AI 中文总结
研究大质量宇宙学关联函数，利用谱表示和谱胶合算法计算其树级关联函数，揭示其潜在数学结构，发现广义超几何函数中的神奇恒等式，展现隐藏简单性并暗示内在几何原理。
AI 中文摘要
大质量宇宙学关联函数在树级就展现出丰富的超几何结构，反映了德西特时空中粒子传播的扭曲。本文揭示这种表面的复杂性隐藏着非常简单的潜在数学结构。利用谱表示，我们计算了具有任意质量的标量场的任意树级关联函数，表明它们由属于劳里切拉广义超几何函数族的基本构建块通过谱积分胶合而成。我们开发了一种谱胶合算法，通过基本的图组合学来评估这些积分，得到明确的级数表示，消除了对内部能量远离软极限的依赖。该算法自然地生成了大质量关联函数所满足的微分方程的解作为相应本征函数的展开。通过一组图湮灭算符，我们在广义超几何函数中发现了一类新的神奇恒等式，揭示了意想不到的简化：一旦去除动力学传播子，剩余的超几何运动学依赖就坍缩为有理函数。我们的结果揭示了由图组合学决定的刚性超几何解析结构中隐藏的简单性，并暗示了一个内在几何原理，大质量关联函数的性质自然地从中浮现。
英文摘要
Massive cosmological correlators exhibit a rich hypergeometric structure already at tree level, reflecting the distorted propagation of particles in de Sitter spacetime. In this paper, we reveal that this apparent complexity conceals a remarkably simple underlying mathematical structure. Using the spectral representation, we compute arbitrary tree-level correlators of scalar fields with generic masses and show that they are constructed from fundamental building blocks belonging to the family of Lauricella generalised hypergeometric functions, glued together by spectral integrals. We develop a spectral gluing algorithm that evaluates these integrals through elementary graph combinatorics, yielding explicit series representations that resum the dependence on internal energies away from soft limits. This algorithm naturally generates solutions to the differential equations satisfied by massive correlators as expansions in the corresponding eigenfunctions. Acting with a set of graph annihilators, we uncover a new class of magical identities among generalised hypergeometric functions, revealing an unexpected simplification: once the dynamical propagators are stripped away, the remaining hypergeometric kinematic dependence collapses to rational functions. Our results expose a hidden simplicity in the rigid hypergeometric analytic structure dictated by graph combinatorics, and hint at an intrinsic geometric principle from which properties of massive correlators naturally emerge.
Comments111 pages, 9 figures
