Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Conformal blocks in 2D CFTs

+ 2 like - 0 dislike
1137 views

I have studied conformal field theories in two dimensions and I understand the basic idea behind conformal blocks too. But I never completely realized what they are when it comes to computing them. Can someone explain at least one concrete example or refer to some articles where it has been done for a particular theory.

This post imported from StackExchange Physics at 2015-11-01 18:14 (UTC), posted by SE-user pinu
asked Jul 22, 2015 in Theoretical Physics by Physics Moron (285 points) [ no revision ]
Possible duplicate: physics.stackexchange.com/q/1799/2451

This post imported from StackExchange Physics at 2015-11-01 18:14 (UTC), posted by SE-user Qmechanic

1 Answer

+ 1 like - 0 dislike

It can be rather involved. A lot of technical progress as been on this subject leading up to the modern conformal bootstrap work. Something you can exploit is that these functions should behave like correlation functions and thus are eigenfunctions of the conformal Casimir. That gives you differential equations which in some cases, especially in $D=2$ and $D=4$, you can solve.

See: http://arxiv.org/abs/hep-th/0309180 and http://arxiv.org/abs/1108.6194

This post imported from StackExchange Physics at 2015-11-01 18:14 (UTC), posted by SE-user SM Kravec
answered Jul 22, 2015 by SM Kravec (60 points) [ no revision ]
Thanks a lot! References look very useful. Can you say something about what is virasoro conformal block..

This post imported from StackExchange Physics at 2015-11-01 18:14 (UTC), posted by SE-user pinu
So, as you may know, in 2D conformal symmetry is large. The above is speaking (mostly) about the \emph{global} conformal group, with generators $L_{-1} , L_{0} , L_{1}$, and its primaries as that's what relevant for $D > 2$. In 2D CFT these are often referred to as "quasi-primaries". Virasoro conformal blocks are the objects which contain information about decedents from primaries of the full Virasoro symmetry. Again they're difficult to compute, see arxiv.org/abs/1502.07742, arxiv.org/abs/1501.05315, and the phone book.

This post imported from StackExchange Physics at 2015-11-01 18:14 (UTC), posted by SE-user SM Kravec

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysic$\varnothing$Overflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...