  We present two examples of non-trivial field theories which are scale
invariant, but not conformally invariant. This is done by placing certain field
theories, which are conformally invariant in flat space, onto curved
backgrounds of a specific type. We define this using the AdS/CFT
correspondence, which relates the physics of gravity in asymptotically Anti-de
Sitter (AdS) spacetimes to that of a conformal field theory (CFT) in one
dimension fewer. The AdS rotating (Kerr) black holes in five and seven
dimensions provide us with the examples, since by the correspondence we are
able to define and compute the action and stress tensor of four and six
dimensional field theories residing on rotating Einstein universes, using the
``boundary counterterm'' method. The rotation breaks conformal but not scale
invariance. The AdS/CFT framework is therefore a natural arena for generating
such examples of non-trivial scale invariant theories which are not conformally
invariant.
