Discrete Geometry, Celestial Holography, and the Geometric Origin of Particle Spectra ------ A Dialogue with the Work of Pasterski

Abstract Building upon our previously constructed framework of discrete geometry (Paper [1]), this paper explores its possible connections with the celestial holography framework developed by Pasterski and her collaborators. We suggest that the celestial holography framework provides a top-down dual description for our geometric construction, which may help establish a theoretical link between first principles of discrete geometry and physical predictions. By attempting to construct a correspondence between gluing rules and celestial sphere support sets, formally transforming bulk higher-point correlation functions into celestial CFT correlators via the Sleight-Taronna extrapolation dictionary, and then deriving the particle mass spectrum through the Källén-Lehmann spectral representation, we tentatively outline a theoretical pathway from discrete geometry to particle physics. In particular, the exponential scaling for particle generations, proposed in our earlier work, receives a systematic derivation within this framework, and a quantitative relationship between the exponent and the recursive folding depth is established. This study aims to explore the possibility of a dialogue between the discrete geometric construction and mainstream high-energy physics, and to provide several testable theoretical predictions for future investigation. 摘要 本文在前期离散几何构建(论文[1])的基础上,探讨其与帕斯特斯基(Pasterski)及其合作者发展的天体全息框架之间的可能联系。我们认为,天体全息框架为我们的几何构建提供了一种自上而下的对偶描述,有助于建立离散几何第一原理与物理预言之间的理论联系。通过尝试构造粘合规则与天球面支撑集之间的对应映射 ΦΦ,将体时空的高阶关联函数通过Sleight-Taronna外推字典形式地转化为天球CFT关联函数,再借助Källén-Lehmann谱表示导出粒子质量谱,我们初步勾勒出一条从离散几何到粒子物理的理论路径。特别地,前期工作中提出的粒子代质量指数标度 mn=m0⋅3Cnmn=m0⋅3Cn,在本文框架内获得了系统的推导,指数 CC 与递归折叠深度 NN 之间建立了定量关系。本研究旨在探索离散几何构建与主流高能物理理论对话的可能性,并为后续研究提供若干可供检验的理论预言。