Magnetically induced QCD Kondo effect

The QCD Kondo effect stems from the color exchange interaction in QCD with non-Abelian property, and can be realized in a high-density quark matter containing heavy-quark impurities. We propose a novel type of the QCD Kondo effect induced by a strong magnetic field. In addition to the fact that the magnetic field does not affect the color degrees of freedom, two properties caused by the Landau quantization in a strong magnetic field are essential for the magnetically induced QCD Kondo effect; (1) dimensional reduction to 1+1-dimensions, and (2) finiteness of the density of states for lowest energy quarks. We demonstrate that, in a strong magnetic field $B$, the scattering amplitude of a massless quark off a heavy quark impurity indeed shows a characteristic behavior of the Kondo effect. The resulting Kondo scale is estimated as $Lambda_{rm K} simeq sqrt{e_qB} alpha_{s}^{1/3} {rm{exp}}{-{4}pi/N_{c} alpha_{s} {rm{log}}( 4 pi/alpha_{s}) }$ where $alpha_{s}$ and $N_c$ are the fine structure constant of strong interaction and the number of colors in QCD, and $e_q$ is the electric charge of light quarks.