Conservation and Integrability in Lower-Dimensional Gravity

TL;DR

This paper investigates the conservation and integrability of charges in 2D and 3D gravity theories, employing holographic renormalization to handle divergences and redefining symmetry parameters to achieve integrability.

Contribution

It provides a unified framework for analyzing charges in asymptotically AdS and flat spacetimes across different dimensions, including explicit models like JT and CGHS.

Findings

Charges are generally finite but not conserved.

Charges can be made integrable via field-dependent redefinitions.

The framework applies to both asymptotically AdS and flat spacetimes.

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.