发表机构
School of Natural Sciences, Institute for Advanced Study（高等研究院自然科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究论证单个负螺旋度胶子与任意多个正螺旋度胶子的散射振幅具有拓扑性质，通过 Lean 形式化依赖图推导新公式，经星形运动学测试与纽结理论文献一致，建立了与拓扑场论和弦论的联系。
AI 中文摘要
我们认为，单个负螺旋度胶子与任意多个正螺旋度胶子的散射振幅具有拓扑性质。该振幅在运动学空间的腔室中为常数，其共振位于壁上，且因式分解由壁交叉决定。Yangian不变性要求该振幅由二维零威尔逊环确定，该环可被提升为正且横向的三维链。通过将壁交叉和Weinberg软定理重新解释为子纽结的 skein 关系和 Reidemeister 移动，我们构建了一种状态计数描述，即添加其 HOMFLY-PT 多项式的“角”。在经典极限之外，我们认为这提供了与拓扑场论和弦论的猜想但精确的联系。该新公式通过 Lean 形式化的依赖图（DAG）严格推导，如配套论文中详细阐述的，明确了包括 Reidemeister III 不变性在内的精确假设。它还经过了详尽测试，包括新颖的“星形”运动学，其中振幅和状态计数被证明成为 Catalan 数，与纽结理论文献一致。
英文摘要
We argue that the scattering amplitude of a single minus helicity gluon with arbitrarily many positive helicity gluons is topological. The amplitude is constant in chambers of kinematic space, its resonances are located at walls and its factorization is determined by wall-crossing. Yangian invariance dictates the amplitude to be determined by a 2d null Wilson loop that can be lifted into a positive and transverse 3d link. By reinterpreting wall-crossing and the Weinberg soft theorem as skein relations and Reidemeister moves of the subknots, we construct a state-counting description consisting of adding the `corners' of their HOMFLY-PT polynomials. Beyond the classical limit, we argue that this provides a conjectured but precise connection to topological field and string theory. The new formula is rigorously derived via a Lean-formalized dependency graph (DAG) as detailed in a companion paper, laying out the precise assumptions including Reidemeister III invariance. It is further tested exhaustively, including novel `star' kinematics where the amplitude and state count are shown to become Catalan numbers, in agreement with knot theory literature.
Comments11 pages
