Expansion in Feynman graphs as simplicial string theory

We show that the series expansion of quantum field theory in the Feynman diagrams can be explicitly mapped on the partition function of the simplicial string theory – the theory describing embeddings of the 2D simplicial complexes into the space-time of the field theory. The summation over 2D geometries in this theory is obtained from the summation over the Feynman diagrams and the integration over the Schwinger parameters of the propagators. We discuss the meaning of the obtained relation and derive the 1D analog of the simplicial theory on the example of the free relativistic particle.