Conformal actions in any dimension
Abstract
In standard ddimensional conformal gauge theory, the volume element scales with weight d, so that a given form of the action is scale invariant only in a single dimension. However, the new biconformal gauging of the conformal group has a scale invariant volume form, permitting a single form of the action to be invariant for any value of d. We show that the simplest scale invariant action is linear in the curvatures, and the resulting field equations are satisfied in a torsionfree biconformal space if and only if the space is in 11 correspondence with a ddim scale invariant geometry in which the Weyl vector possesses a linear momentum dependence. Further, we display curvaturequadratic actions which are conformally invariant for every d.
 Publication:

19th Texas Symposium on Relativistic Astrophysics and Cosmology
 Pub Date:
 December 1998
 Bibcode:
 1998tx19.confE.134W