Conformal Fields in Higher Dimensions

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 $s{o}^{\ast }(2n)$. We study new unitary modules of the conformal algebra in $d>4$, that have no analogue for $d\le 4$ 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.

26 pages, few comments added, new references included, typos corrected

References in corpus (1)

• How massless are massless fields in $Ad{S}_d$

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