Chapter 1 Spontaneous Nambu-goldstone Currents Generation Driven by Mismatch

We review recent progress of understanding and resolving instabilities driven by mismatch between the Fermi surfaces of the pairing quarks in 2-flavor color superconductor. With the increase of mismatch, the 2SC phase exhibits chromomagnetic instability as well as color neutral baryon current instability. We describe the 2SC phase in the nonlinear realization framework, and show that each instability indicates the spontaneous generation of the corresponding pseudo Nambu-Golstone current. The Nambu-Goldstone currents generation state covers the gluon phase as well as the one-plane wave LOFF state. We further point out that, when charge neutrality condition is required, there exists a narrow unstable LOFF (Us-LOFF) window, where not only off-diagonal gluons but the diagonal 8-th gluon cannot avoid the magnetic instability. In this UsLOFF window, the diagonal magnetic instability cannot be cured by off-diagonal gluon condensate in the color superconducting phase.