Residual Weyl symmetry out of conformal geometry and its BRS structure

TL;DR

This paper explores the conformal geometry framework to isolate residual Weyl symmetry using a dressing field approach, connecting it with BRS algebra and providing explicit transformation laws and anomaly-related structures.

Contribution

It introduces a dressing field scheme that decouples inversion and Lorentz symmetries, revealing residual Weyl symmetry and linking it with BRS algebra and anomaly structures.

Findings

Decouples inversion and Lorentz symmetries to isolate Weyl symmetry

Provides explicit finite transformation laws under Weyl rescaling

Connects dressing field method with BRS algebra and Weyl anomaly

Abstract

The conformal structure of second order in $m$-dimensions together with the so-called (normal) conformal Cartan connection, is considered as a framework for gauge theories. The dressing field scheme presented in a previous work amounts to a decoupling of both the inversion and the Lorentz symmetries such that the residual gauge symmetry is the Weyl symmetry. On the one hand, it provides straightforwardly the Riemannian parametrization of the normal conformal Cartan connection and its curvature. On the other hand, it also provides the finite transformation laws under the Weyl rescaling of the various geometric objects involved. Subsequently, the dressing field method is shown to fit the BRS differential algebra treatment of infinitesimal gauge symmetry. The dressed ghost field encoding the residual Weyl symmetry is presented. The related so-called algebraic connection supplies relevant combinations found in the literature in the algebraic study of the Weyl anomaly.