Course description
The course will take place on Tuesdays from 14-16 in room 119 during the first half
of the spring semester (22.2. - 5.4.2022).
Conformal field theory (CFT) is an ubiquitous subject in modern theoretical
physics. Every local quantum field theory approaches a CFT in the large- and
small-distance limits, and even the study of quantum gravity is related to it
through the AdS/CFT correspondence. CFT is also one of the rare frameworks in
which quantum field theory can be studied outside the realm of perturbation
theory.
This is an introductory course in which the students will learn what is conformal
field theory, why it is special, and get a glimpse of modern developments. The
course will begin with a non-perturbative formulation of quantum field theory
(Wightman functions, spectral representation), and then gradually focus on
understanding the implications of scale and special conformal symmetry. The study
of practical tools (embedding space formalism, radial quantization, state-operator
correspondence, conformal blocks) will finally lead to the formulation of the
modern conformal bootstrap and a review of its most recent results. Some advanced
topics will be discussed depending on the students' interests (Virasoro symmetry
in 2 dimensions, UV and IR divergences, Mellin representation, superconformal
symmetry).
Prerequisites:
The only prerequisite for the course is basic knowledge of quantum field theory.
Lecturer:
Marc Gillioz
