A Complete Classification of Higher Derivative Gravity in 3D and Criticality in 4D

Abstract

We study the condition that the theory is unitary and stable in three-dimensional gravity with most general quadratic curvature, Lorentz-Chern-Simons and cosmological terms. We provide the complete classification of the unitary theories around flat Minkowski and (anti-)de Sitter spacetimes. The analysis is performed by examining the quadratic fluctuations around these classical vacua. We also discuss how to understand critical condition for four-dimensional theories at the Lagrangian level.

20 pages, v2: minor corrections, refs. added, v3: logic modified, v4: typos corrected

References in corpus (15)

• Massive Gravity in Three Dimensions
• Holographic c-theorems in arbitrary dimensions
• More on Massive 3D Gravity
• Critical Gravity in Four Dimensions
• Einstein Gravity from Conformal Gravity
• Ghost-free, finite, fourth order D=3 (alas) gravity
• Critical Points of D-Dimensional Extended Gravities
• Classification of Six Derivative Lagrangians of Gravity and Static Spherically Symmetric Solutions
• On the Generalized Massive Gravity in $Ad{S}_3$
• Modes of Log Gravity
• Renormalizability of Massive Gravity in Three Dimensions
• Erratum to `Instability in cosmological topologically massive gravity at the chiral point', arXiv:0805.2610
• Ghosts of Critical Gravity
• Canonical Structure of Higher Derivative Gravity in 3D
• (Curvature)^2-Terms for Supergravity in Three Dimension

Cited by in corpus (33)

• AdS and Lifshitz Black Holes in Conformal and Einstein-Weyl Gravities
• Higher Derivative Gravity and Conformal Gravity From Bimetric and Partially Massless Bimetric Theory
• Charged black hole with a scalar hair in (2+1) dimensions
• Ultraviolet Fixed Points in Conformal Gravity and General Quadratic Theories
• Hawking radiation and propagation of massive charged scalar field on a three-dimensional Gödel black hole
• BRST symmetry and $W$-algebra in higher derivative models
• Covariant Approach to the No-ghost Theorem in Massive Gravity
• Higher derivative couplings and massive supergravity in three dimensions
• Weyl-Invariant Higher Curvature Gravity Theories in n Dimensions
• Unitarity versus Renormalizability of Higher Derivative Gravity in 3D
• Massive N=2 Supergravity in Three Dimensions
• Counterterms, critical gravity and holography
• Signs and Stability in Higher-Derivative Gravity
• Noncritical Einstein-Weyl Gravity and the AdS/CFT Correspondence
• Unitarity Problems in 3$D$ Gravity Theories
• Higher-derivative massive actions from dimensional reduction
• Brane worlds in critical gravity
• New class of spin projection operators for 3D models
• Particle collisions near a three-dimensional warped AdS black hole
• New massless and massive infinite derivative gravity in three dimensions
• Critical Higher Order Gravities in Higher Dimensions
• Interesting features of a general class of higher derivative theories of quantum gravity
• Renormalization of Higher Derivative Quantum Gravity Coupled to a Scalar with Shift Symmetry
• Ghost-free infinite derivative gravity
• Stability of vacua in New Massive Gravity in different gauges
• Fermionic field perturbations of a three-dimensional Lifshitz black hole in conformal gravity
• Finite BRST Mapping in Higher Derivative Models
• Treating Ostrogradski instability for Gallilean invariant Chern Simon's model via \mathcal{PT} symmetry
• Decreasing entropy of dynamical black holes in critical gravity
• Embeddings of the "New Massive Gravity"
• Propagators in AdS for higher-derivative and nonlocal gravity: Heat kernel approach
• Causality Constraint on Noncritical Einstein-Weyl Gravity
• Coarse-graining of the Einstein-Hilbert Action rewritten by the Fisher information metric