Bulk and Boundary Unitary Gravity in 3D: MMG${}_2$

Abstract

We construct a massive spin-2 theory in 2+1 dimensions that is immune to the bulk-boundary unitarity conflict in anti-de Sitter space and hence amenable to holography. The theory is an extension of Topologically Massive Gravity, just like the recently found Minimal Massive Gravity (MMG), but it has two massive helicity modes instead of a single one. The theory admits all the solutions of TMG with a redefined topological parameter. We calculate the Shapiro time-delay and show that flat-space (local) causality is not violated. We show that there is an interesting relation between the theory we present here (which we call MMG${}_2$), MMG and the earlier New Massive Gravity (NMG): Namely, field equations of these theories are non-trivially related. We study the bulk excitations and boundary charges of the conformal field theory that could be dual to gravity. We also find the chiral gravity limit for which one of the massive modes becomes massless. The virtue of the model is that one does not have to go to the chiral limit to achieve unitarity in the bulk and on the boundary and the log-terms that appear in the chiral limit and cause instability do not exist in the generic theory.

arXiv comment6 pages, Causality discussion and related references are added, matches the published version

References in corpus (17)

• Massive Gravity in Three Dimensions
• Energy in Generic Higher Curvature Gravity Theories
• Chiral Gravity in Three Dimensions
• Instability in cosmological topologically massive gravity at the chiral point
• On the new massive gravity and AdS/CFT
• Critical Points of D-Dimensional Extended Gravities
• Born-Infeld extension of new massive gravity
• Minimal Massive 3D Gravity
• Energy in Topologically Massive Gravity
• Classification of solutions in topologically massive gravity
• Mass and angular momentum of asymptotically AdS or flat solutions in the topologically massive gravity
• On the Generalized Massive Gravity in $Ad{S}_3$
• Matter coupling in 3D "Minimal Massive Gravity"
• More on New Massive Gravity: Exact Solutions
• Some exact solutions of all f(Ricci) theories in three dimensions
• Minimal Massive Gravity: Conserved Charges, Excitations and the Chiral Gravity Limit
• On 3D Minimal Massive Gravity

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• On the Generalized Minimal Massive Gravity
• Causality in 3D Massive Gravity Theories
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• Bachian Gravity in Three Dimensions
• Gravity Waves in Three Dimensions
• Unitarity Problems in 3$D$ Gravity Theories
• Kundt solutions of Minimal Massive 3D Gravity
• Homogeneous Solutions of Minimal Massive 3D Gravity
• Holographically Viable Extensions of Topologically Massive and Minimal Massive Gravity?
• Holographic Entanglement Entropy in $T\bar{T}$-deformed CFTs
• Circularly symmetric solutions of Minimal Massive Gravity at its merger point
• Evanescent gravitons in Warped Anti-de Sitter space
• Exotic Massive Gravity: Causality and a Birkhoff-like Theorem
• Hairy Black holes in General Minimal Massive Gravity
• A model of non-minimally coupled gravitation and electromagnetism in (1+2) dimensions
• A New Geometric Flow on 3-Manifolds: the $K$-Flow