On the Nonperturbative Consistency of $d=2$ String Theory

TL;DR

This paper argues that despite many matrix models matching perturbative $d=2$ string theory, none provide a consistent nonperturbative formulation due to causality constraints.

Contribution

It critically examines existing $d=1$ matrix models and demonstrates their failure to define a nonperturbative $d=2$ string theory.

Findings

Many matrix models reproduce perturbative results

Existing models lack nonperturbative consistency

Causality constraints prevent a complete nonperturbative definition

Abstract

An infinite number of distinct $d=1$ matrix models reproduce the perturbation theory of $d=2$ string theory. Due to constraints of causality, however, we argue that none of the existing constructions gives a consistent nonperturbative definition of the $d=2$ string.