Introduction to Conformal Field Theory - Fall 2023
During the fall semester of 2023, I will coordinate an introductory course in Conformal Field Theory. The format of the course will be a `peer-study' course. I will send around material to read, as well as obligatory hand-in exercises on a regular basis. There will be no lectures or office hours due to my time constraints. So it is very improtant for you as students to get togehter and discuss the material as well as the exercises yourselves. So, discussion and collaboration on the exercises is strongly encouraged, though I recuire you to hand in the exercises individually.
During the course, you will be following parts of `Conformal Field Theory', by Di Francesco, P. Mathieu and Sénéchal (Springer, New York, 1997). Please contact me if you do not have acces to this book. The more advanced topics covered during roughly the last quarter of this course will be adjusted according to the interst of the students. For possibilities, see the web-pages for the previous courses: webpage of the 2008 course, webpage of the 2011 course, webpage of the 2013 course and the list below.
This course is an inofficial PhD course, so no precise prerequisites are formulated. The course is geared towards PhD students in theoretical phycics and mathematics. It will be helpful if you worked with quantum field theory before, but this is not necessary.
News
- Welcome to the course!
- Here's the link to a (somewhat tacky) video visualizing conformal transformations.
Points
This course will be a 7.5 point (ECTS) course. In order to receive credit for the course, one has to hand in the problem sets, and receive a pass on all of them.
Topics covered
The basic topics which will be covered are listed below
- Motivation and introduction to conformal invariance
- The Virasoro algebra
- Free bosons and fermions
- Minimal models: structure and correlation functions
- Applications: entanglement entropy and Zamolodchikov's c-theorem
- The Coulomb gas formalism
- Singular vectors and differential equations for correlation functions
- Anyons and topological phases
- CFT on the torus: Modular invariance and the Verlinde Formula
- Extended symmetries: current algebras and the Knizhnik-Zamolodchikov equation
Reading material
During the course, I will refer to my old lecture notes from previous courses. Some material by others that I might use, or that might be interesting, is listed below. These notes all have a somewhat point of view. If you have suggestions for additions, please contact me!
- Lecture notes by J. Cardy
- Lecture notes by J. Fuchs
- Lecture notes by P. Ginsparg
- Lecture notes by A.N. Schellekens
- Entanglement entropy and quantum field theory, P. Calabrese, J. Cardy, J. Stat. Mech. P06002 (2004).
- Entanglement entropy and conformal field theory, P. Calabrese, J. Cardy, J. Phys. A 42 504005 (2009).
Here is an incomplete list of books that I find useful. I have a copy of each, so please contact me if you want to have a look.
- Scaling and renormalizaion in statistical physics (Cambridge lecture notes in physics, Chapter 11), Cardy, Cambridge University Press 2000.
- Conformal field theory (GTCP), Di Francesco, Mathieu, Sénéchal, Springer 1999.
- Conformal invariance and critical phenomena (TMP), Henkel, Springer 1999.
Lecture notes from previous courses
Some lecture notes that I used during a previous course (so, just my lecture notes!). With apology for the handwriting....
- Lecture notes 01.
- Lecture notes 02.
- Lecture notes 03.
- Lecture notes 04. Some notes on the conformal Ward idenity. See in particular section 3.1 of Cardy's lecture notes mentioned under 'Reading material'.
- Lecture notes 05.
- Lecture notes 06.
- Lecture notes 07.
- Lecture notes 08.
- Lecture notes 09.
- Lecture notes 10.
- Lecture notes 11.
- Lecture notes 12.
- Lecture notes 13.
- Lecture notes 14 (entanglement entropy).
Exercise sets for the course
