Reduction of internal degrees of freedom in the large N limit in matrix models

TL;DR

This paper investigates how, in the large N limit of hermitian matrix models coupled to an external matrix, the degrees of freedom reduce from order N^2 to order N, explaining the origin of observable factorization.

Contribution

It demonstrates the reduction of degrees of freedom in large N matrix models and links this to the factorization of observables in the path integral formalism.

Findings

Degrees of freedom reduce to order N in the large N limit.

Reduction explains the factorization of observables.

Large N limit simplifies the matrix model structure.

Abstract

In this paper the large $N$ limit of one hermitian matrix models coupled to an external matrix is considered. It is shown that in the large N limit the number of degrees of freedom are reduced to be order N even though it is order $N^{2}$ for finite N. It is claimed that this result is the origin of the factorization of observables in the path integral formalism.