Quantization of the Gravitational Constant in Odd-Dimensional Gravity

It is pointed out that the action recently proposed by Bañados et al. for gravitation in odd dimensions higher (and lower) than four, provides a natural quantization for the gravitational constant. These theories possess no dimensionful parameters and hence they may be power counting renormalizable. Gravitation in dimensions greater than two is best described by the so-called Lovelock action [1]. This is a linear combination of the dimensional continuations to D dimensions of all the Euler classes of dimensions 2p < D [2,3]. The Lovelock lagrangian could be defined by the previous statement, but it can also be derived in three other seemingly independent ways: i) It is the most general invariant constructed out of the metric and curvature that yields second order covariant field equations [1]; ii) It is the most general local D-form invariant under tangent space rotations, constructed out of the vielbein, the spin connection and their exterior derivatives without using the Hodge-* dual [4]; iii) It is the most general Electronic address: [email protected]