Most general AdS_3 boundary conditions

TL;DR

This paper explores the most comprehensive set of boundary conditions for AdS_3 in Einstein gravity, revealing a rich asymptotic symmetry algebra of two sl(2)_k current algebras with specific levels.

Contribution

It introduces the most general asymptotic boundary conditions in AdS_3 gravity, expanding the known boundary dynamics and symmetry structures.

Findings

The metric includes twelve independent functions, with six as chemical potentials and six as boundary charges.

The asymptotic symmetry algebra is composed of two sl(2)_k current algebras.

The levels of these current algebras are explicitly given by k=l/(4G_N).

Abstract

We consider the most general asymptotically anti-de Sitter boundary conditions in three-dimensional Einstein gravity with negative cosmological constant. The metric contains in total twelve independent functions, six of which are interpreted as chemical potentials (or non-normalizable fluctuations) and the other half as canonical boundary charges (or normalizable fluctuations). Their presence modifies the usual Fefferman-Graham expansion. The asymptotic symmetry algebra consists of two sl(2)_k current algebras, the levels of which are given by k=l/(4G_N), where l is the AdS radius and G_N the three-dimensional Newton constant.