  We consider the statistical description of steady state fully developed
incompressible fluid turbulence at the inertial range of scales in any number
of spatial dimensions. We show that turbulence statistics is scale but not
conformally covariant, with the only possible exception being the direct
enstrophy cascade in two space dimensions. We argue that the same conclusions
hold for compressible non-relativistic turbulence as well as for relativistic
turbulence. We discuss the modification of our conclusions in the presence of
vacuum expectation values of negative dimension operators. We consider the
issue of non-locality of the stress-energy tensor of inertial range turbulence
field theory.
