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

TL;DR

This paper constructs a renormalized symplectic form for higher order large gauge transformations, deriving electric charges and revealing a tower of central extensions in the electromagnetic charge algebra.

Contribution

It introduces a renormalized symplectic form on an extended phase space for $O(r^n)$ large gauge symmetries, providing explicit charge expressions and algebraic structure.

Findings

Derived sub$^n$-leading electric charges consistent with previous proposals.

Established a duality extension and computed the full charge algebra.

Revealed a tower of central extensions in the charge algebra.

Abstract

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.