Gravitational dressing, soft charges, and perturbative gravitational splitting

TL;DR

The paper tackles the challenge of locality in gauge theories and gravity by constructing gauge-invariant dressed operators that carry long-range fields, and by analyzing the associated soft charges. It shows that, perturbatively, the asymptotic observables (soft charges) are largely decoupled from the detailed interior charge or matter distributions and depend mainly on total charges and chosen dressings, enabling a notion of electromagnetic and gravitational splittings as Hilbert-space embeddings. These results yield a framework for localized quantum information (gravitational and electromagnetic qubits) within gauge theories, while highlighting limitations in using soft hair to resolve black-hole information puzzles in the perturbative regime. The work thus provides a perturbative, dressing-based approach to subsystems in gauge theories and gravity and points toward a systematic way to define gravitational splittings and associated observables, with potential implications for locality and unitarity in quantum gravity.

Abstract

In gauge theories and gravity, field variables are generally not gauge-invariant observables, but such observables may be constructed by "dressing" these or more general operators. Dressed operators create particles, together with their gauge or gravitational fields which typically extend to infinity. This raises an important question of how well quantum information can be localized; one version of this is the question of whether soft charges fully characterize a given localized charge or matter distribution. This paper finds expressions for the non-trivial soft charges of such dressed operators. However, a large amount of flexibility in the dressing indicates that the soft charges, and other asymptotic observables, are not inherently correlated with details of the charge or matter distribution. Instead, these asymptotic observables can be changed by adding a general radiative (source-free) field configuration to the original one. A dressing can be chosen, perturbatively, so that the asymptotic observables are independent of details of the distribution, besides its total electric or Poincaré charges. This provides an approach to describing localization of information in gauge theories or gravity, and thus subsystems, that avoids problems associated with nonlocality of operator subalgebras. Specifically, this construction suggests the notions of electromagnetic or gravitational splittings, which involve networks of Hilbert space embeddings in which the charges play an important role.