Chiral Symmetry Breaking, Trace Anomaly and Baryons in Hot and Dense Matter

We propose an effective chiral Lagrangian with a chiral scalar introduced as a dilaton associated with broken conformal symmetry and responsible for the trace anomaly in QCD and discuss the properties of hadronic matter at high density and temperature. As the "dilaton limit" is taken, which drives a system from nuclear matter density to near chiral restoration density, a linear sigma model emerges from the highly non-linear structure. A striking prediction is that as the dilaton limit is approached, the omega-nucleon interaction gets strongly suppressed at high density. This is shown to be a firm statement at the quantum level protected by an infrared fixed point of the renormalization group equations derived in chiral perturbation theory.