Abstract:   Special limits of theories with higher time derivatives in Anti de Sitter space exhibit interesting features: they realize logarithmic representations of the conformal algebra and they possess a structure akin to gauge theory. These results can be obtained by a simple study of the scalar product of free fields.  This study shows that "critical" gravity in dimension larger than 3 is non-unitary, but that the spectrum of certain other higher derivative theories, such as the Flato-Fronsdal  singleton dipole theory, contains a unitary subsector. Unitarity of a high spin generalization of the Randall-Sundrum construction will be also discussed.