Simplicial vs. Continuum String Theory and Loop Equations

TL;DR

This paper establishes a connection between loop equations in scalar matrix field theory and simplicial string theory, providing evidence for an equivalence with continuum string theory in describing embeddings of two-dimensional surfaces into space-time.

Contribution

It derives loop equations and demonstrates their solutions relate to simplicial string theory, supporting the equivalence with continuum string theory.

Findings

Loop equations can be solved using simplicial string theory.

Evidence supports the equivalence between simplicial and continuum string theories.

Partition functions of both theories are shown to be related.

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.