Color–flavor locking

If each quark is represented as ${\displaystyle \psi _{i}^{\alpha }}$ , with color index ${\displaystyle \alpha }$  taking values 1, 2, 3 corresponding to red, green, and blue, and flavor index ${\displaystyle i}$  taking values 1, 2, 3 corresponding to up, down, and strange, then the color-flavor-locked pattern of Cooper pairing is ^[2]

${\displaystyle \langle \psi _{i}^{\alpha }C\gamma _{5}\psi _{j}^{\beta }\rangle \propto \delta _{i}^{\alpha }\delta _{j}^{\beta }-\delta _{j}^{\alpha }\delta _{i}^{\beta }=\epsilon ^{\alpha \beta A}\epsilon _{ijA}}$ 

This means that a Cooper pair of an up quark and a down quark must have colors red and green, and so on. This pairing pattern is special because it leaves a large unbroken^{[clarification needed]} symmetry group.

The CFL phase has several remarkable properties.

• It breaks chiral symmetry.
• It is a superfluid.
• It is an electromagnetic insulator, in which there is a "rotated" photon, containing a small admixture of one of the gluons.
• It has the same symmetries as sufficiently dense hyperonic matter.

There are several variants of the CFL phase, representing distortions of the pairing structure in response to external stresses such as a difference between the mass of the strange quark and the mass of the up and down quarks.

• Color superconductivity