Conformal actions in any dimension

Biconformal gauging of the conformal group gives a scale-invariant volume f orm, permitting a single form of the action to be invariant in any dimensio n. We display several 2n-dimensional scale-invariant polynomial actions and a dual action. We solve the field equations for the most general action li near in the curvatures for a minimal torsion geometry. In any dimension n > 2, the solution is foliated by equivalent n-dimensional Ricci-flat Riemann ian space-times, and the full 2a-dimensional space is symplectic. Two field s defined entirely on the Riemannian submanifolds completely determine the solution: a metric e(mu)(a), and a symmetric tensor k(mu nu). (C) 1999 Else vier Science B.V. All rights reserved.