Flat/AdS boundary conditions in three dimensional conformal gravity

TL;DR

This work analyzes asymptotic structures of three-dimensional gravity theories in a Chern-Simons formulation, focusing on pure gravity with flat boundary and conformal gravity with AdS and flat boundaries. It shows that flat boundaries produce the BMS3 algebra, while conformal gravity yields Virasoro⊕Virasoro with a $\hat{u}(1)_k$ current under AdS, and BMS3⊕$\hat{u}(1)_k$ under flat, with a Sugawara-like shift of central charges. Partial massless modes lead to a chiral Virasoro sector with a conformal-dimension-3/2 current, while Weyl symmetry introduces an additional current and further central-charge modifications. Representation analysis reveals unitarity constraints and potential null states, illustrating how bulk gauge symmetries shape the boundary spectrum and holographic interpretation.

Abstract

We present the asymptotic analysis of 3D conformal gravity as a SO(3,2) Chern-Simons gauge theory with Minkowskian (flat) and AdS boundary conditions. We further extend these boundary conditions to the case where the Weyl mode and the partial massless mode are allowed to fluctuate. The latter leads to loosing one copy of the Virasoro algebra and the former to a u(1) current extension of the asymptotic symmetry algebra and shifting the Virasoro central charge by one. We also give a pedagogical canonical and asymptotic analysis of 3D pure gravity as an ISO(2,1) Chern-Simons gauge theory with flat boundary conditions.