Conformal Fields in Higher Dimensions

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 all gauge theories invariant under so(2,d), both integral and half-integral spins. A similar analysis is carried out for the algebras of so*(2n). We study new unitary modules of the conformal algebra in d > 4, that have no analogue for d < 4 as they cannot be obtained by "squaring" singletons. This suggests 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.