Vector meson effects on multi-Skyrmion states from the rational map ansatz

The roles of the lightest vector mesons ρ and ω in the multi-Skyrmion states are studied using the hidden local symmetry approach up to the next-to-leading order, including the homogeneous Wess-Zumino terms. The low-energy constants in the effective field theory are determined using the Sakai-Sugimoto model and the flat-space five-dimensional Yang-Mills action. With only two inputs, mρ and fπ, it is possible to determine all low-energy constants without ambiguity. The vector meson effects can be investigated by sequentially integrating vector mesons, and their geometry can be elucidated by comparing the results using the low-energy constants estimated from the Sakai-Sugimoto model and the flat-space five-dimensional Yang-Mills action. We found that the ρ meson reduces the masses of the multi-Skyrmion states and increases the overlaps of their constituents, whereas the ω meson repulses the constituents of the multi-Skyrmion states and increases their masses. Therefore, these vector mesons are crucial in the Skyrme model approach to nuclei. We also found that the warping factor, an essential element in the holographic model of QCD, affects the properties of the multi-Skyrmion states and cannot be ignored.