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

Canonical analysis of a recently proposed linear+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.