${\mathcal{O}(r^N)} $ two-form asymptotic symmetries and renormalized charges

TL;DR

This paper studies high-order asymptotic symmetries and charges for two-form gauge fields in four-dimensional Minkowski space, revealing multiple independent charges and the necessity of logarithmic terms in gauge parameters for nontrivial angular dependence.

Contribution

It introduces a framework for analyzing $ ext{O}(r^N)$ asymptotic symmetries with symplectic renormalization, identifying multiple independent charges parametrized by angular functions.

Findings

Identifies N independent asymptotic charges for two-form gauge fields.

Shows gauge parameters require logarithmic terms for nontrivial angular dependence.

Establishes a parallel analysis for electromagnetism with similar features.

Abstract

We investigate $ \mathcal{O}\left( r^N \right) $ asymptotic symmetries for a two-form gauge field in four-dimensional Minkowski spacetime. By employing symplectic renormalization, we identify $ N $ independent asymptotic charges, with each charge being parametrised by an arbitrary function of the angular variables. Working in Lorenz gauge, the gauge parameters require a radial expansion involving logarithmic (subleading) terms to ensure nontrivial angular dependence at leading order. At the same time, we adopt a setup where the field strength admits a power expansion, allowing logarithms in the gauge field expansions within pure gauge sectors. The same setup is studied for electromagnetism.