Effective lagrangian approach to QCD phase transitions

We use an effective low-energy lagrangian for broken chiral and scale invariance to discuss the condensation and confinement of quarks and of gluons in QCD. The Skyrme model convinces us that quark condensation and confinement are identical, and we argue that well-defined glueball states exist only when gluons condense. Previous calculations with chiral lagrangians have indicated that the quark transition at the finite temperature T_q is second order if gluonic degrees of freedom can be neglected, and we argue that the gluonic transition at the finite temperature T_g is generically first order. The scaling properties of the effective lagrangian tell us that T_q≤T_g. We argue that T_q can be below T_g in SU (2) gauge theory, whereas T_q=T_g and both quark and gluon transitions are simultaneous and first order in QCD with its SU(3) gauge group. These results agree qualitatively with lattice results. We speculate that the divergent Hagedorn spectrum may drive the joint quark/gluon transition at some temperature below the Hagedorn temperature.