Renormalized electric and magnetic charges for O(rⁿ) 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 (LGT) act canonically. The expressions of the subⁿ-leading electric charges associated with each O(rⁿ) LGT are then obtained, in agreement with the expressions previously proposed in [1] by means of the tree-level subⁿ-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.