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 ...

  examples of heterotic CFTs

+ 9 like - 0 dislike
528 views

I'm trying to get a global idea of the world of conformal field theories.

Many authors restrict attention to CFTs where the algerbas of left and right movers agree. I'd like to increase my intuition for the cases where that fails (i.e. heterotic CFTs).

What are the simplest models of heterotic CFTs?


There exist beautiful classification results (due to Fuchs-Runkel-Schweigert) in the non-heterotic case that say that rational CFTs with a prescribed chiral algebras are classified by Morita equivlence classes of Frobenius algebras (a.k.a. Q-systems) in the corresponding modular category.

Is anything similar available in the heterotic case?

This post has been migrated from (A51.SE)
asked Nov 21, 2011 in Theoretical Physics by André_1 (215 points) [ no revision ]
I guess you are aware of the article http://arxiv.org/abs/math-ph/0009004 where Prof. Rehren includes the heterotic case from the beginning....

This post has been migrated from (A51.SE)
That's a nice paper... I was more looking for actual examples of heterotic CFTs: ones that are particularly easy to describe, or that are specially relevant for other purposes.

This post has been migrated from (A51.SE)

2 Answers

+ 4 like - 0 dislike

The first example that comes to mind is the heterotic string worldsheet theory, described in the original paper of Gross, Harvey, Martinec, & Rohm.

I don't know if there is a classification result for rational heterotic CFTs which generalizes the FRS result. However, if you want to understand the global space of CFTs, you may not want to emphasize rational CFTs anyways. Most CFTs aren't rational.

This post has been migrated from (A51.SE)
answered Nov 22, 2011 by user388027 (415 points) [ no revision ]
Thanks for your answer. I'm now reading this article. If I understand, there's 2 CFTs constructed: one compactified on the $E_8\times E_8$-torus, and one compactified on the $\Gamma_{16}$-torus. Quote: "In order to achieve a consistent string theory involving only left-moving coordinates $X^I$ to cancel anomalies and to preserve the geometrical structure of string interactions, we are forced to compactify on a special torus". Do I understand that, as far as constructing CFTs is concerned, I may disregard those constraints and compactify on any torus? (or not compactify at all)

This post has been migrated from (A51.SE)
+ 0 like - 0 dislike

I just found by incidence a simple example in some proceedings of Böckenhauer and Evans below. Namely for $\mathrm{Spin}(8\ell)_1$ (so $D_{4\ell}$ lattice) with $\ell=1,2,\ldots$ there exist modular invariants, which should give rise to heterotic models (by Rehrens paper).

see section 7 in http://books.google.de/books?id=yV_RlDznAu8C&lpg=PA120&ots=HwZm5KlDCW&pg=PA119#v=onepage

This post has been migrated from (A51.SE)
answered Nov 23, 2011 by Marcel (300 points) [ no revision ]

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$\hbar$ysicsOverf$\varnothing$ow
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
...