发表机构
SLAC National Accelerator Laboratory, Stanford University; Universität Bonn; Stanford University; University of Oxford; Moscow Institute of Physics and Technology（斯坦福大学; 波恩大学; 斯坦福大学; 牛津大学; 莫斯科物理技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用可积性和对称多项式理论，在强变形平面N=4超杨-米尔斯理论中，构造了更多满足对跖自对偶性的行列式线性组合，并给出了方形鱼网积分满足ASD的替代证明。
AI 中文摘要
对跖自对偶性（ASD）是一个显著的性质，它通过执行合适的运动学映射并反转符号的字母（更精确地说，作用在多重多对数Hopf代数的对跖上），将一个振幅与自身联系起来。在平面$\mathcal{N}=4$超杨-米尔斯理论中，ASD仅在一种过程中被观察到，其物理起源未知，这促使人们在其他背景下寻找ASD。最近，发现ASD在平面$\mathcal{N}=4$的强变形版本中对方形鱼网积分成立。在本文中，我们研究了在保持方形鱼网不变的ASD变换下，梯形积分多项式的性质。我们的基本构建块是某些梯形积分矩阵的行列式，这些行列式由划分或杨图标记，并自动满足Steinmann关系。我们利用这些行列式的基于可积性的表示（本质上是矩阵模型积分）以及对称多项式理论，找到了更多ASD量——行列式的线性组合，其系数使用划分的组合学表示。作为副产品，我们提供了方形鱼网积分满足ASD的另一种证明。
英文摘要
Antipodal self-duality (ASD) is a remarkable property that relates an amplitude to itself, after performing a suitable kinematic map and reversing the letters of the symbol (more precisely, acting with the antipode of the Hopf algebra of multiple polylogarithms). ASD has been seen in only one process in planar $\mathcal{N}=4$ super-Yang-Mills theory, and its physical origin is unknown, motivating a search for ASD in other contexts. Recently, ASD was found to hold for square fishnet integrals in a strongly-deformed version of planar $\mathcal{N}=4$. In this paper, we investigate the properties of polynomials in ladder integrals under the ASD transformation that leaves the square fishnet invariant. Our basic building blocks are determinants of certain matrices of ladder integrals, that are labeled by partitions or Young diagrams, and automatically obey the Steinmann relations. We employ integrability-based representations of such determinants, which are essentially matrix-model integrals, and the theory of symmetric polynomials to find many more ASD quantities -- linear combinations of determinants whose coefficients are expressed using the combinatorics of partitions. As a byproduct, we provide an alternate proof that square fishnet integrals obey ASD.
Comments28 pages, 3 figures
