Flat/AdS boundary conditions in three dimensional conformal gravity

TL;DR

This paper analyzes the asymptotic structure of three-dimensional conformal gravity with flat and AdS boundary conditions, revealing how boundary fluctuations affect the symmetry algebra and central charge.

Contribution

It extends boundary conditions in 3D conformal gravity to include Weyl and partial massless modes, showing their impact on the asymptotic symmetry algebra.

Findings

Weyl mode fluctuations lead to a u(1) current extension.

Partial massless mode fluctuations reduce Virasoro symmetry.

Central charge shifts by one due to boundary mode fluctuations.

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.