Conformal field theories (CFTs) are special kinds of quantum field theories with enhanced spacetime symmetry, relevant in a variety of systems ranging from condensed matter to quantum gravity. par In these lectures we shall discuss CFTs in general spacetime dimension and then focus on the so-called conformal bootstrap, which highly constrains the structure of these theories. This will include a derivation of various necessary concepts such as the OPE, crossing symmetry and conformal blocks. We will then describe how the modern bootstrap reformulates crossing symmetry as a numerical problem that can be systematically studied and solved on a computer. Finally we will show how these methods have been used to achieve state-of-the-art results on important problems in strongly coupled physics such as the three dimensional Ising model.

LPTHE (Jussieu) and CERN (Genève)