Abstract
We show that effective coupling strengths between ungapped and gapped quarks in the two-flavor color superconducting (2SC) phase are renormalized by logarithmic quantum corrections. We obtain a set of coupled renormalization-group (RG) equations for two distinct effective coupling strengths arising from gluon exchanges carrying different color charges. The diagram of RG flow suggests that both of the coupling strengths evolve into a strong-coupling regime as we decrease the energy scale toward the Fermi surface. This is a characteristic behavior observed in the Kondo effect, which has been known to occur in the presence of impurity scatterings via non-Abelian interactions. We propose a novel Kondo effect emerging without doped impurities, but with the gapped quasiexcitations and the residual SU(2) color subgroup intrinsic in the 2SC phase, which we call the 2SC Kondo effect.
Highlights
The Kondo effect gives rise to rich physics from an emergent strong-coupling regime in the low-energy dynamics
The scaling argument clearly indicates that the existence of a Fermi surface is crucial for the Kondo effect to occur [5,6] as we will explain in a brief review part
A negative Jz corresponds to the ferromagnetic Kondo problem of which the fate at low energy depends on the relative strength between JÆ and jJzj
Summary
The Kondo effect gives rise to rich physics from an emergent strong-coupling regime in the low-energy dynamics. Subsequent studies investigated further consequences of the QCD Kondo effect, including interplay/competition with color superconductivity [9], formation of “Kondo condensates” and modification of the QCD phase diagram [10,11,12,13], nonperturbative aspects near the IR fixed point by conformal field theory [14,15], estimates of transport coefficients [16], and QCD equation of state for an application to neutron/quark star physics [17]. We consider the RG evolution of effective coupling strengths between gapped and ungapped quarks appearing in the two-flavor color superconducting (2SC) phase [19,20]. We can focus on the remaining five gluons which mediate the interactions between ungapped and gapped quarks Those gluons have different properties depending on if they are associated with the diagonal or off-diagonal Gell-Mann matrices, so that we introduce two distinct effective coupling strengths.
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