Gribov horizon and i-particles: about a toy model and the construction of physical operators

TL;DR

This paper explores how restricting the gauge field configurations to the Gribov region modifies infrared behavior in Yang-Mills theories, introducing a toy model where composite operators built from unphysical modes exhibit physical properties akin to glueballs.

Contribution

It presents a toy model demonstrating the construction of physical operators from unphysical $i$-particles with real spectral properties, illustrating confinement mechanisms.

Findings

Composite operators have real branch cuts and positive spectral density.

The toy model mimics glueball properties in the Gribov-Zwanziger framework.

Gluons are shown to be unphysical and confined within this approach.

Abstract

Restricting the functional integral to the Gribov region $\Omega$ leads to a deep modification of the behavior of Euclidean Yang-Mills theories in the infrared region. For example, a gluon propagator of the Gribov type, $\frac{k^2}{k^4+{\hat \gamma}^4}$, can be viewed as a propagating pair of unphysical modes, called here $i$-particles, with complex masses $\pm i{\hat \gamma}^2$. From this viewpoint, gluons are unphysical and one can see them as being confined. We introduce a simple toy model describing how a suitable set of composite operators can be constructed out of $i$-particles whose correlation functions exhibit only real branch cuts, with associated positive spectral density. These composite operators can thus be called physical and are the toy analogy of glueballs in the Gribov-Zwanziger theory.