Brane-induced Skyrmion onS3: Baryonic matter in holographic QCD

Abstract

We study baryonic matter in holographic QCD with $\mathrm{D}4/\mathrm{D}8/\overline{\mathrm{D}8}$ multi-D brane system in type IIA superstring theory. The baryon is described as the ``brane-induced Skyrmion,'' which is a topologically nontrivial chiral soliton in the four-dimensional meson effective action induced by holographic QCD. We employ the ``truncated-resonance model'' approach for the baryon analysis, including pion and $\ensuremath{\rho}$ meson fields below the ultraviolet cutoff scale ${M}_{\mathrm{KK}}\ensuremath{\sim}1\text{ }\text{ }\mathrm{GeV}$, to keep the holographic duality with QCD. We describe the baryonic matter in large ${N}_{c}$ as single brane-induced Skyrmion on the three-dimensional closed manifold ${S}^{3}$ with finite radius $R$. The interactions between baryons are simulated by the curvature of the closed manifold ${S}^{3}$, and the decrease of the size of ${S}^{3}$ represents the increase of the total baryon-number density in the medium in this modeling. We investigate the energy density, the field configuration, the mass and the root-mean-square radius of single baryon on ${S}^{3}$ as the function of its radius $R$. We find a new picture of ``pion dominance'' near the critical density in the baryonic matter, where all the (axial) vector meson fields disappear and only the pion fields survive. We also find the swelling phenomena of the baryons as the precursor of the deconfinement, and propose the mechanism of the swelling in the general context of QCD. The properties of the deconfinement and the chiral symmetry restoration in the baryonic matter are examined by taking the proper order parameters. We also compare our truncated-resonance model with another instanton description of the baryon in holographic QCD, considering the role of cutoff scale ${M}_{\mathrm{KK}}$.