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
5,082 questions , 2,232 unanswered
5,353 answers , 22,789 comments
1,470 users with positive rep
820 active unimported users
More ...

  Two loop corrections to T-duality

+ 4 like - 0 dislike
1359 views

T-duality for Type II string theory is conveniently encoded in the Buscher rules, a set of transformations for the metric, Kalb-Ramond field, and dilaton which implements T-duality:

\[\hat{g}_{\bullet \bullet} = \frac{1}{g_{\bullet \bullet}}\] \[\hat{g}_{\mu \bullet} = \frac{B_{\mu \bullet}}{g_{\bullet \bullet}}\] \[\hat{g}_{\mu \nu} = g_{\mu \nu} - \frac{1}{g_{\bullet \bullet}} \left( g_{\mu \bullet} g_{\nu \bullet} - B_{\mu \bullet} B_{\nu \bullet} \right)\] \[\hat{B}_{\mu \bullet} = \frac{g_{\mu \bullet}}{g_{\bullet \bullet}}\] \[\hat{B}_{\mu \nu} = B_{\mu \nu} - \frac{1}{g_{\bullet \bullet}} \left( g_{\mu \bullet} B_{\nu \bullet} - g_{\nu \bullet} B_{\mu \bullet} \right)\]

The Buscher rules are consistent with the required vanishing of the beta functions, at least up to the one-loop level, as shown here. On the other hand, this paper (and others) suggest that the normal Buscher rules are inconsistent with the vanishing of the two loop beta function. The required corrections are known as the two-loop corrections. I have found a few papers which compute the corrections for specific backgrounds, but I am looking for a reference in which the two loop corrections are computed for an arbitrary background (with abelian isometry).

asked Apr 6, 2016 in Theoretical Physics by Mark Bugden (105 points) [ revision history ]
edited Apr 7, 2016 by dimension10

First question - no idea how to put LaTeX into a post :S

Hi Mark, welcome to PhysicsOverflow !

As described here

http://physicsoverflow.org/faq#a15446

You can for example use the TEX button in the middle of the toolbar of the editor to write LaTex.

@Dilaton As far as i can see the source for this question looks fine. Is there a bug somewhere that prevents the post from being displayed correctly? Could somebody more experienced maybe have a look?

@Heterotic yes it looks like a strange bug to me, I have reported it ...

It was in a <pre> environment. Fixed. Sorry for the delay with it.

Thanks for fixing that :)

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$\hbar$ysicsOverfl$\varnothing$w
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
...