发表机构
Beijing Institute of Mathematical Sciences and Applications (BIMSA); University of Waterloo; Tsinghua University（北京国际数学研究中心; 滑铁卢大学; 清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过几何组合学方法，以Tr(φ³)理论为对象，首次完整证明了量子场论中定域性可由隐藏零点这一壳上原理导出，同时结合平面极点字母表和分母界可得到定域性与幺正性。
AI 中文摘要
定域性与幺正性是量子场论的基本原理。对于树级散射振幅，定域性决定了哪些传播子极点可以同时出现，而幺正性则通过因式分解确定这些极点的留数。此前的唯一性定理已多次证明，幺正性可由定域性结合其他物理原理导出。在这篇论文中，我们首次针对该情形给出了定域性导出的全多重度完整证明。我们聚焦于Tr(φ³)理论，将定域性表述为几何组合学中的问题：平面传播子是多边形的弦，当且仅当这些弦对多边形进行三角剖分时，对应的分母才是定域的，否则为非定域的。我们证明，隐藏零点——即振幅消失的正则运动学条件——会强制极点相容性，因此隐含定域奇异性结构。该证明依赖两个关键要素：图形“星检验”可确定所选零点何时消除极点乘积，而“平滑化”程序则能找到此类零点。因此，一旦指定平面极点字母表和分母界，定域性与幺正性便会共同由一个单一的壳上原理——隐藏零点——导出。等价地，我们的证明为一个熟知概念提供了新的刻画：多边形三角剖分恰好是规避所有星检验的弦构型。
英文摘要
Locality and unitarity are fundamental principles of quantum field theory. For tree-level scattering amplitudes, locality determines which propagator poles may occur together, while unitarity fixes their residues through factorization. Previous uniqueness theorems have repeatedly shown that unitarity can emerge from locality combined with other physical principles. In this Letter we give the first complete all-multiplicity proof for the emergence of locality in this setting. We focus on Tr($ϕ^3$) theory and phrase locality as a problem in geometric combinatorics. Planar propagators are chords of a polygon, and a denominator is local exactly when its chords triangulate the polygon, and non-local otherwise. We show that hidden zeros---regular kinematic conditions on which the amplitude vanishes---enforce pole compatibility and therefore imply a local singularity structure. The proof rests on two ingredients: a graphical \emph{star test} determines when a chosen zero eliminates a pole product, and a \emph{smoothing} procedure finds such a zero. Thus, once the planar pole alphabet and denominator bound are specified, locality and unitarity emerge together from a single on-shell principle: hidden zeros. Equivalently, our proof provides a novel characterization of a familiar concept: polygon triangulations are precisely the chord configurations that evade every star test.
Comments6+9 pages;
