Conformal Field Theory

We sketch the main motivations of CFT, including its applications to statistical physics, high-energy physics, and quantum gravity. We introduce CFT in the bootstrap approach, an axiomatic approach that starts from symmetry and consistency conditions for quantum fields, and deduces crossing symmetry equations for correlation functions. 

 

For most of the course, we specialize to 2 dimensions, where the existence of infinitely many conformal transformations leads to exact solutions of a number of nontrivial CFTs. We study the relevant technical constructions, from the Virasoro algebra to conformal blocks. Solving crossing symmetry and other constraints or assumptions, we obtain CFTs such as minimal models, Liouville theory and loop models. We also introduce CFTs that have extra symmetries beyond conformal symmetry, such as free bosons and Wess-Zumino-Witten models.