Matrix and vector models in the strong coupling limit

TL;DR

This paper investigates matrix and vector models in the large N limit, demonstrating that their statistical sums coincide in the strong coupling limit for zero-dimensional and one-dimensional cases.

Contribution

It proves the equivalence of statistical sums for matrix and vector models in the strong coupling limit for D=0 and D=1 dimensions.

Findings

Statistical sums of matrix and vector models coincide at strong coupling for D=0.

The equivalence extends to D=1 models.

Results suggest a deep connection between matrix and vector models in these limits.

Abstract

In this paper we consider matrix and vector models in the large N limit ($N \times N$ matrices and vectors with N^{2} components). For the case of zero-dimensional model (D=0) it is proved that in the strong coupling limit $g \to \infty$ statistical sums of both models coincide up to a coefficient. This is also true for D=1.