Universality and Non-Perturbative Definitions of 2D Quantum Gravity from Matrix Models

TL;DR

This paper explores the universal aspects of non-perturbative definitions of 2D quantum gravity via matrix models, comparing different approaches and highlighting the need for new physical input in certain cases.

Contribution

It introduces an alternative non-perturbative definition of matrix models that emphasizes the necessity of new physical input for connecting to 2D quantum gravity.

Findings

Universality holds for non-perturbative definitions of Hermitian matrix models.

Different procedures like quantum, stochastic, and stabilization are compared.

An alternative definition shows the need for additional physical input in $d=0$ models.

Abstract

The universality of the non-perturbative definition of Hermitian one-matrix models following the quantum, stochastic, or $d=1$-like stabilization is discussed in comparison with other procedures. We also present another alternative definition, which illustrates the need of new physical input for $d=0$ matrix models to make contact with 2D quantum gravity at the non-perturbative level.