  We generalize Gopakumar's microscopic derivation of Witten diagrams in large
N free quantum field theory [1] to interacting theories in perturbative
expansion. For simplicity we consider a matrix scalar field with $\Phi^h$
interaction in d dimensions. Using Schwinger's proper time formulation and
organizing the sum over Feynman diagrams by the number of loops $\ell$, we show
that the two-point function in the massless case can be expressed as a sum over
boundary-to-boundary propagators of massive bulk scalars in $AdS_{d+1}$ with
masses determined by $\ell$. The two-point function of the massive theory has
the same structure given by a sum over boundary-to-boundary propagators but on
a geometry different than AdS. The coefficients in the sum contain information
on the putative string geometry dual to the interacting QFT. We also consider
the three-point function in the field theory and show that it can again be
given as an infinite sum, this time over the products of three bulk-to-boundary
propagators. The issue of divergences and renormalization is discussed in
detail.
  We also notice an intriguing similarity between field theory and string
amplitudes. In particular we observe that, in the large-N limit, embedding
function of string in the holographic direction corresponds to a continuum
limit of Schwinger parameters of Feynman diagrams in the limit where $\ell$
diverges. This provides an interpretation of the holographic dimension emerging
directly from field theory amplitudes.
