Conformal Field Theory intro.

In summary, there are a few great resources for learning about Conformal Field Theory, including introductory notes by Ginsparg and Schellekens, as well as the comprehensive book "Conformal Field Theory" by Di Francesco, Mathieu, and Senechal. For those interested in its application to string theory, Polchinski's "String Theory Vol 1" may also be helpful. Additionally, there are some condensed matter resources such as "Introduction to conformal invariance and its applications to critical phenomena" by Christe and Henkel, and "Applied conformal field theory" by Ginsparg.
  • #1


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Anyone got some introductory notes / books on Conformal Field Theory for someone who know Quantum Field Theory at the level of Peskin's book?

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  • #2
I highly recommend Ginsparg as an introductory set of notes:

As a good second source, which you should keep aside (but is a little less detailed), try Schellekens notes:

In the end there is only one real Tome on conformal field theory, which is the book by Di Francesco, Mathieu and Senechal (title: Conformal Field Theory). But that will take you at least a whole year to read back-to-back. Do note that this book is about CFT - not about its applications (for instance, it hardly involves supersymmetry).

In the context of String theory you should also look for Polchinski, String Theory Vol 1.
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  • #3
Hi and thank you! Yeah, a book with almost 900pages seems really cumbersome ;)
  • #4
xepma makes a point however : it depends whether you want to study conformal field theory by itself, or if you have a specific application for it. There are numerous books on it in condensed matter field theory for instance.

A shorter review is in RMP Vol 34 num 3 (Jul 1962) page 442
  • #5
Well I am mostly interested in its application to string theory AND condensed matter
  • #6
For condensed matter, I have "Introduction to conformal invariance and its applications to critical phenomena" by Christe and Henkel (CUP 1993) (but as you know, I am no condensed matter aficionado, so there may be better references around)

Also, there is "Applied conformal field theory" by Ginsparg (Les Houches 1989)

1. What is Conformal Field Theory (CFT)?

Conformal Field Theory is a branch of theoretical physics that studies the behavior and properties of quantum field theories under conformal transformations. These transformations preserve angles, but not necessarily distances, and are commonly used to study systems that exhibit scale-invariance.

2. What are the applications of CFT?

CFT has a wide range of applications in theoretical physics, including condensed matter physics, statistical mechanics, string theory, and particle physics. It has been used to study phase transitions, critical phenomena, and quantum gravity, among other topics.

3. What are the main features of CFT?

CFT is a powerful tool for studying quantum field theories because it allows for the calculation of correlation functions, partition functions, and other quantities of interest. It also provides insight into the universal properties of critical systems and the behavior of quantum systems at extreme conditions.

4. How is CFT related to other areas of physics?

CFT is closely related to other areas of theoretical physics, such as conformal symmetry, conformal bootstrap, and holography. It also has connections to other mathematical fields, including complex analysis, algebraic geometry, and representation theory.

5. What are the challenges in studying CFT?

One of the main challenges in studying CFT is its non-perturbative nature, which makes analytical calculations difficult. Another challenge is the lack of a complete understanding of the underlying principles of CFT, which limits its applicability to certain systems. Additionally, the mathematical techniques used in CFT can be quite complex and require a strong background in advanced mathematics.

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