$2d$ gravity and matrix models. I. $2d$ gravity

TL;DR

This paper reviews various approaches to two-dimensional gravity, focusing on matrix models and their connections with Liouville and topological theories, highlighting their interrelations and providing illustrative examples.

Contribution

It offers a comprehensive overview of 2D gravity approaches, emphasizing the role and interrelations of matrix models with other methods.

Findings

Matrix models are central to understanding 2D gravity.

Connections between matrix models, Liouville, and topological theories are elucidated.

Examples illustrate the relationships among different approaches.

Abstract

Some approaches to $2d$ gravity developed for the last years are reviewed. They are physical (Liouville) gravity, topological theories and matrix models. A special attention is paid to matrix models and their interrelations with different approaches. Almost all technical details are omitted, but examples are presented.