WEYL GAUGING AND CONFORMAL-INVARIANCE

Scale-invariant actions in arbitrary dimensions rue investigated in cu rved space to clarify the relation between scale, Weyl and conformal i nvariance on the classical level. The global Weyl group is gauged. The n the class of actions is determined for which Weyl gauging may be rep laced by a suitable coupling to the curvature (Ricci gauging). It is s hown that this class is exactly the class of actions which are conform ally invariant in flat space. The procedure yields a simple algebraic criterion for conformal invariance and produces the improved energy-mo mentum tensor in conformally invariant theories in a systematic way. I t also provides a simple and fundamental connection between Weyl anoma lies and central extensions in two dimensions. In particular, the subs et of scale-invariant Lagrangians for fields of arbitrary spin, in any dimension, which are conformally invariant is given. An example of a quadratic action for which scale invariance does not imply conformal i nvariance is constructed. (C) 1997 Elsevier Science B.V.