$p$-Forms on the Celestial Sphere

TL;DR

This paper develops a basis of conformal primary wavefunctions for $p$-form fields in any dimension, analyzes their properties including shadow transforms, and connects these to asymptotic behaviors and dualities in four-dimensional spacetime.

Contribution

It introduces a systematic construction of conformal primary wavefunctions for $p$-forms, analyzes their gauge properties, and relates asymptotic limits to celestial sphere conformal structures.

Findings

Constructed a basis of conformal primary wavefunctions for $p$-forms.

Analyzed shadow transforms and gauge properties at special conformal dimensions.

Reformulated scalar and dual two-form relations in 4D using conformal primary language.

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 $\Delta=p$, 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.