Covariant theory of asymptotic symmetries, conservation laws and central charges

TL;DR

This paper establishes a covariant framework linking asymptotic symmetries, conserved charges, and central extensions in gauge theories, providing explicit formulas and conditions for finiteness and algebraic structure, with applications to fundamental theories.

Contribution

It introduces a universal covariant formula for asymptotic conserved forms and central charges, connecting asymptotic symmetries with conserved quantities in gauge theories.

Findings

Derived a bijective correspondence between asymptotic reducibility parameters and conserved forms.

Provided explicit formulas for central charges as 2-cocycles.

Applied the framework to electrodynamics, Yang-Mills, and Einstein gravity.

Abstract

Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between equivalence classes of asymptotic reducibility parameters and asymptotically conserved n-2 forms in the context of Lagrangian gauge theories. The asymptotic reducibility parameters can be interpreted as asymptotic Killing vector fields of the background, with asymptotic behaviour determined by a new dynamical condition. A universal formula for asymptotically conserved n-2 forms in terms of the reducibility parameters is derived. Sufficient conditions for finiteness of the charges built out of the asymptotically conserved n-2 forms and for the existence of a Lie algebra g among equivalence classes of asymptotic reducibility parameters are given. The representation of g in terms of the charges may be centrally extended. An explicit and covariant formula for the central charges is constructed. They are shown to be 2-cocycles on the Lie algebra g. The general considerations and formulas are applied to electrodynamics, Yang-Mills theory and Einstein gravity.