Conformal Field Theory, Spring 2025

Syllabus

Lecture videos

The first part of this course focuses on 2d CFT, based on my lecture note. The latter part will cover CFT in higher dimensions, for which I follow 3 notes

1. Yu Nakayama, An Invitation to Higher-Dimensional Conformal Field Theory (SGC Library Vol. 153), written in Japanese. 

2. David Simmons-Duffin, Phys 229ab Advanced Mathematical Methods: Conformal Field Theory

3. 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.
 

1. Conformal Symmetry and Universality

2. Conformal Transformations and Radial Quantization

3. Properties of Hilbert Space and Correlation Functions

4. Ward-Takahashi Identities and Primary Fields

5. Operator Product Expansions and Virasoro Algebras

6. Free Bosons and Fermions

7. Minimal Models

8. Ising Models and Onsager’s Exact Results

9. Non-Invertible Symmetry in Ising Models and Conformal Blocks

10. Zamolodchikov c-Theorem

11. Landau-Ginzburg Models and Renormalization Group Flow

Free scalar theory in Higher Dimensions

12. Representation Theory and Primary Fields in Higher Dimensions

13. Operator Product Expansions in Higher Dimensions

14. Conformal Blocks

15. Conformal Bootstrap