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The conformal structure of second order in $m$-dimensions together with theso-called (normal) conformal Cartan connection, is considered as a frameworkfor gauge theories. The dressing field scheme presented in a previous workamounts to a decoupling of both the inversion and the Lorentz symmetries suchthat the residual gauge symmetry is the Weyl symmetry. On the one hand, itprovides straightforwardly the Riemannian parametrization of the normalconformal Cartan connection and its curvature. On the other hand, it alsoprovides the finite transformation laws under the Weyl rescaling of the variousgeometric objects involved. Subsequently, the dressing field method is shown tofit the BRS differential algebra treatment of infinitesimal gauge symmetry. Thedressed ghost field encoding the residual Weyl symmetry is presented. Therelated so-called algebraic connection supplies relevant combinations found inthe literature in the algebraic study of the Weyl anomaly.

Residual Weyl symmetry out of conformal geometry and its BRS structure