Ghost-Free, Finite, Fourth-Order $D=3$ Gravity

Canonical analysis of a recently proposed $\mathrm{\text{linear}}+\mathrm{\text{quadratic}}$ curvature gravity model in $D=3$ establishes its pure, irreducibly fourth derivative, quadratic curvature limit as both ghost-free and power-counting UV finite, thereby maximally violating standard folklore. This limit is representative of a generic class whose kinetic terms are conformally invariant in any dimension, but it is unique in simultaneously avoiding the transverse-traceless graviton ghosts plaguing $D>3$ quadratic actions as well as double pole propagators in its other variables. While the two-term model is also unitary, its additional mode’s second-derivative nature forfeits finiteness.