Other
Scientific paper
May 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985phrvd..31.2497b&link_type=abstract
Physical Review D (Particles and Fields), Volume 31, Issue 10, 15 May 1985, pp.2497-2502
Other
Supergravity, Other Internal And Higher Symmetries
Scientific paper
The possibility of unitarizing the conformal supergravity of Kaku, Townsend, and van Nieuwenhuizen is investigated by examining the representation content of its linearized equations. Conformal (Weyl) gravitons are seen to correspond to a pair of helicity-conjugate, irreducible, and nonunitary representations of so(4,2). The solutions of the linearized gravitino field equation are seen to carry both unitary and nonunitary representations of so(4,2). The linearized constraint equation of Kaku et al., however, removes the unitary content from the gravitino field equation. The solution space of the linearized constraint and field equations of conformal supergravity is seen to carry a direct sum of two nonunitary and irreducible representations of the superalgebra su(2,2/1). These results imply that current models of conformal supergravity cannot be unitarized without breaking both su(2,2/1) and so(4,2) symmetries. A suggestion as to how one might construct a unitary model of conformal supergravity is made.
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