Simplicial vs. continuum string theory and loop equations

We derive loop equations in a scalar matrix field theory. We discuss their solutions in terms of simplicial string theory – the theory describing embeddings of two-dimensional simplicial complexes into the space-time of the matrix field theory. This relation between the loop equations and the simplicial string theory gives further arguments that favor one of the statements of the paper hep-th/0407018. The statement is that there is an equivalence between the partition function of the simplicial string theory and the functional integral in a continuum string theory – the theory describing embeddings of smooth two-dimensional world-sheets into the space-time of the matrix field theory in question.