  We prove a no-go theorem for the construction of a Galilean boost invariant
and $z\neq2$ anisotropic scale invariant field theory with a finite dimensional
basis of fields. Two point correlators in such theories, we show, grow
unboundedly with spatial separation. Correlators of theories with an infinite
dimensional basis of fields, for example, labeled by a continuous parameter, do
not necessarily exhibit this bad behavior. Hence, such theories behave
effectively as if in one extra dimension. Embedding the symmetry algebra into
the conformal algebra of one higher dimension also reveals the existence of an
internal continuous parameter. Consideration of isometries shows that the
non-relativistic holographic picture assumes a canonical form, where the bulk
gravitational theory lives in a space-time with one extra dimension. This can
be contrasted with the original proposal by Balasubramanian and McGreevy, and
by Son, where the metric of a $d+2$ dimensional space-time is proposed to be
dual of a $d$ dimensional field theory. We provide explicit examples of
theories living at fixed point with anisotropic scaling exponent
$z=\frac{2\ell}{\ell+1}\,,\ell\in \mathbb{Z}$
