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Conformal theories including conformal gravity as gauge theories on the hypercone

Par Arvidsson·Robert Marnelius
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Abstract

Conformal theories in a d dimensional spacetime may be expressed as manifestly conformal theories in a d+2 dimensional conformal space as first proposed by Dirac. The reduction to d dimensions goes via the d+1 dimensional hypercone in the conformal space. Here we give a rather extensive expose of such theories. We review and extend the theory of spinning conformal particles. We give a precise and geometrical formulation of manifestly conformal fields for which we give a consistent action principle. The requirement of invariance under special gauge transformations off the hypercone plays a fundamental role here. Maxwell's theory and linear conformal gravity are derived in the conformal space and are treated in detail. Finally, we propose a consistent coordinate invariant action principle in the conformal space and give an action that should correspond to conformal gravity.

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Par Arvidsson, Robert Marnelius. 2006-12-07. Conformal theories including conformal gravity as gauge theories on the hypercone. https://arxiv.org/abs/hep-th/0612060

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