Minimal Massive 3D Gravity

TL;DR

MMG introduces a curvature-squared tensor $J_{1}$ into the 3D gravity equations, yielding a single propagating bulk graviton while achieving positive bulk energy and positive AdS$_3$ boundary central charges. Through a CS-like formulation with auxiliary fields and a simple $L_{MMG}=L_{TMG}+rac{lpha}{2}e\u22c02h imes h$ term, the authors derive an MMG equation that cannot be obtained from a metric-only action but remains dynamically minimal, with a detailed Hamiltonian analysis confirming one local degree of freedom. The linearized theory around AdS$_3$ identifies a massive spin-2 mode with no-tachyon/no-ghost conditions, and the boundary analysis yields central charges $c_ =rac{3ll}{2G_3}(rac{}{}+rac{1}{ll}+lpha C)$, which can be made positive in three parameter regions. Together, these results show that MMG resolves the bulk-vs-boundary unitarity clash characteristic of TMG, while preserving the minimal bulk structure and suggesting a unitary AdS$_3$/CFT$_2$ holographic interpretation.

Abstract

We present an alternative to Topologically Massive Gravity (TMG) with the same "minimal" bulk properties; i.e. a single local degree of freedom that is realized as a massive graviton in linearization about an anti-de Sitter (AdS) vacuum. However, in contrast to TMG, the new "minimal massive gravity" has both a positive energy graviton and positive central charges for the asymptotic AdS-boundary conformal algebra.