# Generalized asymptotics for gauge fields

## TL;DR

This paper investigates the boundary conditions and asymptotic behaviors of gauge fields, including gravity, at infinity, highlighting non-antipodal symmetric solutions and their implications for soft charge conservation and gauge degrees of freedom.

## Contribution

It introduces analysis of non-symmetric boundary conditions for gauge theories, providing explicit solutions and bounds, and discusses their impact on soft charges and gauge invariants.

## Key findings

- Explicit solutions for non-symmetric initial data are derived.
- Bounds on asymptotic behavior of solutions are established.
- Objections based on symplectic form are addressed, showing solutions can be superselected.

## Abstract

An interesting question is to characterize the general class of allowed boundary conditions for gauge theories, including gravity, at spatial and null infinity. This has played a role in discussions of soft charges, where antipodal symmetry has typically been assumed. However, the existence of electric and gravitational line operators, arising from gauge-invariant dressed observables, for example associated to axial or Fefferman-Graham like gauges, indicates the existence of non-antipodally symmetric initial data. This note studies aspects of the solutions corresponding to such non-symmetric initial data. The explicit evolution can be found, via a Green function, and bounds can be given on the asymptotic behavior of such solutions, evading arguments for singular behavior. Likewise, objections to such solutions based on infinite symplectic form are also avoided, although these solutions may be superselected. Soft charge conservation laws, and their modification, are briefly examined for such solutions. This discussion strengthens (though is not necessary for) arguments that soft charges characterize gauge field degrees of freedom, but not necessarily the degrees of freedom associated to the matter sourcing the field.