📝 SummarXiv

Abstract

The surface charges associated to $p$-form gauge fields in arbitrary spacetime dimension for large values of the radial coordinate are computed. We show that, under the Hodge duality between the field strength of the dual formulations, electric-like charges for $p$-forms are mapped to magnetic-like charges for the dual $q$-forms, with $q = D-p-2$. We prove an existence and uniqueness theorem for the duality map linking asymptotic electric-like charges of the dual descriptions and we give it an algebraic topology interpretation. As a result the duality map has a topological nature and ensures the charge of a description has information of the dual description leading to a deeper understanding of gauge theories, of the non-trivial charges associated to them and of the duality of their observables. Moreover a link between higher form symmetry charges, naturally associated to a $p$-form gauge theory, and their asymptotic charges is proposed. The higher form charges are reproduced choosing the gauge parameter to be constant and to have support only on an appropriate codimension submanifold. This could partially answer to an open question of the celestial holography program.