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.
Highlights
Data. (2) Diffeomorphism invariance, meaning that the metric can only be determined up to generic coordinate transformations
We show that there is a choice, the “fundamental basis”, where the null boundary symmetry algebra is the Heisenberg⊕Diff(d − 2) algebra
We focus on the computations of the charges on a null hypersurface, see [35, 36] for earlier analysis of asymptotic symmetry analysis on AdS2
Summary
Our results for charges and symmetries are valid for AdS3, 3d flat space and dS3 cases This is physically expected because we are considering an expansion around the null surface r = 0, and our analysis is local and independent of the asymptotic and global properties of the solution. The structure constants of the algebra (3.34) and its 2d counterpart (2.24) are both v independent, while the charges are v dependent We expect this to be the case for all integrable Lie-algebras related to these algebras by a change of basis (see discussions of the section). Note that this is not the case for the algebra of the original symmetry generators (before coming to the integrable basis), (3.13) and (3.14) for 3d case and (2.9), for the 2d case; they involve derivatives w.r.t. v. The algebra of integrable part of charges obtained through the modified bracket method (see appendix C) would have v derivatives
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
