• 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.


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


(propose a free ad)

Site Statistics

202 submissions , 160 unreviewed
4,981 questions , 2,140 unanswered
5,340 answers , 22,629 comments
1,470 users with positive rep
813 active unimported users
More ...

  Relation between conformal blocks and Belyi functions

+ 3 like - 0 dislike

Belyi functions are maps from Riemann surfaces to $C\mathbb{P}^1$ ramified exactly at three points. Four point Virasoro conformal block on a sphere as a function of the cross-ratio $x$  is believed to posses singularities only at three points. My question is whether the generic four-point Virasoro conformal block on a sphere is a Belyi function? I am also quite interested in references where conformal blocks might be analysed from this point of view.

asked Feb 15, 2016 in Theoretical Physics by Weather Report (240 points) [ no revision ]

How do you use the 4-point function to construct a map $\Sigma \to \mathbb{CP}^1$?

@RyanThorngren  Well, the 4-pt conformal block, being roughly the holomorphic part of the 4-pt correlation function, as a function of the projective invariant $x$ lives on a 3-punctured sphere (Riemann surface) and takes values in complex numbers ($\mathbb{CP^1}$).

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:
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).
To avoid this verification in future, please log in or register.

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

Your rights