Ghost-Free, Finite, Fourth-Order D 1⁄4 3 Gravity

S. Deser* Physics Department, Brandeis University, Waltham Massachusetts 02454, USA and Lauritsen Laboratory, California Institute of Technology, Pasadena California 91125, USA (Received 28 April 2009; published 2 September 2009) Canonical analysis of a recently proposed linearþ quadratic curvature gravity model in D 1⁄4 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.