Baryons in holographic QCD

Abstract

We study baryons in holographic QCD with $\mathrm{D}4/\mathrm{D}8/\overline{\mathrm{D}8}$ multi-D-brane system. In holographic QCD, the baryon appears as a topologically nontrivial chiral soliton in a four-dimensional effective theory of mesons. We call this topological soliton brane-induced Skyrmion. Some review of $\mathrm{D}4/\mathrm{D}8/\overline{\mathrm{D}8}$ holographic QCD is presented from the viewpoints of recent hadron physics and QCD phenomenologies. A four-dimensional effective theory with pions and $\ensuremath{\rho}$ mesons is uniquely derived from the non-Abelian Dirac-Born-Infeld (DBI) action of D8 brane with D4 supergravity background at the leading order of large ${N}_{c}$, without small amplitude expansion of meson fields to discuss chiral solitons. For the hedgehog configuration of pion and $\ensuremath{\rho}$-meson fields, we derive the energy functional and the Euler-Lagrange equation of brane-induced Skyrmion from the meson effective action induced by holographic QCD. Performing the numerical calculation, we obtain the soliton solution and figure out the pion profile $F(r)$ and the $\ensuremath{\rho}$-meson profile $\stackrel{\texttildelow{}}{G}(r)$ of the brane-induced Skyrmion with its total energy, energy density distribution, and root-mean-square radius. These results are compared with the experimental quantities of baryons and also with the profiles of standard Skyrmion without $\ensuremath{\rho}$ mesons. We analyze interaction terms of pions and $\ensuremath{\rho}$ mesons in brane-induced Skyrmion, and find a significant $\ensuremath{\rho}$-meson component appearing in the core region of a baryon.