• 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
4,973 questions , 2,138 unanswered
5,333 answers , 22,596 comments
1,470 users with positive rep
812 active unimported users
More ...

  T duality under a small fluctuation of the compact dimension

+ 1 like - 0 dislike

How do small perturbations around the compact dimension affect T duality. What happens if I chose a compactification of the nature $r+\delta r$. And what keeps the compact dimension stable, i.e from expanding into a large dimension or imploding into itself.

This post imported from StackExchange Physics at 2015-03-23 11:10 (UTC), posted by SE-user Prathyush
asked Jun 15, 2013 in Theoretical Physics by Prathyush (705 points) [ no revision ]

1 Answer

+ 3 like - 0 dislike

T-duality says that the radius $r$ is equivalent to $\alpha' / r$. So $r+\delta r$ is also equivalent to $\alpha'/(r+\delta r)$, too. If the radius fluctuates, so does its T-dual radius.

The radius itself, usefully written as $\sqrt{\alpha'}\exp(\phi_R)$, is a "modulus", a scalar field that has no potential (i.e. all conceivable values are equally allowed: this implies that the scalar field is massless around any point and produces new long-range forces that would invalidate the equivalence principle - the experimentally verified principle that all objects accelerate by the same acceleration in a gravitational field) in non-realistic vacua but a potential is generated in realistic ("stabilized") vacua. In the latter vacua, $r=r_0$ chooses a particular value for which $V'(r_0)=0$, the potential has to be minimized.

One may still describe the same point using $\tilde r_0 =\alpha' / r_0$ but we usually pick the larger among these two T-dual values because large compactification radii (longer than the string length) are those in which string theory agrees with the low-energy effective field theory more directly (the excited strings may be neglected for many purposes).

What are the physical reasons that generate such a potential is an extensive technical topic that has to be solved mostly independently in separate classes of the string vacua. Quite generally, too simple or too supersymmetric vacua tend to have some exact moduli but the most generic SUSY-breaking stationary point has no moduli left. People have found "minor" deformations of SUSY-preserving vacua that are nevertheless fully stabilized.

This post imported from StackExchange Physics at 2015-03-23 11:10 (UTC), posted by SE-user Luboš Motl
answered Jun 15, 2013 by Luboš Motl (10,278 points) [ no revision ]
Thank you, This is exactly what I was looking for.

This post imported from StackExchange Physics at 2015-03-23 11:10 (UTC), posted by SE-user Prathyush

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