Hidden local symmetry and beyond

Gerry Brown was a godfather of our hidden local symmetry (HLS) for the vector meson from the birth of the theory throughout his life. The HLS is originated from very nature of the nonlinear realization of the symmetry $G$ based on the manifold $G/H$, and thus is universal to any physics based on the nonlinear realization. Here, I focus on the Higgs Lagrangian of the Standard Model (SM), which is shown to be equivalent to the nonlinear sigma model based on $G/H=\mathrm{\text{SU}}{(2)}_L\times \mathrm{\text{SU}}{(2)}_R/\mathrm{\text{SU}}{(2)}_V$ with additional symmetry, the nonlinearly-realized scale symmetry. Then, the SM does have a dynamical gauge boson of the SU${(2)}_V$ HLS, “SM $\rho$ meson”, in addition to the Higgs as a pseudo-dilaton as well as the NG bosons to be absorbed in to the $W$ and $Z$. Based on the recent work done with Matsuzaki and Ohki, I discuss a novel possibility that the SM $\rho$ meson acquires kinetic term by the SM dynamics itself, which then stabilizes the skyrmion dormant in the SM as a viable candidate for the dark matter, what we call “dark SM skyrmion (DSMS)”.