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We show that $\mathbb{Z}_3$-valued particle-vortex braiding phases arepresent in high density quark matter. Certain mesonic and baryonic excitations,in the presence of a superfluid vortex, have orbital angular momentum quantizedin units of $\hbar/3$. Such non-local topological features can distinguishphases whose realizations of global symmetries, as probed by local orderparameters, are identical. If $\mathbb{Z}_3$ braiding phases and angularmomentum fractionalization are absent in lower density hadronic matter, as iswidely expected, then the quark matter and hadronic matter regimes of dense QCDmust be separated by at least one phase transition.

Anyonic particle-vortex statistics and the nature of dense quark matter