The connection between the nuclear matter mean-field equation of state and the quark and gluon condensates at high density

It is known now that chiral symmetry restoration requires the meson-nucleon coupling to be density dependent in nuclear-matter mean-field models. We further show that quite generally, the quark and gluon condensates in medium are related to the trace of energy-momentum tensor of nuclear matter and in these models the incompressibility, K, must be less than thrice the chemical potential, $\mu$. In the critical density $\rho _c$, the gluon condensate is only reduced by $20\%$ indicating a larger effective nucleon mass.