标题： 天体共形原初在有效场论中 显示英文标题

标题： Celestial Conformal Primaries in Effective Field Theories

摘要： 在$d+2$维度中的散射振幅可以重新表述为假想全息 CFT$_d$中共形原初算符的相关函数，方法是使用提升本征态的基而不是动量本征态。 之前已经证明，具有$\Delta \in \frac{d}{2} + i {\mathbb R}$的共形原初算符构成了无质量单粒子表示的基。 在本文中，我们考虑更一般的具有$\Delta \in {\mathbb C}$的共形原初算符，并表明完备性、可归一化性和与 CPT 的一致性意味着我们必须将标度维限制为$\Delta \in \frac{d}{2} + i {\mathbb R}$或$\Delta \in {\mathbb R}$。 与具有$\Delta \in \frac{d}{2} + i {\mathbb R}$的情况不同，具有$\Delta \in {\mathbb R}$的共形原初算符可以在不了解紫外理论的情况下构造，因此可以在有效场论中定义。在额外的解析性假设下，我们可以分别限制玻色子或费米子算符的$\Delta \in 2 - {\mathbb Z}_{\geq0}$或$\Delta \in \frac{1}{2}-{\mathbb Z}_{\geq0}$。 显示英文摘要

摘要： Scattering amplitudes in $d+2$ dimensions can be recast as correlators of conformal primary operators in a putative holographic CFT$_d$ by working in a basis of boost eigenstates instead of momentum eigenstates. It has been shown previously that conformal primary operators with $\Delta \in \frac{d}{2} + i {\mathbb R}$ form a basis for massless one-particle representations. In this paper, we consider more general conformal primary operators with $\Delta \in {\mathbb C}$ and show that completeness, normalizability, and consistency with CPT implies that we must restrict the scaling dimensions to either $\Delta \in \frac{d}{2} + i {\mathbb R}$ or $\Delta \in {\mathbb R}$. Unlike those with $\Delta \in \frac{d}{2} + i {\mathbb R}$, the conformal primaries with $\Delta \in {\mathbb R}$ can be constructed without knowledge of the UV and can therefore be defined in effective field theories. With additional analyticity assumptions, we can restrict $\Delta \in 2 - {\mathbb Z}_{\geq0}$ or $\Delta \in \frac{1}{2}-{\mathbb Z}_{\geq0}$ for bosonic or fermionic operators, respectively.