Conformal (super)gravities with several gravitons

Details Conformal (super)gravities with several gravitons Conformal (super)gravities with several gravitons

2002-01-04

arxiv.org/abs/hep-th/0201023v2

JHEP 0201 (2002) 035

Physics

High Energy Physics

High Energy Physics - Theory

19+1 pages, LaTeX. Reference added

Scientific paper

10.1088/1126-6708/2002/01/035

We construct consistent interacting gauge theories for M conformal massless spin-2 fields ("Weyl gravitons") with the following properties: (i) in the free limit, each field fulfills the equation ${\cal B}^{\mu \nu} = 0$, where ${\cal B}^{\mu \nu}$ is the linearized Bach tensor, (ii) the interactions contain no more than four derivatives, just as the free action and (iii) the internal metric for the Weyl gravitons is not positive definite. The interacting theories are obtained by gauging appropriate non-semi-simple extensions of the conformal algebra $so(4,2)$ with commutative, associative algebras of dimension M. By writing the action in terms of squares of supercurvatures, supersymmetrization is immediate and leads to consistent conformal supergravities with M interacting gravitons.

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