Magnetism in Cold-Dense QCD

In this talk I review some of the main findings on magnetism in color superconductivity. The physical characteristic of the different phases that are reached by increasing the applied magnetic field in a three-flavor color superconductor at asymptotically high densities are discussed. A mechanism to boost a seed magnetic field in high-dense quark matter is presented. Also, it is shown how a magnetic field can be generated in a color superconductor at moderate densities. Possible implications of these results for the astrophysics of magnetized compact objects are indicated.