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

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

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,862 answers , 20,637 comments
1,470 users with positive rep
502 active unimported users
More ...

Explicit calculation of bosonic string Weyl invariance at one loop

+ 2 like - 0 dislike
91 views

I have been trying to do all the calculations in the Green, Schwarz and Witten Superstring Theory textbook.

At the end of chapter 3, the author did one-loop calculation for Weyl invariance for the bosonic string, in section 3.4.2 and 3.4.5. In the latter section more fields were included, and not much calculation detail was given.

The actions are

$S_1=\frac{-1}{4\pi\alpha'}\int d^2\sigma\sqrt h h^{\alpha \beta}\partial_\alpha X^\mu \partial_\beta X^\nu g_{\mu \nu}$

$S_2=\frac{-1}{4\pi\alpha'}\int d^2\sigma \epsilon^{\alpha \beta}\partial_\alpha X^\mu \partial_\beta X^\nu B_{\mu \nu}$

$S_3=\frac{1}{4\pi}\int d^2\sigma \sqrt h \Phi (X^\rho) R^{(2)}$

I consider those one-loop calculations to be very good exercise, but as a beginner in string theory I find myself not able to do them.

Therefore may I ask if there are some notes/papers in literature that give explicit calculation or point out key steps? Thank you very much!


This post imported from StackExchange Physics at 2014-04-14 16:23 (UCT), posted by SE-user Han Yan

asked Dec 14, 2013 in Theoretical Physics by Han Yan (110 points) [ revision history ]
edited Apr 20, 2014 by dimension10
I found a reference but it is not easy to read... I let you judge : Ref paragraph $3.2$ p $21$. Maybe somebody has a simplest reference.

This post imported from StackExchange Physics at 2014-04-14 16:23 (UCT), posted by SE-user Trimok

1 Answer

+ 0 like - 0 dislike

Thanks to @Trimok , the reference he provided gives some detailed calculation. To see one of the missing Feynman diagrams (you can draw others once you understand that) and more detailed calculation of the leading order (not one loop), you can also check http://www.itp.phys.ethz.ch/research/qftstrings/archive/13FSProseminar/LEEre_Guns which gives more useful math tricks.

This post imported from StackExchange Physics at 2014-04-14 16:23 (UCT), posted by SE-user Han Yan
answered Dec 18, 2013 by Han Yan (110 points) [ no revision ]
Yes, seems simpler to read...

This post imported from StackExchange Physics at 2014-04-14 16:23 (UCT), posted by SE-user Trimok

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$\varnothing$ysicsOverflow
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
...