Most general AdS_3 boundary conditions

TL;DR

This work identifies the loosest possible AdS3 boundary conditions in 3D Einstein gravity, revealing a boundary data set of twelve functions (six charges and six chemical potentials) that alter the standard Fefferman–Graham expansion. In the Chern–Simons formulation, the boundary data yield a canonical asymptotic symmetry algebra consisting of two copies of affine $\mathfrak{sl}(2)_k$, with $k=\ell/(4G_N)$; this structure persists in the metric formulation through a generalized FG gauge. The authors show consistency through finite, integrable, conserved charges and a well-defined variational principle, and demonstrate that many known AdS3 bc's (Brown–Henneaux, Troessaert, Heisenberg, etc.) arise as special cases within this unifying framework. They interpret the dual theory as a non-chiral $\mathfrak{sl}(2)_k$ WZW model and discuss holographic implications, loopholes to generality, and avenues for generalizations to other dimensions and higher-spin contexts.

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.