• 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 ...

  T-folds and non-geometric backgrounds

+ 4 like - 0 dislike

Recently I attended a talk where the speaker introduced and used some notions of T-folds as non-geometric backgrounds. Although I had heard about doubled geometry, double field theory and about doing physics at both $T_p\mathcal{M}$ and $T_p^*\mathcal{M}$ I knew no details. One of the astonishing things I saw was that it is possible to construct some generalized metric that includes both $G_{\mu \nu}$ and $B_{\mu \nu}$. This metric is defined on some generalization of a manifold, the T-fold. Ok, what is a T-fold? 

 One thing I would also like to understand is how exactly one constructs this generalized metric from the two fields above? Also, once one has this generalized metric, is it used as a "generalized background"? I understand that if the B filed is turned of one recovers classical geometry but I struggle to understand at an intuitive level what this T-geometry really is. How does this construction help us to do physics and what physics one does in these generalized backgrounds? 

asked Dec 8, 2014 in Theoretical Physics by conformal_gk (3,625 points) [ no revision ]

1 Answer

+ 4 like - 0 dislike

Like a manifold is something obtained by using diffeomorphisms to glue Cartesian spaces together,to something that locally is still an R^n, but not globally anymore, so a T-fold is supposed to be something obtained by using diffeomorphisms and T-duality transformations to glue together type II-spacetime manifolds to something that locally is still a manifold, but not globally anymore

The rough idea and the terminology is due to 

further developed in

An actual mathematical definition is still to be published, but some ideas have been developing. 

A precise global definition of T-folds as principal 2-bundles for the T-duality 2-group described in the nLab entry T-Duality and Differential K-Theory is given in

  • Thomas NikolausT-Duality in K-theory and elliptic cohomology, talk at String Geometry Network Meeting, Feb 2014, ESI Vienna (website)
answered Dec 9, 2014 by Urs Schreiber (6,095 points) [ no revision ]
Hi Urs, thanks for the answer. I am aware of the nLab article but I was hopping for something more specific than what it says there at the same time without having to look at the references since I have no time :) Still thanks

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