Publication : t19/229

Abstract:
Paraphrasing Alexander Polyakov, "Conformal Field Theory is a way to learn about elementary particles by studying boiling water". There is a technical statement behind this joke: Euclidean Conformal Field Theory, under certain conditions, can be rotated to the Lorentzian signature, and vice versa. This means that even statistical physicists studying finite-temperature phase transitions on a lattice should learn about the Minkowski space! The goal of this course will be to explain various classical and recent results pertaining to this somewhat surprising conclusion. * Plan of the course: - Elementary introduction to Euclidean CFT in d>2 dimensions - the Osterwalder -Schrader theorem about the Wick rotation of general reflection-positive Euclidean Quantum Field Theories, and its limitations - the Luescher-Mack theorem about continuation of CFT correlation functions to the Lorentzian cylinder, and its limitations - recent results about the analytic structure of Lorentzian CFT correlators. More information: Course URL: https://courses.ipht.fr/?q=en/node/226 Related references: https://arxiv.org/abs/2001.08778 and https://arxiv.org/abs/2104.02090 .

Lecture-notes-Rychkov-IPHT.pdf