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We present a model of Quarkyonic matter that is explicitly dual betweenquarks and baryons. The baryon number and energy densities are expressed asfunctionals of either the baryon momentum distribution, $f_{\rm B}$, or thequark distribution, $f_{\rm Q}$, which are subject to the constraints onfermions, $0 \le f_{\rm B,Q} \le 1$. The theory is ideal in the sense that theconfinement of quarks into baryons is reflected in the duality relation between$f_{\rm Q}$ and $f_{\rm B}$, while other possible interactions among quarks andbaryons are all neglected. The variational problem with the duality constraintsis formulated and we explicitly construct analytic solutions, finding twodistinct regimes: A nuclear matter regime at low density and a Quarkyonicregime at high density. In the Quarkyonic regime, baryons underoccupy states atlow momenta but form a momentum shell with $f_{\rm B}=1$ on top of a quarkFermi sea. Such a theory describes a rapid transition from a soft nuclearequation of state to a stiff Quarkyonic equation of state. At this transition,there is a rapid increase in the sound speed.

Momentum Shell in Quarkyonic Matter from Explicit Duality: A Solvable Model Analysis