Deconfinement transition in QCD at finite temperature

The main subject of this thesis is the problem of confinement in QCD. Since the discovery of quarks in high energy experiments, their absence as free particles in nature became one of the hot topics in modern physics. The non abelian gauge field theories developed in the 50s by Yang and Mills and successively generalized in the Standard Model have proved successful in describing the real world. Electroweak and short distance interactions are well explained by perturbative expansions in gauge coupling powers. Perturbative calculations, however, cannot account for the confinement problem which is inherently non perturbative in nature. The non perturbative region of strongly coupled theories was out of reach for any analytical calculation since the proposal by Wilson of a regularization on the lattice of gauge field theories. Soon, in early works of lattice field theory it was realized that Yang Mills theories could also account for confinement of quarks by a potential linearly rising with distance. In finite temperature calculations it was also shown that this linear behavior disappears as some temperature Tc , called deconfinement temperature, above which quarks are not bounded inside hadrons. At present time there are no widely accepted explanations from first principles of the dynamics of confinement. Several mechanisms were proposed to describe confinement at low temperatures by means of the topological properties of Yang Mills theories. We shall concentrate on the so called Dual Superconductor Picture which conjectures that confinement is related to condensation of magnetic charges in analogy with common superconductors where condensation of electric charges “confines” magnetic monopoles. We shall propose and test a way to prove its correctness in several gauge theories (see chapter 3). Although no definitive conclusions can be drawn, we shall show, by using an operator that detects the condensation of magnetic charges in the vacuum, that the Dual Superconductor Picture is indeed a proper candidate for the description of the confinement dynamics. The problem was deeply studied in the last years by the Pisa group. The confinement by condensation of monopoles was demonstrated in an U(1) abelian theory both analytically (Frölich and Marchetti) and numerically (Pisa group). During my PhD we discovered that some of our previous data on non abelian gauge theories were misinterpreted. In pure non abelian gauge theories, the presence of unphysical bulk transitions spoils the relation of the operator singularities to a confinement-deconfinement transition. Conversely, similar calculations in theories with fermions in different representations do not show any signal of bulk transitions and results are consistent with the Dual Superconductor Picture. We are dedicating our efforts to clarify this unwelcome behavior of the operator. I will present the first attempts to redefine the operator in pure gauge theories to circumvent these issues. The problem of a suitable definition of the operator on the lattice is still open and a detailed discussion on the subject will be proposed in chapter 3. If the confinement-deconfinement transition is related to the breaking of some symmetry of the theory we then expect that a true phase transition takes place. Strictly speaking, we have explicit symmetries only in the two opposite regions of zero and infinite quark masses (respectively chiral and center symmetries). We aim at establishing if, even at finite quark masses, the path from the low temperature region (confined) to the high temperature region where quarks are free, encounters singularities. A positive answer demonstrates the non trivial fact this two phases have different symmetries, otherwise confinement is ambiguously defined. In this respect, the problem of determining the order of the chiral transition in QCD with two degenerate quarks, a case close to the physical one, becomes a relevant point (chapter 4). In few words, if the transition is second order for massless quarks we then expect that it turns into a crossover for light masses, while if the transition is first order then the non analyticity could survive in a region of small masses (or beyond). The later possibility could explain naturally the experimental evidence of free quark suppression in nature. In chapter 4 we shall address the problem with Finite Size Scaling techniques (chapter 2). By isolating the dependence on one of the two variables (temperature and bare quark mass) we shall analyze the volume scaling of thermodynamical quantities like specific heat and chiral condensate susceptibility. The task of unambiguously determining the order is hard to accomplish but we shall give some evidences that, despite the common lore, the transition could be first order, and that surely is not second order in the class predicted by effective theories. Summarizing the objectives of this thesis is twofold: • address the confinement problem by probing the vacuum with a magnetically charged operator to establish if the dual superconductor picture is a valid picture; • address the confinement problem by studying the related issue of the order of the transition in two flavors quantum chromodynamics.