Weyl-Gauging and Conformal Invariance
摘要
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.
引用
@article{arxiv.hep-th/9607110,
title = {Weyl-Gauging and Conformal Invariance},
author = {A. Iorio and L. O'Raifeartaigh and I. Sachs and C. Wiesendanger},
journal= {arXiv preprint arXiv:hep-th/9607110},
year = {2009}
}
备注
Extended version including discussion of arbitrary spin in any dimensions. References added