Symmetries at Null Boundaries: Two and Three Dimensional Gravity Cases

TL;DR

This paper analyzes the symmetry structures and charges near null boundaries in 2d and 3d gravity, revealing a rich algebraic structure and conditions for charge integrability without fixing boundary conditions.

Contribution

It provides a general analysis of null boundary symmetries in low-dimensional gravity without specific boundary conditions, identifying a fundamental algebraic basis and conditions for integrability.

Findings

Existence of infinitely many charge choices for integrability.

Null boundary symmetry algebra is Heisenberg+Diff(d-2) in a fundamental basis.

Results likely extend to higher dimensions without Bondi news.

Abstract

We carry out in full generality and without fixing specific boundary conditions, the symmetry and charge analysis near a generic null surface for two and three dimensional (2d and 3d) gravity theories. In 2d and 3d there are respectively two and three charges which are generic functions over the codimension one null surface. The integrability of charges and their algebra depend on the state-dependence of symmetry generators which is a priori not specified. We establish the existence of infinitely many choices that render the surface charges integrable. We show that there is a choice, the "fundamental basis", where the null boundary symmetry algebra is the Heisenberg+Diff(d-2) algebra. We expect this result to be true for d>3 when there is no Bondi news through the null surface.