The asymptotic structure of electromagnetism in higher spacetime dimensions

TL;DR

This work analyzes the asymptotic structure of free electromagnetism in Minkowski space for spacetime dimensions d ≥ 4, focusing on spatial infinity and the connection to null infinity. It shows that for d > 4 parity conditions are unnecessary, provided a boundary term in the symplectic form and a boundary degree of freedom Ψ are introduced to make boosts canonical, revealing two independent angle-dependent u(1) asymptotic symmetries. The authors derive boundary conditions, compute Poincaré charges, and establish a comprehensive algebra that includes these two u(1) sectors and their matching across I^+ and I^- via generalized conditions that incorporate both parity branches. The results extend the understanding of infrared structure in higher dimensions and set the stage for analogous analyses in gravity, highlighting richer symmetry content beyond the familiar d = 4 case.

Abstract

We investigate the asymptotic structure of electromagnetism in Minkowski space in even and odd spacetime dimensions $\geq 4$. We focus on $d>4$ since the case $d=4$ has been studied previously at length. We first consider spatial infinity where we provide explicit boundary conditions that admit the known physical solutions and make the formalism well defined (finite symplectic structure and charges). Contrary to the situation found in $d=4$ dimensions, there is no need to impose parity conditions under the antipodal map on the leading order of the fields when $d>4$. There is, however, the same need to modify the standard bulk symplectic form by a boundary term at infinity involving a surface degree of freedom. This step makes the Lorentz boosts act canonically. Because of the absence of parity conditions, the theory is found to be invariant under two independent algebras of angle-dependent $u(1)$ transformations ($d>4$). We then integrate the equations of motion in order to find the behaviour of the fields near null infinity. We exhibit the radiative and Coulomb branches, characterized by different decays and parities. The analysis yields generalized matching conditions between the past of $\mathscr{I}^+$ and the future of $\mathscr{I} ^-$.