Baryon-rich QCD matter

Properties of high-density strong-interaction matter of relevance for astrophysical scenarios that involve neutron stars are discussed. It is argued that theoretical and experimental insights from the small baryo-chemical potential ($\mu_B$) and high-temperature regions of the QCD phase diagram can guide realistic model building at high density, as this regime is currently not accessible to first-principles numerical calculations of the QCD partition function. Special attention is payed to the chiral properties of high-density matter and the nature of a possible first-order chiral phase transition. In this transition hadronic parity-partners, in particular baryons, become spectrally degenerate with finite (pole) masses, as expected from general insight into the mass generation in QCD. Possible signals in heavy-ion dielectron production at beam energies of a few GeV are discussed. Based on evidence for an emergent "chiral spin symmetry" above the pseudo-critical chiral transition temperature at small $\mu_B$, speculations on the physical state of dense hadronic matter beyond the chiral phase transition are presented.