双伴纯量树的幅与相交对偶结合面
Biadjoint scalar tree amplitudes and intersecting dual associahedra
摘要：
基于对偶结合面体的组合学，提出了一个新的双伴纯量树振幅公式$m(α|β)$。我们的建设基本上使用的锥在'运动空间'介绍Arkani哈米德，白，他，和严。然后，我们考虑对偶运动空间中的对偶结合面。如果适当地嵌入，这些对偶缔合面体的交点编码幅度$m(α|β)$。事实上，我们编码的所有部分振幅在$n$点使用一个单一的对象（风扇）在双运动空间。等价地，作为我们构造的一个令人愉快的推论，所有的$n$-点分振幅都可以理解为来自单个复曲面簇中子簇上的积分。振幅的显式公式然后通过使用等变局部化（或Duistermaat-Heckman）公式来评估这些积分。最后，通过在运动学空间中引入一个格，我们观察到我们的风扇也与逆KLT核有关，有时表示为$m_{α'}(α|β)$。
英文摘要：
We present a new formula for the biadjoint scalar tree amplitudes $m(α|β)$ based on the combinatorics of dual associahedra. Our construction makes essential use of the cones in 'kinematic space' introduced by Arkani-Hamed, Bai, He, and Yan. We then consider dual associahedra in 'dual kinematic space.' If appropriately embedded, the intersections of these dual associahedra encode the amplitudes $m(α|β)$. In fact, we encode all the partial amplitudes at $n$-points using a single object (a fan) in dual kinematic space. Equivalently, as a pleasant corollary of our construction, all $n$-point partial amplitudes can be understood as coming from integrals over subvarieties in a single toric variety. Explicit formulas for the amplitudes then follow by evaluating these integrals using the equivariant localisation (or Duistermaat-Heckman) formula. Finally, by introducing a lattice in kinematic space, we observe that our fan is also related to the inverse KLT kernel, sometimes denoted $m_{α'}(α|β)$.
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