  Globally conformal invariant quantum field theories in a D-dimensional
space-time (D even) have rational correlation functions and admit an infinite
number of conserved (symmetric traceless) tensor currents. In a theory of a
scalar field of dimension D-2 they were demonstrated to be generated by bilocal
normal products of free massless scalar fields with an O(N), U(N), or Sp(2N)
(global) gauge symmetry [BNRT].
  Recently, conformal field theories "with higher spin symmetry" were
considered for D=3 in [MZ] where a similar result was obtained (exploiting
earlier study of CFT correlators). We suggest that the proper generalization of
the notion of a 2D chiral algebra to arbitrary (even or odd) dimension is
precisely a CFT with an infinite series of conserved currents. We shall recast
and complement (part of) the argument of Maldacena and Zhiboedov into the
framework of our earlier work. We extend to D=4 the auxiliary Weyl-spinor
formalism developed in [GPY] for D=3. The free field construction only follows
for D>3 under additional assumptions about the operator product algebra. In
particular, the problem of whether a rational CFT in 4D Minkowski space is
necessarily trivial remains open.
