Effective lagrangian approach to QCD phase transitions

Abstract

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.