Generally Covariant vs. Gauge Structure for Conformal Field Theories

TL;DR

This paper explores the gauge structure of conformal gravity, emphasizing that conformal transformations should be treated as gauge transformations affecting fields rather than spacetime points, and discusses the implications of this perspective.

Contribution

It introduces the natural lift of spacetime diffeomorphisms for conformal gravity and analyzes the equivalence between natural and gauge natural structures in the theory.

Findings

Conformal transformations are best understood as gauge transformations.

The natural and gauge natural structures in conformal gravity are physically equivalent.

Splitting the conformal group reveals special structural implications.

Abstract

We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must be introduced as gauge transformations (affecting fields but not spacetime point) and then discuss special structures implied by the splitting of the conformal group.