Scale breaking in dense nuclear matter

We extend the standard relativistic mean-field treatment of dense nuclear matter to make it consistent with the anomalous trace of the energy-momentum tensor of QCD. This is accomplished by introducing a field for scalar gluonium and coupling it to nucleons and to scalar and vector mesons. Only the gluonium potential, proportional to the bag constant, breaks scale invariance. A physically sensible, first-order, phase transition to quark matter occurs at high baryon density.