Quark-hadron continuity  is a scenario that the hadronic matter is continuously connected to a color superconducting phase without phase transitions as the baryon chemical potential increases. This scenario is based on the fact that the two phases have the same symmetry breaking pattern, in the spirit of Landau's classification of phases. When we consider quantum phases of matter, it is known that the classification based on symmetry is insufficient: it fails to detect so-called topological orders. We address the question whether this continuity is true as quantum phases of matter, which requires the treatment beyond Ginzburg-Landau description [2,3].
To examine the topological nature of color superconductor, we study the low-energy theory describing U(1) Nambu-Goldstone (NG) bosons and vortices of the color-flavor locked phase, and discuss the fate of emergent higher-form symmetries. The theory has the form of a topological BF theory coupled to NG bosons, and fractional statistics of test quarks and vortices arises as a result of an emergent Z3 two-form symmetry. We find that the two-form symmetry is not spontaneously broken, indicating that quark-hadron continuity is still a consistent scenario.
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 Y. Hirono, Y. Tanizaki, [arXiv:1904.08570]