AI 中文总结
本文是天球全息的入门教材，从AdS/CFT对偶出发，介绍Bondi-Sachs形式、BMS群等基础，讲解将四维散射振幅映射为天球上2D CCFT关联函数的Mellin变换全息映射，帮助初学者进入渐近平直时空量子引力研究前沿。
AI 中文摘要
本入门教材首次介绍天球全息（Celestial Holography）——一个旨在描述渐近平直时空中量子引力的快速发展框架。我们从已确立的AdS/CFT对偶基础出发，随后进入闵可夫斯基空间的研究领域。内容涵盖核心的Bondi-Sachs形式体系、类光无穷远（$\mathscr{I}^\pm$）的几何，以及无穷维BMS渐近对称群的发现。我们阐释了由Mellin变换给出的核心全息映射，该映射将四维散射振幅重构为天球上一个被猜想的二维天球共形场论（CCFT）的关联函数。讲解力求直观但数学依然（但愿）严谨，旨在让初学者掌握概念图景与技术词汇，以探索这一令人兴奋的前沿领域。
英文摘要
This primer offers an first introduction to Celestial Holography, a rapidly evolving framework aiming to describe quantum gravity in asymptotically flat spacetimes. We start from the established foundation of the AdS/CFT correspondence before venturing into the wilds of Minkowski space. The journey covers the essential Bondi-Sachs formalism and the geometry of null infinity ($\mathscr{I}^\pm$), the discovery of the infinite-dimensional BMS asymptotic symmetry group. We explain the core holographic map given by Mellin transform that recasts four-dimensional scattering amplitudes as correlation functions of a conjectured 2D Celestial Conformal Field Theory (CCFT) on the celestial sphere. The presentation is made intuitive but the mathematics is still precise (hopefully!). It is designed to equip newcomers with both the conceptual landscape and the technical vocabulary to explore this exciting frontier.
Comments30 pages, 7 figures
