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Conformal Fields in Higher Dimensions

S. Ferrara·C. Fronsdal
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Abstract

We generalize, to any space-time dimension, the unitarity bounds of highest weight UIR's of the conformal groups with Lie algebras $so(2,d)$. We classify gauge theories invariant under $so(2,d)$, both integral and half-integral spins. A similar analysis is carried out for the algebras $so^*(2n)$. We study new unitary modules of the conformal algebra in $d>4$, that have no analogue for $d\leq 4$ as they cannot be obtained by "squaring" singletons. This may suggest the interpretation of higher dimensional non-trivial conformal field theories as theories of "tensionless" $p$-branes of which tensionless strings in $d=6$ are just particular examples.

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S. Ferrara, C. Fronsdal. 2000-06-09. Conformal Fields in Higher Dimensions. https://arxiv.org/abs/hep-th/0006009

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