Thermal effects in conformal field theories

Conformal Field Theories (CFTs) are special classes of quantum field theories thatfind applications ranging from critical phenomena to theories of quantum gravity viaholography. Understanding thermal effects in CFTs is crucial: criticality is experimen-tally probed at finite temperature, and, from the holographic perspective, the studyof thermal CFTs is dual to the study of black holes in Anti-de Sitter space. In thisthesis, we explore the kinematics and dynamics of finite-temperature CFTs by analyz-ing broken and unbroken symmetries and adapting various analytical and numericalbootstrap approaches to finite-temperature correlation functions. These methods arenon-perturbatively valid and can be tested against exactly solvable models, such asfree theories and two-dimensional systems, as well as compared with perturbative cal-culations. The main applications discussed in this thesis concern one- and two-pointfunctions and the free energy density in the O(N) models in three dimensions, withparticular focus on the 3d Ising, XY, and Heisenberg models (N = 1,2,3).