1206.4362 (Sofiane Faci)

From Weyl invariance to SO(2,4) invariance    [PDF]

Sofiane Faci

The present work deals with two different but related notions of conformal transformations: Weyl rescaling and the restricted conformal group SO(2,4) transformations. It is not well known but when a Weyl invariant field theory is restricted into Minkowski space, the Weyl invariance is lost but a residual conformal symmetry is preserved, it is the invariance under the SO(2,4) group. This result, due to Zumino, is important since it provides the explicit link between a Weyl and SO(2,4) invariant theories and thus allows to reduce SO(2,4) transformation calculations into Weyl rescaling calculations, much easier. The present work extends Zumino's result to an arbitrary conformally flat space (CFS). The demonstration is based on the structure transport from Minkowski space into a CFS and on an important feature of the CFSs: each isometry group of a CFS is a subgroup of the SO(2,4) group.

View original: http://arxiv.org/abs/1206.4362