Operator state mapping in Conformal Field Theory

In summary, For those looking for reading material on operator state mapping in conformal field theory, the bible on the subject by Di Francesco is a comprehensive resource. For a more concise and accessible option, David Tong's lecture notes (specifically page 99+) are also recommended. The amount of material needed to understand the mapping may vary depending on its intended use, but starting with Tong's notes is a good starting point. Other introductory articles on CFTS may also be helpful.
  • #1
kau
53
0
can anyone suggest any good reading material on operator state mapping in conformal field theory? I know only elementary field theory... So it might be helpful ifsomeone suggest a book where it is done in little detailed way..
 
Physics news on Phys.org
  • #2
As usual for Conformal field theory, the relevant material is almost assuredly found in the bible on the subject by Di Francesco.
You can also review the following lecture notes online by David Tong:
http://www.damtp.cam.ac.uk/user/tong/string/four.pdf (page 99+)
 
  • #3
ok.thanks for your suggestion. can you tell me exactly how far i should cover to understand it in order to understan this mapping.. since that book is a very big in volume... thanks..
 
  • #4
It depends of course on what you want to use it for. If you need to understand the mapping for its applications in something like Ads/CFT, then Tong's lecture notes should suffice, if you are interested in the far more general applications then you'll have to read through the relevant material/sections in Di Francesco. I'd try Tong's notes first, (and there are plenty of other intros/review articles on CFTS) as its a little less formalism rich.
 

1. What is operator state mapping in Conformal Field Theory?

Operator state mapping is a mathematical technique used in Conformal Field Theory (CFT) to study the correlation functions of operators. It allows us to map the states of a CFT onto a Hilbert space, making it possible to calculate the correlation functions between these states.

2. How does operator state mapping work in CFT?

Operator state mapping works by using the conformal symmetry of a CFT to relate the correlation functions of operators at different points on a complex plane. This allows us to express the correlation functions in terms of a set of conformal blocks, which are functions of the conformal dimensions of the operators involved.

3. What is the significance of operator state mapping in CFT?

Operator state mapping is significant because it allows us to study the behavior of a CFT at different points on the complex plane. This provides a powerful tool for understanding the underlying structure of the theory and making predictions about its behavior.

4. What are some applications of operator state mapping in CFT?

Operator state mapping has a wide range of applications in CFT, including the calculation of correlation functions and the study of scaling dimensions and operator product expansions. It is also used in the study of critical phenomena, string theory, and topological quantum field theory.

5. How does operator state mapping relate to other techniques used in CFT?

Operator state mapping is closely related to other techniques used in CFT, such as conformal bootstrap and conformal perturbation theory. These methods all rely on the conformal symmetry of a CFT and provide complementary approaches to studying the theory.

Similar threads

A Is The Seiberg-Witten Map Unique?
    • High Energy, Nuclear, Particle Physics
Replies
1
Views
823
I Field theories in 4 dimensions
    • High Energy, Nuclear, Particle Physics
Replies
7
Views
2K
A Primaries, descendents and transformation properties in CFT
    • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
A The Quantum State as a Function of The Quantum Field
    • Quantum Interpretations and Foundations
Replies
13
Views
676
A Conformal Window: Understanding the Basics
    • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
A Measurement in QFT: Mapping Fields to Theory's Math Formalism
    • Quantum Physics
Replies
31
Views
2K
A The double copy of (2,0) theory
    • Beyond the Standard Models
Replies
1
Views
2K
A QFT with vanishing vacuum expectation value and perturbation theory
    • Quantum Physics
Replies
3
Views
1K
A Field operator eigenstates & Fock states(Hatfield's Sch rep)
    • High Energy, Nuclear, Particle Physics
Replies
2
Views
1K
A Problem with fields and operators in holographic duality
    • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top