Abstract
This chapter addresses the spontaneous breaking of chiral symmetry and Nambu-Goldstone (NG) modes from the vacuum to high-density quark matter. In the vacuum, pions and kaons are NG modes associated with the spontaneous breaking of chiral symmetry. The Nambu-Goldstone theorem states that there is a one-to-one correspondence between the broken symmetries and NG modes. The situation is different in high-density quark matter. It is known that two types of NG modes appear in the kaon-condensed color-flavor locked phase: One is an NG mode with linear dispersion, which is the same property as pions in the vacuum. The other is an NG mode with quadratic dispersion, which is no counterpart in the vacuum. In addition, the number of NG modes differs from the number of broken symmetries. This chapter discusses the generalization of the Nambu-Goldstone theorem to cover the high-density quark matter and gives a unified description of these two NG modes.
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