论文标题
从动量扩增子边界到振幅奇点和背部
From Momentum Amplituhedron Boundaries to Amplitude Singularities and Back
论文作者
论文摘要
动量Amplituhedron是一个积极的几何形状，编码$ \ Mathcal {n} = 4 $ Super Yang-Mills中的树级散射幅度直接直接在旋转器中。在本文中，我们对动量amplituhedron $ \ Mathcal {m} _ {n，k} $的所有边界进行了分类，并解释了这些边界与预期的分解通道以及树振幅的软和共线限制。相反，在此边界分层中编码了树幅度的所有物理奇点。最后，我们发现动量Amplituhedron $ \ Mathcal {m} _ {n，k} $具有等于一个的Euler特征，这为证明它对球是同质的第一步提供了第一步。
The momentum amplituhedron is a positive geometry encoding tree-level scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills directly in spinor-helicity space. In this paper we classify all boundaries of the momentum amplituhedron $\mathcal{M}_{n,k}$ and explain how these boundaries are related to the expected factorization channels, and soft and collinear limits of tree amplitudes. Conversely, all physical singularities of tree amplitudes are encoded in this boundary stratification. Finally, we find that the momentum amplituhedron $\mathcal{M}_{n,k}$ has Euler characteristic equal to one, which provides a first step towards proving that it is homeomorphic to a ball.
