  Interesting theories with short range interactions include QCD in the
hadronic phase and cold atom systems. The scattering length in two-to-two
elastic scattering process captures the most elementary features of the
interactions, such as whether they are attractive or repulsive. However, even
this basic quantity is notoriously difficult to compute from first principles
in strongly coupled theories. We present a method to compute the two-to-two
amplitudes and the scattering length using the holographic duality. Our method
is based on the identification of the residues of Green's functions in the
gravity dual with the amplitudes in the field theory. To illustrate the method
we compute a contribution to the scattering length in a hard wall model with a
quartic potential and find a constraint on the scaling dimension of a scalar
operator $\Delta > d/4$. For $d< 4$ this is more stringent than the unitarity
constraint and may be applicable to an extended family of large-$N$ theories
with a discrete spectrum of massive states. We also argue that for scalar
potentials with polynomial terms of order $K$, a constraint more restrictive
than the unitarity bound will appear for $d<2K/(K-2)$.
