  We continue with the program of hep-th/0308184 to implement open-closed
string duality on free gauge field theory (in the large $N$ limit). In this
paper we consider correlators such as $\la \prod_{i=1}^n
\Tr\Phi^{J_i}(x_i)\ra$. The Schwinger parametrisation of this $n$-point
function exhibits a partial gluing up into a set of basic skeleton graphs. We
argue that the moduli space of the planar skeleton graphs is exactly the same
as the moduli space of genus zero Riemann surfaces with $n$ holes. In other
words, we can explicitly rewrite the $n$-point (planar) free field correlator
as an integral over the moduli space of a sphere with $n$ holes. A preliminary
study of the integrand also indicates compatibility with a string theory on
$AdS$. The details of our argument are quite insensitive to the specific form
of the operators and generalise to diagrams of higher genus as well. We take
this as evidence of the field theory's ability to reorganise itself into a
string theory.
