Symmetries at Null Boundaries: 3-dimensional Einstein gravity

Abstract

Gauge transformations are usually viewed as redundancies in the description of gauge theories and the physical observables must be gauge invariant. This should be revisited in presence of boundaries where a part of gauge transformations to which there are non vanishing surface charges associated, can become physical "non proper" gauge transformations. One can use these surface charges to label different points of the solution phase space. Here we consider the Einstein gravity in presence of a given null boundary. We construct the maximal solution-phase space, find its symmetries and calculate the associated surface charges. Surface charges and their algebra depend on the slicing in solution phase space. We discuss the implications of the change of slicing in different aspects of solution phase space, from integrability to algebra of surface charges.