Renormalized electric and magnetic charges for $O(r^n)$ large gauge symmetries

In this work we present the construction of a renormalized symplectic form on an extended phases space where the higher order large gauge transformations act canonically. The expressions of the sub${}^n$-leading electric charges associated to each $O(r^n)$ LGT are then obtained, in agreement with the expressions previously proposed in arXiv:1810.04619 by means of the tree-level sub${}^n$-leading formulas. We also present the duality extension of the extended phase space, computing the full electromagnetic charge algebra, showing a tower of central extensions.