Size, shape and properties of calorons in high-temperature SU(3) Yang-Mills theory

Quantum Chromodynamics provides the most comprehensive framework for understanding the physics of strong interactions. This theory describes the interactions between quarks and gluons, with the gluon sector represented by a Yang-Mills SU(3) model, which constitutes by itself a nontrivial theory. The topological properties related to the theta-dependence of QCD arise from the dynamics of gauge fields. For this reason, theta-dependence is often studied in the quenched approximation, where dynamical fermions are neglected. Recent studies suggest that the deconfined phase of SU(3) Yang-Mills theory, for temperatures just above the critical one, can be effectively described as a dilute gas of instantons. This thesis focuses on the study of local topological properties, investigated by means of numerical simulations, to check whether the high-T regime of SU(3) Yang-Mills theory can be effectively described by a gas of non-interacting topological excitations (the calorons). The identification of caloron configurations on the lattice is achieved using an algorithm specifically designed. This new methodology permits the analysis of topological properties of the theory directly evaluating local observables on calorons structures. The primary objective is to determine the geometric properties of calorons, such as their shape and size. This analysis is carried out at various temperatures, all above the critical temperature, to explore the temperature dependence of these properties.