Intersection of black hole theory and quantum chromodynamics: the gluon propagator corresponding to linear confinement at large distances and relativistic bound states in the confining SU(N)-Yang-Mills fields

TL;DR

This paper derives a nonperturbative gluon propagator linked to linear confinement in SU(N)-Yang-Mills fields using black hole theory techniques, and explores relativistic bound states relevant to mesons and quarkonia.

Contribution

It introduces a novel nonperturbative construction of the gluon propagator based on black hole theory, connecting confinement with relativistic bound states in SU(N) gauge fields.

Findings

Gluon propagator matches perturbative QCD at high energies

Provides a scenario for linear confinement in mesons and quarkonia

Analyzes relativistic bound states for N=2,3,4

Abstract

The exact nonperturbative confining solutions of the SU(3)-Yang-Mills equations recently obtained by author in Minkowski spacetime with the help of the black hole theory techniques are analysed and on the basis of them the gluon propagator corresponding to linear confinement at large distances (small momenta) is constructed in a nonperturbative way. At small distances (large momenta) the resulting propagator passes on to the standard (nonperturbative) gluon propagator used in the perturbative quantum chromodynamics (QCD). The results suggest some scenario of linear confinement for mesons and quarkonia which is also outlined. As a consequence there arises a motivation for studying the relativistic bound states in the above confining SU($N$)-Yang-Mills fields. This possiblity is realized for $N=2,3,4$ with the aid of the black hole theory results about spinor fields on black holes with a subsequent application to the charmonium spectrum in the most important physical case N=3. Incidentally uniqueness of the confining solutions is discussed and a comparison with the nonrelativistic potential approach is given.