Higher-order $p$-form asymptotic symmetries in $D = p + 2$

TL;DR

This work studies higher-order asymptotic symmetries for a $p$-form gauge field in $D=p+2$ dimensions, revealing a dual scalar description via $d\mathcal{B}=\star d\phi$ and performing a covariant phase space analysis with symplectic renormalization to obtain finite charges. Through a Hodge decomposition, the charges acquire a universal, $p$-independent form, parametrized by arbitrary functions on the angular sphere, and take the structure of a scalar factor multiplying a $ur$-component of the field strength on ${\cal I}^+_-$. The charges are organized as $Q_B=\sum_{n=0}^N Q_B^{(n)}$, with explicit relations linking $H^{\prime}_{ur}$ to the boundary data $B^{(n-2,0)}$ for both even and odd $p$, and a renormalization prescription that cancels $t$- and $u$-divergences without affecting the finite parts. The results provide a new perspective on scalar charges in odd dimensions and suggest a broad, potentially infinite tower of higher-order asymptotic charges with implications for soft theorems and the infrared structure of $p$-form gauge theories.

Abstract

We investigate higher-order asymptotic symmetries for a $p$-form gauge field in $(p + 2)$-dimensional Minkowski spacetime, where Hodge duality with a scalar holds. Employing symplectic renormalization, we identify $N + 1$ independent asymptotic charges, with each charge being parametrised by an arbitrary function of the angular variables. By means of the Hodge decomposition, these charges share the same formal structure independently from p and are manifestly dual to a scalar charge. We work in Lorenz gauge, therefore the gauge parameters require a radial expansion involving logarithmic (subleading) terms to ensure nontrivial angular dependence at leading order. At the same time we assume a power expansion for the field strength, allowing logarithms in the gauge field expansions within pure gauge sectors.