New phases in QCD at finite temperature and chemical potential

Understanding the phases of quantum chromodynamics (QCD) at finite temperature and baryon density is crucial for describing matter in heavy-ion collisions and the interior of neutron stars. While the transition from the confined phase to the deconfined phase has been extensively studied at vanishing chemical potential, recent theoretical work suggests the existence of intermediate phases with partial deconfinement, where only a subset of the color degrees of freedom is deconfined. In this paper, we study the generalization of partial deconfinement in QCD in the Veneziano large-$N_{\rm c}$ limit ($N_{\rm f}/N_{\rm c}$ fixed) to finite baryon chemical potential. We find that the partially deconfined phase has finer structure, and hence that there are four phases in QCD at finite temperature and moderately large chemical potential: complete confinement, complete deconfinement, and two kinds of partial deconfinement. A key ingredient is the refined understanding of the meaning of the 'Gross-Witten-Wadia point', i.e., the opening of a gap in the distribution of Polyakov line phases: either string condensation or baryon condensation causes the GWW transition. As a by-product, we observe the emergence of the QCD critical point from the interplay between baryon condensation and partial deconfinement. While our approach is necessarily qualitative due to the fermion sign problem, it provides a unified theoretical framework for understanding the rich phase structure of dense QCD matter and offers new perspectives on the location and nature of the QCD critical point.