The phase space structure of zero temperature Quarkyonic matter is a Fermi sphere of Quark Matter, surrounded by a shell of Nucleonic matter. We construct a quasi particle model of Quarkyonic Matter based on the constituent quark model, where the quark and nucleon masses are related by mQ = mN /Nc, and Nc is the number of quark colors. The region of occupied states is for quarks kQ < kF /Nc, and for nucleons kF < kN < kF + ∆. We first consider the general problem of Quarkyonic Matter with hard core nucleon interactions. We then specialize to a quasi-particle model where the hard core nucleon interactions are accounted for by an excluded volume. In this model, we show that the nucleonic shell forms past some critical density related to the hard core size, and for large densities becomes a thin shell. We explore the basic features of such a model, and argue this model has the semi-quantitative behaviour needed to describe neutron stars.

Common lore suggests that N-color QCD with massive quarks has no useful order parameters that can be nontrivial at zero baryon density. However, such order parameters do exist when there are n f quark flavors with a common mass and d ≡ gcdðn f ; NÞ > 1. These theories have a Z d color-flavor center symmetry arising from intertwined color center transformations and cyclic flavor permutations. The symmetry realization depends on the temperature, baryon chemical potential, and value of n f =N, with implications for conformal window studies and dense quark matter.

We analyze the chiral magnetic effect in a homogeneous neutral plasma from the point of view of energy conservation, and construct an effective potential for the growth of maximally helical perturbations of the electromagnetic field. We show that a negative curvature at the origin of the potential, indicating instability of the plasma, is induced by a chiral asymmetry in electron Fermi energy, as opposed to number density, while the potential grows at large field value. It follows that the ground state for a plasma has zero magnetic helicity; a nonzero electron mass will allow an excited state of a plasma with nonzero helicity to relax to that ground state quickly. We conclude that a chiral plasma instability triggered by weak interactions is not a viable mechanism for explaining magnetic fields in stars except possibly when dynamics drives the system far from equilibrium.

We show that Z3-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 /3. Such non-local topological features can distinguish phases whose realizations of global symmetries, as probed by local order parameters, are identical. If Z3 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.

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