The Casher argument, which is believed to be quite general, states that in the confining regime chiral symmetry is necessarily broken. In the large-$N_c$ limit and at moderate and low temperatures, QCD is confining up to arbitrary large densities, and there should appear a quarkyonic matter. It has been demonstrated, within a manifestly confining and chirally symmetric model, which is a $3+1$ dimensional generalization of the ’t Hooft model, that, at zero temperature and at a density exceeding a critical one, the chiral symmetry is restored while quarks remain confined in color-singlet hadrons. This is in conflict with the Casher argument. Here, we explain the reason why the Casher argument fails and clarify the physical mechanism lying behind such confined but chirally symmetric hadrons.

• Received 10 July 2009

DOI:https://doi.org/10.1103/PhysRevD.80.037701