Precise Computation of Thermal Phase Transition Parameters

Our understanding of field theories at finite temperature (FTQFT) has undergone significant progress in the last decade. It has been boosted in part by the necessity of correctly interpreting the data from current and future detectors of gravitational waves (GWs) produced during Phase Transitions (PT) in the early and hot Universe. By now it is well established that the correct description is provided by a 3-dimensional Euclidean effective field theory (EFT) involving only those degrees of freedom that do not acquire large effective masses in their interaction with the thermal bath; all others being removed from the theory in favor of Lagrangian terms of increasing number of fields and derivatives of light particles.However, there are strong reasons to push perturbative calculations within this context beyond the current level of accuracy, computing also Lagrangian terms with more than two derivatives, so far mostly ignored. Remarkably, this would also allow us to address the fundamental question, to the best of my knowledge not yet conceived before, of whether there exist degrees of freedom that have gone unnoticed so far. The most important of these are the so-called skyrmions, namely localized field configurations topologically distinct from the vacuum that can be only stable in the presence of four-derivative interactions, which could very well ensue from thermal effects.The main goal of this project is to improve the accuracy of the EFT description of FTQFT as well as to analyse the impact of higher-order corrections on PT and GW parameters and also, on a different note, on the potential existence of skyrmions inhabiting only at high temperatures. To overcome the numerous difficulties, I will combine innovative ideas inherited from a variety of fields, including scattering-amplitude techniques or functional perturbative methods.