Quantum Link Models with Many Rishon Flavors and with Many Colors

TL;DR

This paper introduces quantum link models using rishon fermions, demonstrating their continuum limit, large N_c behavior, and strong coupling properties, revealing confinement and topological features.

Contribution

It presents a novel rishon-based formulation of quantum link models that enables analysis of large N_c limits and continuum behavior.

Findings

Recovery of Yang-Mills action in continuum limit

Area law for Wilson loops in 't Hooft limit

Topological suppression in strong coupling expansion

Abstract

Quantum link models are a novel formulation of gauge theories in terms of discrete degrees of freedom. These degrees of freedom are described by quantum operators acting in a finite-dimensional Hilbert space. We show that for certain representations of the operator algebra, the usual Yang-Mills action is recovered in the continuum limit. The quantum operators can be expressed as bilinears of fermionic creation and annihilation operators called rishons. Using the rishon representation the quantum link Hamiltonian can be expressed entirely in terms of color-neutral operators. This allows us to study the large N_c limit of this model. In the 't Hooft limit we find an area law for the Wilson loop and a mass gap. Furthermore, the strong coupling expansion is a topological expansion in which graphs with handles and boundaries are suppressed.