  There have been some speculations about the existence of critical unitary
O(N)-invariant scalar field theories in dimensions 4<d<6 and for large N. Using
the functional renormalization group equation, we show that in the lowest order
of the derivative expansion, and assuming that the anomalous dimension vanishes
for large $N$, the corresponding critical potentials are either unbounded from
below or singular for some finite value of the field.
