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We study the photon self-energy for the in-medium photon in a three-flavorcolor superconductor in the presence of a magnetic field. At strong magneticfield, the quark dynamics becomes $(1+1)$-dimensional and the self-energytensor only has longitudinal components. In this approximation there is noDebye or Meissner screenings at zero temperature, but the electricsusceptibility is nonzero and highly anisotropic. In the direction transverseto the applied field, the electric susceptibility is the same as in vacuum,while in the longitudinal direction it depends on the magnitude of the magneticfield. Such a behavior is a realization in cold-dense QCD of themagnetoelectric effect, which was first discovered in condensed matter physics.The magnetic permeability remains equal to that in vacuum for both transverseand longitudinal components. We discuss the importance of the Pauli-Villarsregularization to get meaningful physical results in the infrared limit of thepolarization operator. We also find the covariant form of the polarizationoperator in the reduced (1+1)-D space of the lowest Landau level and proves itstransversality.

Photon Self-Energy and Electric Susceptibility in a Magnetized Three-flavor Color Superconductor