Poisson Structure of the Boundary Gravitons in 3D Gravity with Negative $\Lambda$

TL;DR

This paper analyzes the boundary structure of 3D gravity with negative cosmological constant using Hamiltonian formalism, revealing the Poisson structure of boundary gravitons and classifying boundary conditions.

Contribution

It provides a general framework for understanding boundary conditions and the Poisson structure of boundary gravitons in 3D gravity with negative .

Findings

Derived the Poisson structure of boundary gravitons.

Classified possible boundary conditions and boundary Hamiltonians.

Connected previous boundary conditions within a unified framework.

Abstract

We use the hamiltonian formalism to study the asymptotic structure of 3 dimensional gravity with a negative cosmological constant. We start by defining very general fall-off conditions for the canonical variables and study the implied poisson structure of the boundary gravitons. From the allowed differentiable gauge transformations, we can extract all the possible boundary conditions on the lagrange multipliers and the associated boundary hamiltonians. In the last section, we use this general framework to describe some of the previoussly known boundary conditions.