• 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
5,054 questions , 2,207 unanswered
5,347 answers , 22,728 comments
1,470 users with positive rep
818 active unimported users
More ...

  Orbifold with discrete torsion

+ 1 like - 0 dislike

I'm trying to understand some of the early works of Vafa and Witten [1-3]. The way I look at orbifolds is they are the quotient space $M/G$. This is simply a quotient manifold when the action of $G$ on $M$ does not have any fixed points, but if it does then this is not a manifold but an orbifold. I don't see how exactly "orbifolding" takes care of the singularities?

And what exactly is an orbifold with discrete torsion ? Despite many research I could not find any source where orbifolding or orbifolds with discrete torsion is introduced and discussed in a physics point of view. Any reference? Thanks!

[1] Vafa, Witten; On Orbifolds with Discrete Torsion

[2] Vafa; Modular invariance and discrete torsion on orbifolds

[3] Dixon, Harvey, Vafa, Witten; Strings on orbifolds

This post imported from StackExchange Physics at 2015-10-31 22:05 (UTC), posted by SE-user Jon Snow

asked Oct 29, 2015 in Theoretical Physics by Jon Snow (15 points) [ revision history ]
edited Oct 31, 2015 by Dilaton
To answer the first question I would suggest to look at Becker, Becker, Schwarz, Chapter 9 and at Vafa's review hep-th/0410178.

This post imported from StackExchange Physics at 2015-10-31 22:05 (UTC), posted by SE-user g3n1uss
Thanks! Schwarz was a bit helpful.

This post imported from StackExchange Physics at 2015-10-31 22:05 (UTC), posted by SE-user Jon Snow

2 Answers

+ 3 like - 0 dislike

What came to be called "discrete torsion" is simply the data that makes the B-field gerbe be equivariant over the orbifold. This was clarified by Eric Sharpe, see the references here:

Eric Sharpe,

 Discrete Torsion and Gerbes I (arXiv:hep-th/9909108)

 Discrete Torsion and Gerbes II (arXiv:hep-th/9909120)

 Discrete Torsion, Quotient Stacks, and String Orbifolds (arXiv:math/0110156)

answered Nov 2, 2015 by Urs Schreiber (6,095 points) [ revision history ]
+ 0 like - 0 dislike

I can only answer the mathematical part of your question (or make a stab at it). We could say that by describing a space as an orbifold, the singularities are taken care of by somehow declaring them to be under control.

Where a manifold is a topological space that may be very complicated, but locally looks very nice, namely like $\mathbb R^n$, an orbifold locally still looks very nice, though slightly less so (or rather, slightly more general), namely like the orbit space of $\mathbb R^n$ under the action of a finite group.

In reality this local quotient may still look like $\mathbb R^n$, and the local, linear group action is part of the orbifold atlas, so actually it is an additional structure on the space.

An intermediate class of spaces is that of manifolds with boundary. This is a space that locally looks like a Euclidean half-space.

Rather than saying that an orbifold is a space of the form $M/G$, I would say that an example (the main example) of an orbifold is a quotient space $M/G$ (where $M$ is a manifold and the group action is sufficiently good).

This post imported from StackExchange Physics at 2015-10-31 22:05 (UTC), posted by SE-user doetoe
answered Oct 29, 2015 by doetoe (125 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:
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