能量关联函数的正性与事例分布公式
Positivity in energy correlators and the event distribution formula
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中文总结 AI 辅助
本文研究能量关联函数的正性问题，提出事例分布公式作为无限层级正性的最一般解，推导两点、三点关联函数多极系数的严格最优双边界，并展示其在对撞机物理与共形场论中的应用。
中文摘要 AI 辅助
能量关联函数是普适的可观测量，在从规范理论、共形场论到弦理论的广泛理论及时空维度中均有良好定义，其受三个基本性质约束：能流的逐点正性、源自幺正理论中态范数解释的全局正性，以及组织多点能量关联函数形成无限一致层级的能量守恒。本文提出，能量关联函数无限层级正性问题的最一般解由事例分布公式给出，该公式将能量关联函数表示为天球上概率测度空间上测度的矩。我们详细推导了正性对两点和三点能量关联函数的影响，表明其对多极展开系数蕴含非平凡的双边界；通过要求能量关联函数无限层级的一致性得到的界，比仅施加两点和三点关联函数正性得到的界严格更强。对于本文研究的低自旋多极系数，推导得到的界是最优的，其极值由有限粒子事例的有限混合实现。我们进一步展示了正性在对撞机物理和共形场论的能量关联函数中的应用结果。
英文摘要
Energy correlators are universal observables, well defined across a wide range of theories and spacetime dimensions, from gauge theory and conformal field theory to string theory. Energy correlators are constrained by three fundamental properties: pointwise positivity of the energy flux, global positivity originating from their interpretation as state norms in a unitary theory, and energy conservation organizing multi-point energy correlators into an infinite consistent hierarchy. We argue that the most general solution to the infinite hierarchy positivity problem of energy correlators is given by the event distribution formula, which expresses energy correlators as moments of the measure on the space of probability measures on the celestial sphere. We work out in detail implications of positivity for two- and three-point energy correlators and show that it implies nontrivial two-sided bounds on their multipole expansion coefficients. The bounds obtained by requiring consistency of the infinite hierarchy of energy correlators are strictly stronger than those obtained by imposing positivity of the two- and three-point correlators alone. For the low-spin multipole coefficients studied in the paper, the derived bounds are optimal in the sense that their extrema are realized by finite mixtures of finite-particle events. We further demonstrate consequences of positivity in energy correlators in collider physics and conformal field theories.
