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 $\sim 2M_{\odot }$ and surprisingly gives the sound velocity close to the “conformal velocity” $1/\sqrt{3}$ at densities $\gtrsim 3n_0$. At the core of this result is the observation that parity-doubling occurs in the nucleon structure as density goes above $\sim 2n_0$ with a chiral-singlet mass $m_0\sim (0.6–0.9)m_N$, 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.

The dilaton-limit fixed point and the scaling properties of hadrons in the close vicinity of the fixed point in dense baryonic matter uncovered in hidden local symmetry implemented with spontaneously broken scale symmetry are shown to reveal a surprisingly intricate interplay, hitherto unsuspected, between the origin of the bulk of proton mass and the renormalization-group flow of the $$\omega${}$-nuclear interactions. This rends theoretical support to the previous (phenomenologically) observed correlation between the dropping nucleon mass and the behavior of the $$\omega${}$-nuclear interactions in dense matter described in terms of half Skyrmions that appear at a density denoted ${n}_{1/2}$ in Skyrmion crystals. The role of the $$\omega${}$-meson degree of freedom in the source for nucleon mass observed in this paper is highly reminiscent of its important role in the Skyrmion description of nucleon mass in hidden local symmetric theory. One of the most notable novel results found in this paper is that the nucleon mass in a dense baryonic medium undergoes a drop roughly linear in density up to a density (denoted $\stackrel{\texttildelow{}}{n}$) slightly above the nuclear matter density (${n}_{0}$) and then stays more or less constant up to the dilaton-limit fixed point. The possibility that we entertain is that $\stackrel{\texttildelow{}}{n}$ coincides with or is at least close to ${n}_{1/2}$. We note that this feature can be economically captured by the parity-doublet model for nucleons with the chiral-invariant mass ${m}_{0}$\sim${}(0.7\char21{}0.8){m}_{N}$. It is found in one-loop renormalization-group analysis with the Lagrangian adopted that, while the $$\rho${}\mathrm{\text{-}}NN$ coupling ``runs'' in density, the $$\omega${}\mathrm{\text{-}}NN$ coupling does not scale: It will scale at two-loop or higher-loop order, but at a slower pace, so it is more appropriate to say it ``walks'' rather than runs. The former implies a drastic change in the nuclear tensor forces, affecting, among others, the nuclear symmetry energy and the latter generating the stiffness of the equation of state at density higher than that of normal nuclear matter.

We study nucleon structure with positive and negative parities using a parity-doublet model endowed with hidden local symmetry with the objective to probe dense baryonic matter. The model\char22{}that we shall refer to as the ``parity-doublet hidden local symmetry model'' for short\char22{}allows a chiral-invariant mass of the nucleons unconnected to spontaneously broken chiral symmetry, which comes out to be m0$\sim${}200\,\,MeV at tree level, from fitting to the decay width of the parity doubler, N(1535), to nucleon-pion and nucleon axial coupling gA=1.267. The presence of a substantial m0 that remains nonvanishing at chiral restoration presents a deep issue for the origin of the nucleon mass and will affect nontrivially the equation of state for dense baryonic matter relevant for compact stars. We construct a chiral perturbation theory at one-loop order and explore the phase structure of the model using renormalization group equations. We find a fixed point that we identify with the ``dilaton limit'' at which the hidden local symmetry vector mesons decouple from the nucleons. We suggest that the cold baryonic system will flow to this limit either before or at reaching the vector manifestation fixed point of hidden local symmetry theory as density increases toward that of chiral restoration.

We use the evolution operator method to find the one-loop effective action of scalar and spinor QED in electric field backgrounds in terms of the Bogoliubov coefficient between the ingoing and the outgoing vacua. We obtain the exact one-loop effective action for a Sauter-type electric field, $E_0{\mathrm{sech}}^2(t/\tau )$, and show that the imaginary part correctly yields the vacuum persistence. The renormalized effective action shows the general relation between the vacuum persistence and the total mean number of created pairs for the constant and the Sauter-type electric field.

Hadron properties in dense medium are treated in a unified way in a skyrmion model constructed with an effective Lagrangian, in which the $$\rho${}$ and $$\omega${}$ vector mesons are introduced as hidden gauge bosons, valid up to $O({p}^{4})$ terms in chiral expansion including the homogeneous Wess-Zumino terms. All the low energy constants of the Lagrangian\char22{}apart from the pion decay constant and the vector meson mass\char22{}are fixed by the master formula derived from the relation between the five-dimensional holographic QCD and the four-dimensional hidden local symmetry Lagrangian. This Lagrangian allows one to pin down the density ${n}_{1/2}$ at which the skyrmions in medium fractionize into half-skyrmions, bringing in a drastic change in the equation of state of dense baryonic matter. We find that the $U(1)$ field that figures in the Chern-Simons term in the five-dimensional holographic QCD action or equivalently the $$\omega${}$ field in the homogeneous Wess-Zumino term in the dimensionally reduced hidden local symmetry action plays a crucial role in the half-skyrmion phase. The importance of the $$\omega${}$ degree of freedom may be connected to what happens in the instanton structure of elementary baryon noticed in holographic QCD. The most striking and intriguing in what is found in the model is that the pion decay constant that smoothly drops with increasing density in the skyrmion phase stops decreasing at ${n}_{1/2}$ and remains nearly constant in the half-skyrmion phase. In accordance with the large ${N}_{c}$ consideration, the baryon mass also stays nonscaling in the half-skyrmion phase. This feature which is reminiscent of the parity-doublet baryon model with a chirally invariant mass ${m}_{0}$ is supported by the nuclear effective field theory with the parameters of the Lagrangian scaling modified at the skyrmion\char21{}half-skyrmion phase transition. It also matches with one-loop renormalization group analysis based on hidden local symmetry. A link between a nonvanishing ${m}_{0}$ and the origin of nucleon mass distinctive from dynamically generated mass is suggested. We briefly discuss the possible consequences of the topology change found in this paper on the forthcoming experiments at the rare isotope beam machines under construction.

We find the Bogoliubov coefficient from the tunneling boundary condition on charged particles in a static electric field E0sech2(z/L) and, using the regularization scheme in Phys. Rev. D 78, 105013 (2008), obtain the exact one-loop effective action in scalar and spinor QED. It is shown that the effective action satisfies the general relation between the vacuum persistence and the mean number of produced pairs. We advance an approximation method for general electric fields and show the duality between the space-dependent and time-dependent electric fields of the same form at the leading order of the effective actions.