Compressibility of dense nuclear matter in the $\rho$-meson variant of the Skyrme model

We show that coupling the $\text{SU}(2)$-valued Skyrme field to the $\rho$-meson solves the long-standing issue of (in)compressibility in the solitonic Skyrme model. Even by including only one $\rho \pi$ interaction term, motivated by a holographic-like reduction of Yang-Mills action by Sutcliffe, reduces the compression modulus from $K_0\simeq 1080$ MeV, in the massive Skyrme model, to $K_0\simeq 351$ MeV.