Localization and anomalous reference frames in gravity

TL;DR

This paper develops a gauge-invariant phase space framework for gravitational degrees of freedom along null rays, incorporating edge modes and Virasoro deformations to facilitate quantum gravity analysis.

Contribution

It introduces a novel construction of localized gauge-invariant observables on null segments using dressing time and edge modes, accounting for quantum anomalies.

Findings

Constructed gauge-invariant observables localized on null segments.

Identified Virasoro-type deformations in classical structures due to quantum anomalies.

Established a foundation for quantizing gravitational null ray segments with a quantum reference frame.

Abstract

In this work, we study the classical phase space for the gravitational degrees of freedom along a null ray. We construct gauge-invariant observables localized on a null ray segment that commute with those localized on the complement; thus, the phase space describes a genuine gravitational subsystem compatible with both locality and diffeomorphism invariance. Our construction employs 'dressing time' (a null time coordinate built from spin 0 gravitational degrees of freedom) as a dynamical reference frame. The existence of such a frame depends on the use of edge mode variables, which we argue are generally required to upgrade a local gauge-fixing condition to a global 'frame-fixing'. To analyze the effects of quantum diffeomorphism anomalies on these structures, we then establish an 'effective' classical description in which the Raychaudhuri equation, symplectic form, and edge mode variables all acquire Virasoro-type deformations. Within this framework, we identify three distinct diffeomorphism actions: reparametrizations (gauge transformations), reorientations (physical symmetries of the reference frame), and dressed reparametrizations. Each acquires its own central extension and plays a different crucial role in the effective theory. The resulting structures provide a foundation for quantizing gravitational null ray segments, including promoting dressing time to a genuine quantum reference frame.