Higher-dimensional gravity, propagating torsion and AdS gauge invariance

The most general theory of gravity in d dimensions which leads to second-order field equations for the metric has [(d - 1)/2] free parameters. It is shown that requiring the theory to have the maximum possible number of degrees of freedom, fixes these parameters in terms of the gravitational and the cosmological constants. In odd dimensions, the Lagrangian is a Chem-Simons form for the (A)dS or Poincare groups. In even dimensions, the action has a Born-Infeld-like form. Torsion may occur explicitly in the Lagrangian in the odd-parity sector and the torsional pieces respect local (A)dS symmetry for d = 4k - 1 only. These torsional Lagrangians are related to the Chern-Pontryagin characters for the (A)dS group. The additional coefficients in front of these new terms in the Lagrangian are shown to be quantized.