$p$-Forms on the Celestial Sphere

TL;DR

This work develops a complete framework for p-form conformal primary wavefunctions on the celestial sphere in arbitrary dimensions, constructing CPWs for scalars and higher-form fields, computing their inner products, and relating plane-wave and conformal bases. It systematically builds shadow transforms via embedding formalism and identifies pure-gauge sectors at conformal weight $\Delta=p$, with special behavior at the critical dimension $D=2+2p$; the large-$r$ asymptotics near null infinity are analyzed using the method of regions, including contact-term structure and logarithmic terms. In $D=4$ the paper illuminates the Hodge-duality between scalar and two-form primaries and discusses the implications for scalar soft charges, dual memory effects, and celestial amplitudes, tying celestial holography to asymptotic symmetries of form fields. These results provide a robust toolkit for celestial holography involving $p$-forms and open avenues to connect dual form charges with soft theorems and memory phenomena in higher-spin contexts.

Abstract

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 $Δ=p$, 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.