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VOLUME 81 (2005) | ISSUE 8 | PAGE 445
Simplicial vs. continuum string theory and loop equations
PACS: 11.10.-z, 11.15.Bt, 11.25.Tq
Abstract
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.