论文标题
关于天体振幅的共振和单位性的注释
Notes on Resonances and Unitarity from Celestial Amplitudes
论文作者
论文摘要
我们研究了Coleman，Jackiw和Politzer引入的$ o（n）$ sigma模型的天体描述。为了关注三个维度，我们分析了紫外线完整的全环阶振幅的含义在天体圆上定义的相关函数方面。我们发现这些保留了先前研究的树级案例中的许多关键特征，例如它们与广义自由田间理论和交叉对称性的关系，但还结合了新属性，例如IR/UV柔软性和S-Matrix亚稳态状态。特别是，为了理解单位性，我们提出了一种光学定理的形式，该形式仅基于这些共振的存在来控制相关器的假想部分。我们还明确分析了四点函数的共形块扩展和分解为三点函数。我们发现，对共振的总结是这些分解属性掌握的关键。我们以一些供将来研究的主题结尾。
We study the celestial description of the $O(N)$ sigma model in the large $N$ limit as introduced by Coleman, Jackiw and Politzer. Focusing on three dimensions, we analyze the implications of a UV complete, all-loop order 4-point amplitude of pions in terms of correlation functions defined on the celestial circle. We find these retain many key features from the previously studied tree-level case, such as their relation to Generalized Free Field theories and crossing-symmetry, but also incorporate new properties such as IR/UV softness and S-matrix metastable states. In particular, to understand unitarity, we propose a form of the optical theorem that controls the imaginary part of the correlator based solely on the presence of these resonances. We also explicitly analyze the conformal block expansions and factorization of four-point functions into three-point functions. We find that summing over resonances is key for these factorization properties to hold. We end with some topics for future study.
