论文标题
关于四分之一相互作用的积极几何形状iii：一个循环集成。
On the Positive Geometry of Quartic Interactions III : One Loop Integrands from Polytopes
论文作者
论文摘要
在Arkani Ham的开创性工作的基础上，我们，Salvatori和Thomas（AHST）探索了编码一个环形散射幅度的正面几何形状，以实现四分之一的标量相互作用。我们定义了一类新的组合型多型，我们称之为伪accordiohedra，其poset结构与与标量四分之一相互作用相关的一个循环积分的奇异性相关。伪accordiohedra在AHST定义的抽象运动学空间和这些形式对Dype-d AssociaHedra的限制下，参数为一个投影形式的家族可以与四环综合体相关联，以进行四重奏相互作用。 （投影形式）的限制也可以被认为是伪accordiohedra的某些几何实现的规范顶形式。我们的工作探讨了包括所有AHST实现的Dype-d Associahedra的一大批几何实现。这些实现基于Ceballos和Pilaud发现的Dype-D群集代数的伪三体调节模型。
Building on the seminal work of Arkani-Hamed, He, Salvatori and Thomas (AHST), we explore the positive geometry encoding one loop scattering amplitude for quartic scalar interactions. We define a new class of combinatorial polytopes that we call pseudo-accordiohedra whose poset structures are associated to singularities of the one loop integrand associated to scalar quartic interactions. Pseudo-accordiohedra parametrize a family of projective forms on the abstract kinematic space defined by AHST and restriction of these forms to the type-D associahedra can be associated to one-loop integrands for quartic interactions. The restriction (of the projective form) can also be thought of as a canonical top form on certain geometric realisations of pseudo-accordiohedra. Our work explores a large class of geometric realisations of the type-D associahedra which include all the AHST realisations. These realisations are based on the pseudo-triangulation model for type-D cluster algebras discovered by Ceballos and Pilaud.
