  We consider the four-point correlator of the stress tensor multiplet in
${\cal N}=4$ SYM in the limit of large central charge $c \sim N^2$. For finite
values of $g^2N$ single-trace intermediate operators arise at order $1/c$ and
this leads to specific poles in the Mellin representation of the correlator.
The sign of the residue at these poles is fixed by unitarity. We consider
solutions consistent with crossing symmetry and this pole structure. We show
that in a certain regime all solutions result in a negative contribution to the
anomalous dimension of twist four operators. The reason behind this is a
positivity property of Mack polynomials that leads to a positivity condition
for the Mellin amplitude. This positivity condition can also be proven by
assuming the correct Regge behaviour for the Mellin amplitude. For large $g^2N$
we recover a tower of solutions in one to one correspondence with local
interactions in a effective field theory in the $AdS$ bulk, with the
appropriate suppression factors, and with definite overall signs. These signs
agree with the signs that would follow from causality constraints on the
effective field theory. The positivity constraints arising from CFT for the
Mellin amplitude take a very similar form to the causality constraint for the
forward limit of the S-matrix.
