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

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.