The Compactification of QCD${}_4$ to QCD${}_2$ in a Flux Tube

Abstract

We show from the action integral that in the special environment of a flux tube, QCD${}_4$ in (3+1) dimensional space-time can be approximately compactified into QCD${}_2$ in (1+1) dimensional space-time. In such a process, we find out how the coupling constant $g_{2D}$ in QCD${}_2$ is related to the coupling constant $g_{4D}$ in QCD${}_4$. We show how the quark and the gluon in QCD${}_2$ acquire contributions to their masses arising from their confinement within the tube, and how all these quantities depend on the excitation of the partons in the transverse degrees of freedom. The compactification facilitates the investigation of some dynamical problems in QCD${}_4$ in the simpler dynamics of QCD${}_2$ where the variation of the gluon fields leads to a bound state.

Latex 17 pages, to be published in Physical Review D

References in corpus (2)

• The phase boundary for the chiral transition in (2+1)-flavor QCD at small values of the chemical potential
• The QCD phase diagram at nonzero quark density

Cited by in corpus (5)

• Open string QED meson description of the X17 particle and dark matter
• On the stability of the open-string QED neutron and dark matter
• On the question of quark confinement in the Abelian U(1) QED gauge interaction
• Dynamics of quarks and gauge fields in the lowest-energy states in QCD and QED
• QED meson description of the anomalous particles at ~17 and ~38 MeV