Conformal actions in any dimension Original Research Article

Biconformal gauging of the conformal group gives a scale-invariant volume form, permitting a single form of the action to be invariant in any dimension. We display several 2n-dimensional scale-invariant polynomial actions and a dual action. We solve the field equations for the most general action linear in the curvatures for a minimal torsion geometry. In any dimension n > 2, the solution is foliated by equivalent n-dimensional Ricci-flat Riemannian space-times, and the full 2n-dimensional space is symplectic. Two fields defined entirely on the Riemannian submanifolds completely determine the solution: a metric eμα, and a symmetric tensor kμν.