Effective theory of color superconductivity

We briefly review an effective theory of QCD at high baryon density, describing the relevant modes near the Fermi surface. The high density effective theory has properties of reparametrization invariance and gauge invariance, maintained in a subtle way. It also has a positive measure, allowing lattice simulations at high baryon density. We then apply it to gapless superconductors and discuss recent proposals to resolve the magnetic instability of gapless superconductivity.