# Asymptotic $\mathcal O(r)$ gauge symmetries and gauge-invariant Poincar\'e generators in higher spacetime dimensions

## TL;DR

This paper extends the understanding of asymptotic symmetries in higher-dimensional electromagnetism, revealing a rich algebraic structure with central charges and a method to define gauge-invariant Poincaré generators across all dimensions $d \,\geq\, 4$.

## Contribution

It introduces a consistent set of angle-dependent $u(1)$ gauge transformations in higher dimensions and constructs gauge-invariant Poincaré generators by decoupling $u(1)$ charges from the Poincaré algebra.

## Key findings

- Asymptotic symmetry algebra includes a six-fold set of angle-dependent $u(1)$ transformations.
- Presence of central charges in the algebra of asymptotic symmetries.
- A nonlinear redefinition of Poincaré generators achieves gauge invariance in all $d\geq4$.

## Abstract

The asymptotic symmetries of electromagnetism in all higher spacetime dimensions $d>4$ are extended, by incorporating consistently angle-dependent $u(1)$ gauge transformations with a linear growth in the radial coordinate at spatial infinity. Finiteness of the symplectic structure and preservation of the asymptotic conditions require to impose a set of strict parity conditions, under the antipodal map of the $(d-2)$-sphere, on the leading order fields at infinity. Canonical generators of the asymptotic symmetries are obtained through standard Hamiltonian methods. Remarkably, the theory endowed with this set of asymptotic conditions turns out to be invariant under a six-fold set of angle-dependent $u(1)$ transformations, whose generators form a centrally extended abelian algebra. The new charges generated by the $\mathcal O(r)$ gauge parameter are found to be conjugate to those associated to the now improper subleading $O(r^{-d+3})$ transformations, while the standard $\mathcal O(1)$ gauge transformations are canonically conjugate to the subleading $\mathcal{O}(r^{-d+4})$ transformations. This algebraic structure, characterized by the presence of central charges, allows us to perform a nonlinear redefinition of the Poincar\'e generators, that results in the decoupling of all of the $u(1)$ charges from the Poincar\'e algebra. Thus, the mechanism previously used in $d=4$ to find gauge-invariant Poincar\'e generators is shown to be a robust property of electromagnetism in all spacetime dimensions $d\geq 4$.