Duality, asymptotic charges and higher form symmetries in $p$-form gauge theories

TL;DR

This paper investigates the duality and asymptotic charges in $p$-form gauge theories, revealing a topological duality map, and explores their implications for celestial holography and higher-form symmetries.

Contribution

It introduces a topological duality map for asymptotic charges in $p$-form theories and links higher-form symmetries to celestial holography.

Findings

Electric and magnetic charges are related by duality via a M"obius transformation.

A topological duality map ensures charge information is preserved across dual descriptions.

Higher-form symmetry charges can be characterized by constant gauge parameters supported on submanifolds.

Abstract

The surface charges associated with $p$-form gauge fields in the Bondi patch of $D$-dimensional Minkowski spacetime are computed. We show that, under the Hodge duality between the field strengths 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 observe that the complex combination of electric-like and magnetic-like charges transforms under duality according to a specific M\"obius transformation. This leads to a possible construction of CCFT in $D=4$ as a M\"obius-principal equivariant bundle, together with its associated bundles, in order to recover celestial operators. We prove an existence and uniqueness theorem for the duality map relating the asymptotic electric-like charges of the dual descriptions, and we provide an algebraic-topological interpretation of this map. As a result, the duality map has a topological nature and ensures that the charge of one formulation contains information about the dual formulation, leading to a deeper understanding of gauge theories, the non-trivial charges associated with them, and the duality of their observables. Moreover, we propose a link between higher-form symmetry charges, naturally associated with a $p$-form gauge theory, and their asymptotic charges. The higher-form charges are reproduced by choosing the gauge parameter to be constant and supported only on an appropriate codimension submanifold. This could partially answer an open question in the celestial holography program.