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

TL;DR

This paper classifies all unitary higher derivative gravity theories in 3D, analyzing their stability around flat and (A)dS spaces, and explores critical conditions in 4D at the Lagrangian level.

Contribution

It provides a complete classification of unitary higher derivative gravity theories in 3D and discusses criticality conditions in 4D.

Findings

Complete classification of unitary theories in 3D

Conditions for stability around flat and (A)dS backgrounds

Insights into criticality in 4D theories

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.