More on Massive 3D Gravity

TL;DR

The paper analyzes three-dimensional New Massive Gravity with a cosmological term, focusing on static solutions, black holes, domain walls, and unitarity in (A)dS vacua. By deriving a reduced energy functional and exploring domain-wall and KK sectors, it uncovers a novel class of λ=-1 AdS black holes and extremal near-horizon geometries, alongside a detailed linearization and unitarity study that reveals tensions between bulk unitary gravitons and boundary central charges on AdS. Special points λ=3 and λ=-1 exhibit unique spectra: Proca-like spin-1 modes in AdS at λ=3 and a partially massless mode due to gauge enhancement at λ=-1. The work highlights fundamental bulk/boundary consistency constraints in CNMG and points to possible chiral or supersymmetric resolutions and lower-dimensional reductions as fruitful directions for further research.

Abstract

We explore the space of static solutions of the recently discovered three-dimensional `New Massive Gravity' (NMG), allowing for either sign of the Einstein-Hilbert term and a cosmological term parametrized by a dimensionless constant $λ$. For $λ=-1$ we find black hole solutions asymptotic (but not isometric) to the unique (anti) de Sitter vacuum, including extremal black holes that interpolate between this vacuum and (a)dS$_2 \times S^1$. We also investigate unitarity of linearized NMG in (a)dS vacua. We find unitary theories for some dS vacua, but (bulk) unitarity in adS implies negative central charge of the dual CFT, except for $λ=3$ where the central charge vanishes and the bulk gravitons are replaced by `massive photons'. A similar phenomenon is found in the massless limit of NMG, for which the linearized equations become equivalent to Maxwell's equations.