• 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

204 submissions , 162 unreviewed
5,024 questions , 2,178 unanswered
5,344 answers , 22,683 comments
1,470 users with positive rep
815 active unimported users
More ...

  Massive states of the closed bosonic string fitting into a representation of $SO(D-1)$

+ 3 like - 0 dislike

It is usually shown in the literature that massive light-cone gauge states for a closed bosonic string combine at mass level $N=\tilde{N}=2$ into representations of the little group $SO(D-1)$ and then it is claimed (see, for example, David Tong's lecture notes on string theory) that it can be shown that ALL excited states $N=\tilde{N}>2$ fit into representations of $SO(D-1)$. Is there a systematic way of showing this, as well as finding what those representations are? Maybe it was discussed in some papers, but I couldn't find anything remotely useful, everyone just seems to state this fact without giving a proof or a reference. 

For OPEN strings at $N=3$ level the counting is:
$$(D-2)+(D-2)^2+\binom{D}{2} = \frac{(D-1)(D-2)}{2}+\left(\binom{D+1}{3}-(D-1)\right),$$
where on the LHS are $SO(24)$ representations, and on the RHS are $SO(25)$ representations. I'd like to find the same type of counting for CLOSED strings at any mass level $N,\tilde{N}>2$, as claimed by Tong above.

asked Jan 21, 2017 in Theoretical Physics by thinice (15 points) [ revision history ]
edited Jan 21, 2017 by thinice

String Theory is Lorentz-invariant (in critical dimension), so string states must furnish representations of the full Lorentz group. Isn't it enough?

@AndreyFeldman, I'm guessing OP wants to see an explicit calculation/proof, e,g, these and these string states lump together to form an irrep of the explicitly written down Poincare charges.

@JiaYiyang I think that I cited the proof.

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