Loops versus Matrices - The nonperturbative aspects of noncritical string

TL;DR

This paper compares loop equations and matrix models in non-critical string theory, revealing that matrix models can assign a definite chemical potential to instantons, unlike loop equations, which suggests limitations in nonperturbative formulations using only closed strings.

Contribution

It demonstrates the differing capabilities of loop equations and matrix models in capturing nonperturbative effects, highlighting the unique ability of matrix models to assign definite instanton chemical potentials.

Findings

Matrix models can universally yield a definite instanton chemical potential.

Loop equations cannot assign a definite chemical potential to instantons.

Implication that nonperturbative string theory may require open string effects.

Abstract

The nonperturbative aspects of string theory are explored for non-critical string in two distinct formulations: loop equations and matrix models. The effects corresponding to D-brane in these formulations are especially investigated in detail. It is shown that matrix models can universally yield a definite value of the chemical potential for an instanton while loop equations can not. This implies that string theory may not be nonperturbatively formulated solely in terms of closed strings.