标题： 库仑分支振幅来自变形的振幅多面体几何 显示英文标题

标题： Coulomb Branch Amplitudes from a Deformed Amplituhedron Geometry

摘要： 通过几何方法，Amplituhedron 提供了最大超对称杨-米尔斯理论中所有环状积分的被积函数。 不幸的是，传统用于积分的维度正则化方法破坏了优美的几何图景。 这促使我们提出一个“变形”的Amplituhedron。 聚焦于四粒子振幅，我们引入两个变形参数，这些参数可以解释为粒子质量。 我们提供了证据，表明质量模式对应于Coulomb分支上特定真空期望值的选择。 变形振幅在红外方面是有限的，使得答案在四维空间中定义明确。 利用基于微分方程的四维积分技术，我们将振幅计算到两环。 在变形参数趋于零的极限下，我们恢复了已知的Bern-Dixon-Smirnov振幅。 在仅有一个变形参数趋于零的极限下，我们发现与角度依赖的尖点异常维数之间的联系。 显示英文摘要

摘要： The Amplituhedron provides, via geometric means, the all-loop integrand of scattering amplitudes in maximally supersymmetric Yang-Mills theory. Unfortunately, dimensional regularization, used conventionally for integration, breaks the beautiful geometric picture. This motivates us to propose a 'deformed' Amplituhedron. Focusing on the four-particle amplitude, we introduce two deformation parameters, which can be interpreted as particle masses. We provide evidence that the mass pattern corresponds to a specific choice of vacuum expectation values on the Coulomb branch. The deformed amplitude is infrared finite, making the answer well-defined in four dimensions. Leveraging four-dimensional integration techniques based on differential equations, we compute the amplitude up to two loops. In the limit where the deformation parameters are taken to zero, we recover the known Bern-Dixon-Smirnov amplitude. In the limit where only one deformation parameter is taken to zero, we find a connection to the angle-dependent cusp anomalous dimension.