论文标题
来自广义散射方程的一环积分
One-loop integrand from generalised scattering equations
论文作者
论文摘要
从刺穿的$ \ mathbb {cp}^{k-1} $上的集成空间中获得的一般性双聚体标量振幅是Chy形式主义的新型扩展。这些幅度在格拉曼尼亚群集代数方面具有实现。最近，已经建立了用于双聚合物立体标量理论的单循环集成与$ \ Mathcal {d} _n $ cluster polytope之间的连接。在本文中，使用$ \ text {gr} \ left（3,6 \右）$ cluster代数，我们将$ \ left（3,6 \右）$振幅的奇异性与四点一环的四环集成电和双方立量表中的四个环内综合器进行，通过$ \ \ \ \ \ \ \ \ Mathcal {d} d} _ {4} $ clust prot clust poltot clust the Bi-Adjoint Integrand。我们还研究了世界表格中各个边界的$（3,6）$振幅的分解属性。
Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured $\mathbb{CP}^{k-1}$, are novel extensions of the CHY formalism. These amplitudes have realisations in terms of Grassmannian cluster algebras. Recently connections between one-loop integrands for bi-adjoint cubic scalar theory and $\mathcal{D}_n$ cluster polytope have been established. In this paper using the $\text{Gr}\left(3,6\right)$ cluster algebra, we relate the singularities of $\left(3,6\right)$ amplitude to four-point one-loop integrand in the bi-adjoint cubic scalar theory through the $\mathcal{D}_{4}$ cluster polytope. We also study factorisation properties of the $(3,6)$ amplitude at various boundaries in the worldsheet.
