Abstract
We show that $\mathbb{Z}_3$-valued particle-vortex braiding phases are present in high density quark matter. Certain mesonic and baryonic excitations, in the presence of a superfluid vortex, have orbital angular momentum quantized in units of $\hbar/3$. Such non-local topological features can distinguish phases whose realizations of global symmetries, as probed by local order parameters, are identical. If $\mathbb{Z}_3$ braiding phases and angular momentum fractionalization are absent in lower density hadronic matter, as is widely expected, then the quark matter and hadronic matter regimes of dense QCD must be separated by at least one phase transition.
Highlights
The behavior of QCD as a function of baryon density, at vanishing temperature, is of fundamental importance to nuclear physics and astrophysics [1,2,3,4]
Can the hadronic and quark matter regimes be smoothly connected, or are they necessarily separated by a phase transition?. We consider this question in the simplified, more symmetric setting of three-color, three-flavor QCD with degenerate quark masses and SUð3ÞV flavor symmetry
In high density quark matter, we find that quarks acquire nontrivial Z3 Aharonov-Bohm phases, arising from color holonomies, when encircling a superfluid vortex with minimal circulation
Summary
The behavior of QCD as a function of baryon density, at vanishing temperature, is of fundamental importance to nuclear physics and astrophysics [1,2,3,4]. Some transitions separating distinct phases can only be diagnosed by changes in behavior of topological observables such as the ground state degeneracy on large topologically nontrivial manifolds, or suitable nonlocal order parameters from which one infers, for example, particle-vortex braiding statistics [11,12,13] Given this motivation, we examine topological ground state degeneracies and quark-vortex braiding statistics in asymptotically high-density quark matter, and compare results with the expected properties of hadronic nuclear matter. Quasiparticle excitations, this means that certain mesonic and baryonic excitations have orbital angular momentum quantized in units of ħ=3 in the presence of a minimal superfluid vortex These results can be interpreted in terms of anyonic particle-vortex braiding statistics. If the standard picture of the low density hadronic regime is correct, the hadronic and quark matter regimes must be separated by at least one phase transition
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