Weyl-Gauging and Conformal Invariance

Details Weyl-Gauging and Conformal Invariance Weyl-Gauging and Conformal Invariance

1996-07-14

arxiv.org/abs/hep-th/9607110v3

Nucl.Phys. B495 (1997) 433-450

Physics

High Energy Physics

High Energy Physics - Theory

Extended version including discussion of arbitrary spin in any dimensions. References added

Scientific paper

10.1016/S0550-3213(97)00190-9

Scale-invariant actions in arbitrary dimensions are investigated in curved space to clarify the relation between scale-, Weyl- and conformal invariance on the classical level. The global Weyl-group is gauged. Then the class of actions is determined for which Weyl-gauging may be replaced by a suitable coupling to the curvature (Ricci gauging). It is shown that this class is exactly the class of actions which are conformally invariant in flat space. The procedure yields a simple algebraic criterion for conformal invariance and produces the improved energy-momentum tensor in conformally invariant theories in a systematic way. It also provides a simple and fundamental connection between Weyl-anomalies and central extensions in two dimensions. In particular, the subset 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 invariance is constructed.

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