Three Lectures on QCD Phase Transitions

Abstract

AbstractIn this chapter, the contents of three lectures are presented, which elucidate aspects of phase transitions in QCD .In the first lecture, we discuss chiral symmetry and different types of phase transitions, likewise possible sigma models for chiral symmetry and the chiral anomaly. Speaking about gauge theory, people usually start with a deconfinement, because it is a fundamental feature of QCD. But we would like to start with chiral symmetry because its degrees of freedom (pions, kaons, etc.) are very well known, and we will use them to describe some properties of the phase transitions.We begin with a brief summary of the knowledge about flavor and chiral symmetries, describing what they are in a very elementary way. Then we consider a two-flavor case, where at finite temperature there is a second-order transition. Going further, we consider the case of three flavors, where because of the cubic terms, at least in the chiral limit, we are bound at first-order phase transition. In the last section, we discuss the influence of the tetraquarks on the chiral phase transitions, showing the recent results from the lattice.The second lecture is about deconfinement in pure gauge theories. At the beginning, we describe the order parameters of the phase transitions in a pure gauge theory. We also explain what deconfinement really means. At last, we present a matrix model in a pure gauge and compare it with lattice results.In the third lecture, a presentation of a chiral matrix model is given. The predicted equations of state for the chiral symmetry restoration and deconfinement transitions are compared to the recent lattice QCD results.