Conformal Field Theory in Conformal Space

TL;DR

This paper introduces a novel Lagrangian framework for conformal field theories using a local conformal space, enabling a gauge theory of conformal gravity coupled with matter and deriving gravity constraints automatically.

Contribution

It develops a new local conformal space approach for formulating conformal field theories, including conformal gravity and matter coupling, with automatic constraint derivation.

Findings

Established a gauge theory of conformal gravity in four dimensions.

Demonstrated automatic derivation of conformal gravity constraints.

Unified matter and gravity in a new conformal space framework.

Abstract

We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d+2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d=(1,3) and any standard matter coupled to it. An important feature is the automatic derivation of the conformal gravity constraints, which are necessary for the analysis of the matter systems.