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.