The Area Law in Matrix Models for Large N QCD Strings

TL;DR

This paper investigates whether a specific Hermitian matrix model can replicate the area law behavior of Wilson loops in large N QCD strings, finding evidence of such behavior within a finite scale range.

Contribution

It demonstrates that a zero-volume limit matrix model exhibits the area law for Wilson loops, suggesting potential equivalence to QCD strings at large N.

Findings

Area law observed for Wilson loops in the matrix model

Range of scale with area law remains stable up to N=768

Potential for the model to describe QCD strings within finite regimes

Abstract

We study the question whether matrix models obtained in the zero volume limit of 4d Yang-Mills theories can describe large N QCD strings. The matrix model we use is a variant of the Eguchi-Kawai model in terms of Hermitian matrices, but without any twists or quenching. This model was originally proposed as a toy model of the IIB matrix model. In contrast to common expectations, we do observe the area law for Wilson loops in a significant range of scale of the loop area. Numerical simulations show that this range is stable as N increases up to 768, which strongly suggests that it persists in the large N limit. Hence the equivalence to QCD strings may hold for length scales inside a finite regime.