论文标题
关于格拉曼尼亚弦积分的多面体，振幅和边界配置的注释
Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals
论文作者
论文摘要
我们继续研究{\ it grassmannian string积分}基础的积极几何形状，该{\ it Grassmannian string stymalls}是一类“严格的规范形式”，或者是正面的Grassmannian mod torus torus Action，$ g _+（k，n）/t $。任何此类弦乐积分的领先顺序是由多型的规范函数给出的，可以使用牛顿多型的Minkowski和积分的调节剂的Minkowski总和获得，或者由所谓的散射平均图映射给出。 Grassmannian String积分的多面体的规范函数，或其双重多面的体积，也称为广义Bi-Ad-Ad-Ad-Ad-Ad-Ad-Ad-Adoct $ ϕ^3 $振幅。我们计算各个方面的所有线性函数，这些功能将所有情况下的多层板切出最高$ n = 9 $，最高为k = 4，并且它们的奇偶校验偶联案例。计算的主要新颖性是，我们以明显的量规和环状方式呈现这些方面，并确定与这些方面相对应的$ g _+（k，n）/t $的边界配置，这些方面的几何学解释在$（k { - } 1）$ - 上限空间中具有$ n $的$ n $点。我们发现的所有方面和配置最多可直接概括为所有$ n $，尽管对于较高的$ n $仍然需要新的类型。
We continue the study of positive geometries underlying the {\it Grassmannian string integrals}, which are a class of "stringy canonical forms", or stringy integrals, over the positive Grassmannian mod torus action, $G_+(k,n)/T$. The leading order of any such stringy integral is given by the canonical function of a polytope, which can be obtained using the Minkowski sum of the Newton polytopes for the regulators of the integral, or equivalently given by the so-called scattering-equation map. The canonical function of the polytopes for Grassmannian string integrals, or the volume of their dual polytopes, is also known as the generalized bi-adjoint $ϕ^3$ amplitudes. We compute all the linear functions for the facets which cut out the polytope for all cases up to $n=9$, with up to k=4 and their parity conjugate cases. The main novelty of our computation is that we present these facets in a manifestly gauge-invariant and cyclic way, and identify the boundary configurations of $G_+(k,n)/T$ corresponding to these facets, which have nice geometric interpretations in terms of $n$ points in $(k{-}1)$-dimensional space. All the facets and configurations we discovered up to $n=9$ directly generalize to all $n$, although new types are still needed for higher $n$.
