Momentum Shell in Quarkyonic Matter from Explicit Duality: A Dual Model for Cold, Dense QCD

TL;DR

This paper introduces a duality-based model of cold QCD matter that captures the transition from nuclear to Quarkyonic matter, revealing a momentum shell structure and a rapid change in the equation of state at high density.

Contribution

It develops an analytic duality model connecting baryon and quark distributions, explicitly constructing solutions that describe nuclear and Quarkyonic regimes.

Findings

Identification of a momentum shell in Quarkyonic matter

Explicit analytic solutions for duality constraints

Observation of a rapid pressure increase at the transition

Abstract

We present a model of cold QCD matter that bridges nuclear and quark matter through the duality relation between quarks and baryons. The baryon number and energy densities are expressed as functionals of either the baryon momentum distribution, $f_{\rm B}$, or the quark distribution, $f_{\rm Q}$, which are subject to the constraints on fermions, $0 \le f_{\rm B,Q} \le 1$. The theory is ideal in the sense that the confinement of quarks into baryons is reflected in the duality relation between $f_{\rm Q}$ and $f_{\rm B}$, while other possible interactions among quarks and baryons are all neglected. The variational problem with the duality constraints is formulated and we explicitly construct analytic solutions, finding two distinct regimes: A nuclear matter regime at low density and a Quarkyonic regime at high density. In the Quarkyonic regime, baryons underoccupy states at low momenta but form a momentum shell with $f_{\rm B}=1$ on top of a quark Fermi sea. Such a theory describes a rapid transition from a soft nuclear equation of state to a stiff Quarkyonic equation of state. At this transition, there is a rapid increase in the pressure.