplituhedron的新三角剖分，与平面$ \ Mathcal {n} = 4 $ Super-Yang-Mills中的散射幅度相关，直接从几何学的组合定义中获得。使用Amplituhedron的“标志翻转”表征，我们将典型的形式复制为全属性的临时违反（NMHV）（NMHV）和临时违反最终范围的直升机，违反（$ \ $ \ text {n}^n}^2 $ MHV 2 $ MHV）不使用任何nmhv and nmhv and usple us us untude uptude uptude uptive。 方法。我们的结果为Amplituhedron \ cite {arkani-Hamed：2013jha}和拓扑{arkani-hamed {arkani-hamed：2017vfh}的原始定义等效提供了有力的证据，并提出了一种新的途径，以计算出更高的循环速度的较高的循环态度。特别是，我们意识到NMHV一环扩增子是两个较低维度的两个扩增性的相交，这反映在相应规范形式的新结构中。
We present new triangulations of the $m=4$ amplituhedron relevant for scattering amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills, obtained directly from the combinatorial definition of the geometry. Using the "sign flip" characterization of the amplituhedron, we reproduce the canonical forms for the all-multiplicity next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating ($\text{N}^2$MHV) tree-level as well as the NMHV one-loop cases, without using any input from traditional amplitudes methods. Our results provide strong evidence for the equivalence of the original definition of the amplituhedron \cite{Arkani-Hamed:2013jha} and the topological one \cite{Arkani-Hamed:2017vfh}, and suggest a new path forward for computing higher loop amplitudes geometrically. In particular, we realize the NMHV one-loop amplituhedron as the intersection of two amplituhedra of lower dimensionality, which is reflected in the novel structure of the corresponding canonical form.
