We study baryons in a holographic model of QCD by Sakai and Sugimoto, realized as small instantons with fundamental string hairs. We introduce an effective field theory of the baryons in the five-dimensional setting, and show that the instanton interpretation implies a particular magnetic coupling. Dimensional reduction to four dimensions reproduces the usual chiral effective action, and, in particular, we estimate the axial coupling $g_A$ between baryons and pions and the magnetic dipole moments, both of which are proportional to $N_c$. We extrapolate to finite $N_c$ and discuss subleading corrections.

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 vector dominance of the electromagnetic form factors both for mesons and baryons arises naturally in holographic QCD, where both the number of colors and the ’t Hooft coupling are taken to be very large, offering a bona-fide derivation of the notion of vector dominance. The crucial ingredient for this is the infinite tower of vector mesons in the approximations made which share features that are characteristic of the quenched approximation in lattice QCD. We approximate the infinite sum by contributions from the lowest four vector mesons of the tower which turn out to saturate the charge and magnetic moment sum rules within a few percent and compute them totally free of unknown parameters for momentum transfers $Q^2\lesssim 1{\mathrm{GeV}}^2$. We identify certain observables that can be reliably computed within the approximations and others that are not, and discuss how the improvement of the latter can enable one to bring holographic QCD closer to QCD proper.

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 construct an effective chiral Lagrangian for hadrons implemented by the conformal invariance and discuss the properties of nuclear matter at high density. The model is formulated based on two alternative assignment, “naive” and mirror, of chirality to the nucleons. It is shown that taking the dilaton limit, in which the mended symmetry of Weinberg is manifest, the vector-meson Yukawa coupling becomes suppressed and the symmetry energy becomes softer as one approaches the chiral phase transition. This leads to softer equations of state (EoS) and could accommodate the EoS without any exotica consistent with the recent measurement of a $1.97\pm 0.04M_{\odot }$ neutron star. DOI: http://dx.doi.org/10.1103/PhysRevD.84.034011 © 2011 American Physical Society