• 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.


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


(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 ...

  How can we demand $N=2$ supersymmetry on the worldsheet?

+ 2 like - 0 dislike

I have been trying to understand why one should look into $c=9, N=2$ superconformal models like the Gepner models or the Kazama-suzuki models, and I am quite confused..

This is what I understood from the arguments I've seen: (mainly from [1])

The usual way to deal with the $6$ spacetime dimensions which we do not observe in reality is by assuming that we can write the $10$-dimensional spacetime manifold as a product $M_4 \times K$, where $M_4$ is Minkowski space together with the $4$-dimensional superstring action with $4$ free bosons and $4$ free fermions, forming a $c= 4\times \frac{3}{2} = 6$, $N=1$ superconformal field theory, and the six dimensional manifold $K$ is called the internal manifold and has to be compactified. It's field theory must be supersymmetric and have central charge $c=15-6=9$.

In order to ensure $\mathcal{N}=1$ spacetime supersymmetry, one forces both the internal and the external CFTs to actually be $N=2$ SCFTs: the spectral flow plays the part of spacetime supersymmetry  generator $Q$.
Therefore, if we want to understand the internal manifold, we should study $c=9$, $N=2$ SCFTs.

My problems with this:

  1. We deduced that $c=9$ because we used that the superstring action was just an action with free bosons and free fermions (the RNS action). This action is not $N=2$ supersymmetric (only $N=1$), so by demanding the theory to have $N=2$ SUSY don't we have to throw away all the results we obtained from the RNS superstring? In particular, $c\ne 15$ if $N=2$, because in that case we would have two fermionic superpartners for each boson, not one.
  2. This seems to ensure 10D spacetime SUSY, but don't we also want 4D spacetime SUSY? 
  3. What is the connection between this and the Calabi-Yau approach? Is ine approach more general than the other? Do these SCFTs somehow correspond to specific CY manifolds?

Please answer if even if you only know the answer to one of my questions.
Thank you.


[1] Greene, B. (1997). String theory on calabi-yau manifolds.
arXiv preprint hep-th/9702155.

asked Oct 4, 2019 in Theoretical Physics by Soap (40 points) [ revision history ]

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).
Please complete the anti-spam verification

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

Your rights