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Exploiting certain robust topological inputs from the skyrmion description of compressed baryonic matter with a scale-chiral symmetric Lagrangian, we predict the equation of state that is consistent with the properties of nuclear matter at the equilibrium density, supports the maximum mass of massive compact star ∼ 2M ⊙ and surprisingly gives the sound velocity close to the "conformal velocity" 1/ √ 3 at densities ∼ > 3n 0 . At the core of this result is the observation that parity-doubling occurs in the nucleon structure as density goes above ∼ 2n 0 with a chiral-singlet mass m 0 ∼ (0.6 − 0.9)m N , hinting at a possible up-to-date unsuspected source of proton mass and an emergence at high density of scale symmetry and flavor local symmetry, both hidden in the QCD vacuum.

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A scale-invariant chiral effective Lagrangian is constructed for octet pions and a dilaton figuring as Nambu-Goldstone bosons with vector mesons incorporated as hidden gauge fields. The Lagrangian is built to the next-to-leading order in chiral-scale counting without baryon fields and then to leading order including baryons. The resulting theory is hidden scale-symmetric and local symmetric. We also discuss some possible applications of the present Lagrangian.Comment: 12 page, changes to match the published versio