Conformal actions in any dimension

Abstract

Biconformal gauging of the conformal group has a scale-invariant volume form, permitting a single form of the action to be invariant in any dimension. We display several 2n-dim 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-dim Ricci-flat Riemannian spacetimes, and the full 2n-dim space is symplectic. Two fields defined entirely on the Riemannian submanifolds completely determine the solution: a metric, and a symmetric tensor.

35 pages, now includes comparisons with other theories; one added reference

References in corpus (2)

• Gauge Theory Correlators from Non-Critical String Theory
• New Conformal Gauging and the Electromagnetic Theory of Weyl

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• Dynamical spacetime symmetry
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• Internal symmetry in Poincare gauge gravity