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Recent lattice QCD studies at vanishing density exhibit the parity-doublingstructure for the low-lying baryons around the chiral crossover temperature.This finding is likely an imprint of the chiral symmetry restoration in thebaryonic sector of QCD, and is expected to occur also in cold dense matter,which makes it of major relevance for compact stars. By contrast, typicaleffective models for compact star matter embody chiral physics solely in thedeconfined sector, with quarks as degrees of freedom. In this contribution, wepresent a description of QCD matter based on the effective hybridquark-meson-nucleon model. Its characteristic feature is that, underneutron-star conditions, the chiral symmetry is restored in a first-order phasetransition deep in the hadronic phase, before the deconfinement of quarks takesplace. We discuss the implications of the parity doubling of baryons on themass-radius relation for compact stars obtained in accordance with the modernconstraints on the mass from PSR J0348+0432, the compactness from GW170817, aswell as the direct URCA process threshold. We show that the existence ofhigh-mass stars might not necessarily signal the deconfinement of quarks.

Chiral symmetry restoration by parity doubling and the structure of neutron stars