Resolving the scales of the Yang-Mills theory by means of an extra dimension

TL;DR

This paper proposes that an extra dimension in a lattice regularized Yang-Mills theory enables a unified description of all energy scales, linking classical and quantum regimes, and offers insights into confinement and the glueball spectrum.

Contribution

It introduces a model where an extra dimension resolves the energy scales of Yang-Mills theory, connecting classical and quantum descriptions and providing new perspectives on confinement.

Findings

The model describes classical motion with a large extra dimension.

Quantum mechanical behavior emerges in the small extra dimension limit.

The glueball spectrum is of the Hagedorn type and bounded below.

Abstract

The Yang-Mills theory is part of the Standard Model of particle physics. The lack of the mathematical understanding of the theory stands out in theoretical physics. In order to address this problem we observe that a recently proposed general model beyond the Standard Model resolves the energy scales of a lattice regularized Yang-Mills theory by means of an extra dimension. The extra dimension ensures that all intermediate length scales of the physical system are available by definition. In this paper we study the role of the extra dimension also in the case of the free boson field. We find that if the extra dimension size is large, the model describes the classical motion of the system. In the opposite limit we recover its standard quantum mechanical motion without loss of information. Therefore, the Hilbert space of states in the presence of the extra dimension describes physical phenomena at all energy scales. This observation allows us to raise the description of length scales by an extra dimension at the level of a principle for the theories beyond the Standard Model, the only modeling constraint being the correspondence principle. As it was shown recently, the fermion ground state energy of a gauge invariant Hamilton operator of Dirac fermions gives a particular lattice regularization of the Yang-Mills theory. Integration of gauge fields gives a pure fermion theory of color singlet fermion-antifermion pairs at each lattice site evolving along the extra dimension. Color confinement follows directly from this property. It allows for a saddle point solution in the limit of a large number of colors. In this paper we find that the glueball spectrum of the Yang-Mills regularized theory is of the Hagedron type and bounded below by a positive value. We show also that the color charge is screened and the quark-antiquark potential is constant.