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.
Deser
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Physics Department, Brandeis University, Waltham, Massachusetts 02454, USA. deser@brandeis.edu