Quark-hadron continuity beyond Ginzburg-Landau paradigm

Quark-hadron continuity is a scenario that hadronic matter is continuously connected to color superconductor without phase transitions as the baryon chemical potential increases. This scenario is based on Landau's classification of phases since they have the same symmetry breaking pattern. We address the question whether this continuity is true as quantum phases of matter, which requires the treatment beyond Ginzburg-Landau description. To examine the topological nature of color superconductor, we derive a dual effective theory for $U(1)$ 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 $\mathbb Z_3$ two-form symmetry. We find that this symmetry cannot be spontaneously broken, indicating that quark-hadron continuity is still a consistent scenario.