论文标题
标量理论的积极几何形状的权重，递归关系和投射三角形
Weights, Recursion relations and Projective triangulations for Positive Geometry of scalar theories
论文作者
论文摘要
在[1]的背景下，在[1]中率先提出了质量质量标量理论的正面几何形状的故事。进一步的研究提出，具有多项式相互作用的通用无质量标量理论的正阳性几何形状是一类称为Accordiohedra的多面体[2]。该理论的树级平面散射幅度可以从Accordiohedra的规范形式的加权总和中获得。在本文中，使用最近工作的结果[3]，我们表明，在具有多项式相互作用的理论中，所有权重都可以从AccordioHedron的分解属性确定。我们还将[4,5]中引入的投影递归关系扩展到这些理论。然后，我们详细分析了$ ϕ^p $理论中的递归关系如何与多项式相互作用的理论对应于Accordiohedra的投影三角剖分。随着最近的发展[6]，我们还将分析扩展到了四分之一理论中的一环集成。
The story of positive geometry of massless scalar theories was pioneered in [1] in the context of bi-adjoint $ϕ^3$ theories. Further study proposed that the positive geometry for a generic massless scalar theory with polynomial interaction is a class of polytopes called accordiohedra [2]. Tree-level planar scattering amplitudes of the theory can be obtained from a weighted sum of the canonical forms of the accordiohedra. In this paper, using results of the recent work [3], we show that in theories with polynomial interactions all the weights can be determined from the factorization property of the accordiohedron. We also extend the projective recursion relations introduced in [4,5] to these theories. We then give a detailed analysis of how the recursion relations in $ϕ^p$ theories and theories with polynomial interaction correspond to projective triangulations of accordiohedra. Following the very recent development [6] we also extend our analysis to one-loop integrands in the quartic theory.
