Asymptotic charges of $p-$forms and their dualities in any $D$

TL;DR

<3-5 sentence high-level summary> This work analyzes the asymptotic charges of $p$-form gauge fields in arbitrary dimensions, focusing on radiation and Coulomb falloffs and the critical dimension $D_c=2p+2$ that separates leading behaviors. By deriving residual symmetries in Lorenz gauge, the authors construct two families of charges, $Q_p^r$ (radiation order) and $Q_p^C$ (Coulomb order), and show how their finiteness or divergence depends on $D$ relative to $D_c$ and on the form degree $p$. They then establish a duality map between $p$-form charges and $(D-p-2)$-form charges via Hodge duality, revealing that electric charges map to magnetic charges in the dual theory and that the dual picture can reveal overleading or subleading structures depending on the sector. The results generalize known Maxwell and two-form dualities to arbitrary $p$ and $D$, with implications for celestial holography and the structure of asymptotic symmetries across dual formulations.

Abstract

We compute the surface charges associated to $p-$form gauge fields in arbitrary spacetime dimension for large values of the radial coordinate. In the critical dimension where radiation and Coulomb falloff coincide we find asymptotic charges involving asymptotic parameters, i.e. parameters with a component of order zero in the radial coordinate. However, in different dimensions we still find nontrivial asymptotic charges now involving parameters that are not asymptotic times the radiation-order fields. For $p$=1 and $D>4$, our charges thus differ from those presented in the literature. We then show that under Hodge duality electric charges for $p-$forms are mapped to magnetic charges for the dual $q-$forms, with $q = D-p-2$. For charges involving fields with radiation falloffs the duality relates charges that are finite and nonvanishing. For the case of Coulomb falloffs, above or below the critical dimension, Hodge duality exchanges overleading charges in one theory with subleading ones in its dual counterpart.