Matrix Models

TL;DR

This paper reviews various matrix models, especially IKKT and BFSS, highlighting their origins from Yang-Mills theories and their role in connecting string theory with noncommutative geometry.

Contribution

It provides a comprehensive overview of matrix models, their derivations, and classical solutions relevant to noncommutative gauge theories.

Findings

IKKT and BFSS models as reductions of Yang-Mills theories

Classical solutions lead to noncommutative gauge models

Matrix models connect string theory with noncommutative geometry

Abstract

Matrix models and their connections to String Theory and noncommutative geometry are discussed. Various types of matrix models are reviewed. Most of interest are IKKT and BFSS models. They are introduced as 0+0 and 1+0 dimensional reduction of Yang--Mills model respectively. They are obtained via the deformations of string/membrane worldsheet/worldvolume. Classical solutions leading to noncommutative gauge models are considered.