标题： $p$-在天球上的形式 显示英文标题

标题： $p$-Forms on the Celestial Sphere

摘要： 我们为任意维度中的 $p$-形式场构建了共形主波函数（CPWs）的基底，并计算了它们的标量积，展示了从常规平面波模展开到CPW模展开的基底变换。我们还对相关的影子变换进行了分析。对于每组 $p$-形式CPWs，我们观察到存在共形维数为 $\Delta=p$ 的纯规范波函数，而这种权重的影子 $p$-形式在临界时空维数值 $D=2p+2$ 下才是纯规范的。然后，我们基于区域方法提供了一种系统的技术，用于在 $\mathscr I$ 附近求取大 $r$ 渐近极限，这种方法自然考虑了天球上普通项和接触项的同时存在。 在$D=4$中，这使我们能够用保角主语言重新表述标量和对偶二形式之间的联系。 显示英文摘要

摘要： We construct a basis of conformal primary wavefunctions (CPWs) for $p$-form fields in any dimension, calculating their scalar products and exhibiting the change of basis between conventional plane wave and CPW mode expansions. We also perform the analysis of the associated shadow transforms. For each family of $p$-form CPWs, we observe the existence of pure gauge wavefunctions of conformal dimension $\Delta=p$, while shadow $p$-forms of this weight are only pure gauge in the critical spacetime dimension value $D=2p+2$. We then provide a systematic technique to obtain the large-$r$ asymptotic limit near $\mathscr I$ based on the method of regions, which naturally takes into account the presence of both ordinary and contact terms on the celestial sphere. In $D=4$, this allows us to reformulate in a conformal primary language the links between scalars and dual two-forms.