Conservation and Integrability in Lower-Dimensional Gravity

TL;DR

This work analyzes conservation and integrability of gravitational charges at infinity in two and three dimensions within Bondi gauge, allowing asymptotically locally AdS and flat spacetimes. By performing holographic renormalization of the action and the covariant symplectic structure, it obtains finite surface charges that are generically non-conserved, but can be rendered integrable through field-dependent redefinitions of the asymptotic symmetry parameters. In 2D dilaton gravity, the asymptotic symmetry algebra is the direct sum of three abelian algebras with a Heisenberg-type central extension, and a flat limit connects JT and CGHS models while preserving integrable charges. In 3D, the analysis yields integrable charges with a central extension that reproduces Brown-Henneaux in AdS_3 and the BMS_3 central extension in the flat limit, illustrating how open systems with fluctuating boundary data encode the infinity’s symmetry and flux structure across dimensions.

Abstract

We address the questions of conservation and integrability of the charges in two and three-dimensional gravity theories at infinity. The analysis is performed in a framework that allows us to treat simultaneously asymptotically locally AdS and asymptotically locally flat spacetimes. In two dimensions, we start from a general class of models that includes JT and CGHS dilaton gravity theories, while in three dimensions, we work in Einstein gravity. In both cases, we construct the phase space and renormalize the divergences arising in the symplectic structure through a holographic renormalization procedure. We show that the charge expressions are generically finite, not conserved but can be made integrable by a field-dependent redefinition of the asymptotic symmetry parameters.