The understanding of the phase diagram of quantum chromodynamics, motivated by recent data, is an open and challenging question. The main formalism which is applied to describe it -- quantum field theory at finite temperature -- does not lead to well-defined results for a range of physically relevant parameters. Apart from the very intrincated nature of the theory of elementary particles (gauge theories), one finds additional problems to perform calculations at finite temperature and densities, a context where the usual perturbation theory fails. We propose new approaches which are essentially non-perturbative to cope with these problems. Such methods have already been successfully applied to simpler systems, and their extension to more realistic cases rely on a deep understanding of gauge theories. Thus, we will be concentrated on two main issues: the use of semiclassical methods to describe the thermodynamics of quantum field theories; the construction of more fundamental effective theories using Wilson lines, key quantities to characterize phase transitions in gauge theories.
News published in Agência FAPESP Newsletter about the scholarship: