All Bulk and Boundary Unitary Cubic Curvature Theories in Three Dimensions

Abstract

We construct all the bulk and boundary unitary cubic curvature parity invariant gravity theories in three dimensions in (anti)-de Sitter spaces. For bulk unitarity, our construction is based on the principle that the free theory of the cubic curvature theory reduces to one of the three known unitary theories which are the cosmological Einstein-Hilbert theory, the quadratic theory of the scalar curvature or the new massive gravity (NMG). Bulk and boundary unitarity in NMG is in conflict; therefore, cubic theories that are unitary both in the bulk and on the boundary have free theories that reduce to the other two alternatives. We also study the unitarity of the Born-Infeld extensions of NMG to all orders in curvature.

arXiv comment18 pages, clarifying remarks added, version to appear in Phys. Rev. D

References in corpus (25)

• Black Hole Entropy is Noether Charge
• Massive Gravity in Three Dimensions
• Energy in Generic Higher Curvature Gravity Theories
• More on Massive 3D Gravity
• Partial Masslessness of Higher Spins in (A)dS
• The Asymptotic Safety Scenario in Quantum Gravity -- An Introduction
• Microscopic Black Hole Entropy in Theories with Higher Derivatives
• Diffeomorphisms and Holographic Anomalies
• A field-theory motivated approach to symbolic computer algebra
• Ghost-free, finite, fourth order D=3 (alas) gravity
• On the new massive gravity and AdS/CFT
• Born-Infeld extension of new massive gravity
• On Unitarity of Massive Gravity in Three Dimensions
• Statistical Entropy of BTZ Black Hole in Higher Curvature Gravity
• Non-Trivial Vacua in Higher-Derivative Gravitation
• New massive gravity, extended
• Massive Higher Derivative Gravity in D-dimensional Anti-de Sitter Spacetimes
• Tractors, Mass and Weyl Invariance
• c-functions in the Born-Infeld extended New Massive Gravity
• Unitarity analysis of general Born-Infeld gravity theories
• AdS Black Hole Solutions in the Extended New Massive Gravity
• Canonical Structure of Higher Derivative Gravity in 3D
• Charged Black Holes in New Massive Gravity
• Born-Infeld-Horava gravity
• On Born-Infeld Gravity in Three Dimensions

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• All unitary cubic curvature gravities in D dimensions
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• AdS-plane wave and pp-wave solutions of generic gravity theories
• Some exact solutions of all f(Ricci) theories in three dimensions
• Conserved Charges in Extended Theories of Gravity
• Weyl-Invariant Higher Curvature Gravity Theories in n Dimensions
• Particle Content of Quadratic and $f(R_{\mu \nu \sigma \rho })$ Theories in $(A)dS$
• Born-Infeld Gravity with a Massless Graviton in Four Dimensions
• Born-Infeld Gravity with a Unique Vacuum and a Massless Graviton
• Holographic c-theorem and Born-Infeld Gravity Theories
• Bachian Gravity in Three Dimensions
• Three Dimensional Modified Gravities as Holographic Limits of Lancsoz-Lovelock Theories
• Spectra, vacua and the unitarity of Lovelock gravity in D-dimensional AdS spacetimes
• Unitarity Problems in 3$D$ Gravity Theories
• Type N Spacetimes as Solutions of Extended New Massive Gravity
• Unitarity of Weyl-Invariant New Massive Gravity and Generation of Graviton Mass via Symmetry Breaking
• A Wald-like Formula for Energy
• 3D Lovelock Gravity and the Holographic c-Theorem
• Nonlocal Massive Gravity from Einstein Gravity
• Holographic anomaly in 3d f(Ric) gravity
• Instability of BTZ black holes in parity-even massive gravity
• Born-Infeld Gravity Revisited
• Spinor coupling to the weak Poincare gauge theory of gravity in three dimensions
• Aspects of three-dimensional higher-curvature gravities