ABSTRACT: Heavy-ion collision experiments carried out at the Brookhaven National Laboratory, or BNL, and at the European Organization for Nuclear Research, or CERN, provide evidence that matter can be driven from a confined, low-temperature phase into a deconfined high temperature phase of liberated quarks and gluons. Understanding of the deconfinement transition can bring our knowledge of strongly-interacting matter to a deeper level. Ab initio equilibrium studies of the thermodynamic equation of state in the deconfined phase are possible in the framework of lattice gauge theory. It is often desired in such studies to approach the infinite volume thermodynamic limit. To accomplish it quickly, most studies have implemented lattices with periodic boundary conditions. However, the physical volumes created at the Brookhaven National Laboratory are small and exploratory work for pure SU(3) lattice gauge theory suggests that boundary effects cannot be neglected. In this work we study the SU(3) deconfined equilibrium phase in small volumes with inside and outside temperatures in the SU(3) scaling region, using a lattice geometry of the double-layered torus. Our results show substantial finite size effects on the deconfining transition temperature under realistic boundary conditions.

ABSTRACT: Recent experiments carried out at the Relativistic Heavy Ion Collider at the Brookhaven National Laboratory provide strong evidence that a matter can be driven from a confined, low-temperature phase, observed in our every day world into a deconfined high-temperature phase of liberated quarks and gluons. The equilibrium and dynamical properties of the deconfining phase transition are thus of great theoretical interest, since they also provide an information about the first femtoseconds of the evolution of our Universe, when the hot primordial soup while cooling has undergone a chain of phase transitions. The aspects of the deconfining phase transition studied in this work include: the dynamics of the SU(3) gauge theory after the heating quench (which models rapid heating in the heavy-ion collisions), equilibrium properties of the phase transition in the SU(3) gauge theory with boundaries at low temperature (small volumes at RHIC suggest that boundary effects cannot be neglected and periodic boundary conditions normally used in lattice simulations do not correspond to the experimental situation), and a study of the order of the transition in U(1) gauge theory.

- Wherever possible simple examples, which illustrate the main ideas, are provided before embarking on the actual discussion of the problem of interest - The book introduces the readers to problems of great current interest, like instantons, calorons, vortices, magnetic monopoles - QCD at finite temperature is discussed at great length, both in perturbation theory and in Monte Carlo simulations - The book contains many figures showing numerical results of pioneering work

The AdS/CFT correspondence is a powerful tool in studying strongly coupled phenomena in gauge field theories, using results from a weakly coupled gravity background studied in the realm of string theory. AdS/CFT was first successfully applied to the study of phenomena such as the quark-gluon plasma produced in heavy ions collisions. Soon it was realized that its applicability can be extended, in a more phenomenological approach, to condensed matter systems and to systems described by fluid dynamics. The set of tutorial reviews in this volume is intended as an introduction to and survey of the principle of the AdS/CFT correspondence in its field/string theoretic formulation, its applicability to holographic QCD and to heavy ions collisions, and to give a first account of processes in fluid dynamics and condensed matter physics, which can be studied with the use of this principle. Written by leading researchers in the field and cast into the form of a high-level but approachable multi-author textbook, this volume will be of benefit to all postgraduate students, and newcomers from neighboring disciplines wishing to find a comprehensive guide for their future research.