  A sensitive correlation between the ground-state properties of light kaonic
nuclei and the symmetry energy at high densities is constructed under the
framework of relativistic mean-field theory. Taking oxygen isotopes as an
example, we see that a high-density core is produced in kaonic oxygen nuclei,
due to the strongly attractive antikaon-nucleon interaction. It is found that
the $1S_{1/2}$ state energy in the high-density core of kaonic nuclei can
directly probe the variation of the symmetry energy at supranormal nuclear
density, and a sensitive correlation between the neutron skin thickness and the
symmetry energy at supranormal density is established directly. Meanwhile, the
sensitivity of the neutron skin thickness to the low-density slope of the
symmetry energy is greatly increased in the corresponding kaonic nuclei. These
sensitive relationships are established upon the fact that the isovector
potential in the central region of kaonic nuclei becomes very sensitive to the
variation of the symmetry energy. These findings might provide another
perspective to constrain high-density symmetry energy, and await experimental
verification in the future.
