London model of dual color superconductor

¹ Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež (Prague), Czech Republic
² Institute of Experimental and Applied Physics, Czech Technical University in Prague, Husova 240/5, 110 00 Prague 1, Czech Republic

^* e-mail: hosek@ujf.cas.cz

Published online: 22 December 2022

Abstract

The Meissner effect for the chromoelectric field E⃗_a is a property of the non-perturbative QCD vacuum medium assumed to explain the observed confinement of color. The color dielectric function ϵ of such a medium should vanish. By Lorentz invariance ϵμ = 1 i.e., its color magnetic permeability μ should diverge. The assumption based on analogy is well motivated: Ordinary superconductor is the physical medium with μ = 0, confining the opposite magnetic charges (would they exist). For the first successful phenomenological description of both the Meissner effect and superconductivity within Maxwell equations Fritz London guessed two equations for the superconductivity current. We adapt his arguments to QCD and come with two analogous manifestly non-Abelian London-like equations. One equation describes the dual Meissner effect. The analogy is, however, not perfect: We can only speculate that there is some sort of chromo-magnetic superfluidity in QCD phenomena to which the second equation might be ascribed. Moreover, from more advanced Ginzburg-Landau (GL) theory of superconductivity it follows that the Meissner effect is a consequence of spontaneous breaking of the underlying global U(1) symmetry. This is certainly not the case of the dual Meissner effect. Fortunately, the derived London-like equations suggest a strongly color-paramagnetic behavior. We interpret it as a guide to the phenomenological Ginzburg-Landau-like manifestly gauge-invariant low-momentum QCD with the confining vacuum which behaves as a perfect color paramagnet (μ = +∞).