Conformal Field Theory, Spring 2025
Syllabus
Lecture videos
Course Materials
The first part of this course focuses on 2d CFT, based on my lecture notes. The latter part will cover CFT in higher dimensions, for which I follow 3 notes.
- Yu Nakayama, An Invitation to Higher-Dimensional Conformal Field Theory (SGC Library Vol. 153), written in Japanese.
- David Simmons-Duffin, Phys 229ab Advanced Mathematical Methods: Conformal Field Theory.
- Slava Rychkov, EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions.
Due to copyright restrictions, I will not be uploading the lecture notes publicly for higher-dimensional CFT.
Lecture 1 Conformal Symmetry and Universality
Lecture 2 Conformal Transformations and Radial Quantization
Lecture 3 Properties of Hilbert Space and Correlation Functions
Lecture 4 Ward–Takahashi Identities and Primary Fields
Lecture 5 Operator Product Expansions and Virasoro Algebras
Lecture 6 Free Bosons and Fermions
Lecture 7 Minimal Models
Lecture 8 Ising Models and Onsager’s Exact Results
Lecture 9 Non-Invertible Symmetry in Ising Models and Conformal Blocks
Lecture 10 Zamolodchikov c-Theorem
Lecture 11 Landau–Ginzburg Models and Renormalization Group Flow in Higher Dimensions
Lecture 12 Representation Theory and Primary Fields in Higher Dimensions
Lecture 13 Operator Product Expansions in Higher Dimensions
Lecture 14 Conformal Blocks
Lecture 15 Conformal Bootstrap