Chirally symmetric but confining dense and cold matter

TL;DR

This paper demonstrates, using an exactly solvable model, that dense, cold matter can be both confining and chirally symmetric at finite chemical potential, challenging traditional views of deconfinement at chiral restoration.

Contribution

It provides the first explicit example of a confining, chirally symmetric phase at finite density within a solvable QCD-inspired model.

Findings

Chiral symmetry is restored at a critical chemical potential.

Confined hadrons form complete chiral multiplets above the critical point.

Chirally symmetric, confined matter could have implications for astrophysics.

Abstract

The folklore tradition about the QCD phase diagram is that at the chiral restoration phase transition at finite density hadrons are deconfined and there appears the quark matter. We address this question within the only known exactly solvable confining and chirally symmetric model. It is postulated within this model that there exists linear Coulomb-like confining interaction. The chiral symmetry breaking and the quark Green function are obtained from the Schwinger-Dyson (gap) equation while the color-singlet meson spectrum results from the Bethe-Salpeter equation. We solve this model at T=0 and finite chemical potential $\mu$ and obtain a clear chiral restoration phase transition at the critical value \mu_{cr}. Below this value the spectrum is similar to the previously obtained one at \mu = 0. At \mu > \mu_{cr} the quarks are still confined and the physical spectrum consists of bound states which are arranged into a complete set of exact chiral multiplets. This explicitly demonstrates that a chirally symmetric matter consisting of confined but chirally symmetric hadrons at finite chemical potential is also possible in QCD. If so, there must be nontrivial implications for astrophysics.