论文标题
使用BCFW递归来限制Stokes多面体的重量
Constraining the weights of Stokes Polytopes using BCFW recursions for Phi^4
论文作者
论文摘要
某些称为多层的几何对象与散射幅度之间的关系揭示了QFT中的深层结构。它是在$ \ Mathcal {n} = 4〜 \ text {sym} $理论中以$ \ mathcal {n} = 4〜 \ toseal的深度开发的，并已扩展到标量$ ϕ^3 $和$ ϕ^4 $的理论在树级别。在本文中，我们将广义的BCFW递归关系用于无质量的平面$ ϕ^4 $理论来限制称为Stokes polytopes的一类几何对象的权重，这些对象在$ ϕ^4 $ amplududes的几何公式中表现出来。我们看到，stokes多面体的权重与$ ϕ^4 $理论中的边界项相关。我们计算$ n = 1,2 $的权重，以及$ 3 $ dimensional stokes polytopes分别对应于六，八和十点振幅。我们将结果推广到更高点的幅度，并表明广义BCFW递归唯一地固定了$ n $ - 点振幅的权重。
The relationship between certain geometric objects called polytopes and scattering amplitudes has revealed deep structures in QFTs. It has been developed in great depth at the tree- and loop-level amplitudes in $\mathcal{N}=4~\text{SYM}$ theory and has been extended to the scalar $ϕ^3$ and $ϕ^4$ theories at tree-level. In this paper, we use the generalized BCFW recursion relations for massless planar $ϕ^4$ theory to constrain the weights of a class of geometric objects called Stokes polytopes, which manifest in the geometric formulation of $ϕ^4$ amplitudes. We see that the weights of the Stokes polytopes are intricately tied to the boundary terms in $ϕ^4$ theories. We compute the weights of $N=1,2$, and $3$ dimensional Stokes polytopes corresponding to six-, eight- and ten-point amplitudes respectively. We generalize our results to higher-point amplitudes and show that the generalized BCFW recursions uniquely fix the weights for an $n$-point amplitude.
