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Dilatons in Hidden Local Symmetry for Hadrons in Dense Matter

With the explicit breaking of scale invariance by the trace anomaly of QCD rephrased in terms of spontaneous breaking, low-energy strong interaction dynamics of dense (and also hot) matter can be effectively captured by -- in addition to the Nambu-Goldstone bosons and the vector mesons -- two dilaton fields, the "soft" ($χ_s$) field that is locked to chiral symmetry and the "hard" ($χ_h$) field which remains unaffected by chiral symmetry. The interplay of the soft and hard dilatons plays a subtle role in how chiral symmetry is manifested in hot and/or dense matter. The scale anomaly in which the soft component intervenes vanishes at the chiral transition in a way analogous to the restoration of scale symmetry in the Freund-Nambu model, while that of the hard component remains broken throughout the QCD sector. Most remarkable of all is its role in the chiral anomaly sector through a "homogeneous Wess-Zumino (hWZ) term" of the form $ω_μB^μ$ on the structure of a single baryon as well as dense baryonic matter. It figures crucially in predicting a "Little Bag" for the nucleon and a "quarkyonic phase" in the form of a half-skyrmion matter at high density. We show how the vanishing of the vector-meson mass at the vector manifestation fixed point in hidden local symmetry theory can be related to the property of the "matter field" in the Freund-Nambu model that leaves scale symmetry invariant. The emerging structure of dense hadronic matter in the model so constructed suggests what could be amiss in describing dense matter in holographic dual QCD at its large $N_c$ and 't Hooft limit.