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A Complete Classification of Higher Derivative Gravity in 3D and Criticality in 4D
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.Comment: 20 pages, v2: minor corrections, refs. added, v3: logic modified, v4:
typos correcte