Asymptotic Renormalization in Flat Space: Symplectic Potential and Charges of Electromagnetism

TL;DR

The paper develops an asymptotic renormalization scheme for the Maxwell symplectic potential at null infinity in Minkowski space for $D\geq6$, canceling divergences with boundary and corner counterterms to produce finite action and charges. It introduces a conformal current and radial evolution framework, identifies the free data and radiative/soft sectors, and constructs renormalized charges whose Ward identities reproduce the QED soft theorem, supporting the method's physical viability. The work also analyzes anomalies, extends to higher dimensions, and discusses how this approach parallels holographic renormalization while potentially enabling a GR extension and a connection to edge-mode dynamics. The results lay groundwork for a covariant Hamiltonian treatment of asymptotic symmetries in flat space and motivate future comparisons with AdS holography and soft-theorem structures.

Abstract

We present a systematic procedure to renormalize the symplectic potential of the electromagnetic field at null infinity in Minkowski space. We work in $D\geq6$ spacetime dimensions as a toy model of General Relativity in $D\geq4$ dimensions. Total variation counterterms as well as corner counterterms are both subtracted from the symplectic potential to make it finite. These counterterms affect respectively the action functional and the Hamiltonian symmetry generators. The counterterms are local and universal. We analyze the asymptotic equations of motion and identify the free data associated with the renormalized canonical structure along a null characteristic. This allows the construction of the asymptotic renormalized charges whose Ward identity gives the QED soft theorem, supporting the physical viability of the renormalization procedure. We touch upon how to extend our analysis to the presence of logarithmic anomalies and upon how our procedure compares to holographic renormalization.