Asymptotic $\mathcal{O}(r)$ gauge symmetries and gauge-invariant Poincaré generators in higher spacetime dimensions

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 Poincaré generators, that results in the decoupling of all of the $u(1)$ charges from the Poincaré algebra. Thus, the mechanism previously used in $d=4$ to find gauge-invariant Poincaré generators is shown to be a robust property of electromagnetism in all spacetime dimensions $d\ge 4$.

25 pages, no figures. References added. Matches with published version

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• $\mathcal{O}(r^N)$ two-form asymptotic symmetries and renormalized charges
• Boundary conditions for Ashtekar-Barbero variables in the context of asymptotically flat spacetimes which lead to supertranslations at spatial infinity