Remarks on the eigenvalues distributions of D\leq 4 Yang-Mills matrix models

TL;DR

This paper reviews the eigenvalue distributions in low-dimensional Yang-Mills matrix models, highlighting their role in emergent fuzzy geometry and noncommutative gauge theories.

Contribution

It provides a discussion on the eigenvalue distributions in the commuting phase of Yang-Mills matrix models in dimensions less than or equal to four.

Findings

Eigenvalue distributions characterize the emergent geometry.

Analysis of the commuting phase reveals specific distribution patterns.

Insights into noncommutative gauge theories from matrix model eigenvalues.

Abstract

The phenomena of emergent fuzzy geometry and noncommutative gauge theory from Yang-Mills matrix models is briefly reviewed. In particular, the eigenvalues distributions of Yang-Mills matrix models in lower dimensions in the commuting (matrix or Yang-Mills) phase of these models are discussed.