发表机构
Institut des Hautes Études Scientifiques（高等科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对世界线量子场论推导在壳递推关系，借助新软引力子定理解决振幅衰减问题，得到d维递推公式并通过双、三引力子振幅验证，可构造理论任意有理振幅。
AI 中文摘要
我们推导了世界线量子场论（WQFT，一种与大质量世界线耦合的引力有效理论，适用于计算经典引力可观测量）振幅的一组在壳递推关系。通过推导并利用存在世界线时的新软引力子定理，我们克服了全复动量变形下振幅的大z衰减不足问题。该定理推广了领头阶（Weinberg）和次领头阶软定理，新增了世界线软辐射带来的贡献。我们的主要结果是一个d维递推公式，将任意n引力子有理振幅表示为WQFT和纯引力的低阶点振幅。利用软世界线定理，我们可从对应的全引力子振幅得到任意数量外部世界线涨落的振幅，该递推足以构造理论的任意有理振幅。我们通过显式计算双引力子和三引力子振幅验证了结果。
英文摘要
We derive a set of on-shell recursion relations for amplitudes in worldline quantum field theory (WQFT), an effective theory of gravity coupled to a massive worldline which is relevant for computing classical gravitational observables. We overcome the poor large-$z$ falloff of amplitudes under an all-line complex momentum deformation by deriving and exploiting a new soft-graviton theorem in the presence of a worldline. This theorem generalizes the leading (Weinberg) and subleading soft theorems with additional contributions due to soft emission from the worldline. Our main result is a $d$-dimensional recursion formula, expressing any $n$-graviton rational amplitude in terms of lower-point amplitudes from WQFT and pure gravity. Using the soft-worldline theorem, we can obtain amplitudes with any number of external worldline fluctuations from the corresponding all-graviton amplitudes, making the recursion sufficient to construct any rational amplitude of the theory. We verify our results by explicitly computing two-graviton and three-graviton amplitudes.
