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

Please welcome our new moderators!

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

122 submissions , 103 unreviewed
3,497 questions , 1,172 unanswered
4,544 answers , 19,342 comments
1,470 users with positive rep
408 active unimported users
More ...

Spectrum of Free Strings

+ 3 like - 0 dislike
8 views

As far as I understand, both in bosonic and superstring theory one considers initially a free string propagating through D-dimensional Minkowskispace. Regardless of what quantization one uses, at the end one arrives at a spectrum, where the excitations are classified among other things by the representation of the Poincaré group (or maybe a cover) they are in.

This enables one to speak of their masses, but seems to make the construction very dependent on the background. Do massless modes remain massless in an other background, for example? And how does one define the mass of excitations in this case? As far as I can tell even after compactification, at least 4 dimensions are usually left to be some symmetric space (so there is probably some notion of mass) and the space of harmonic forms on the calabiyau is supposed to correspond to the space of massless excitations (of a low energy effective theory?).

Moreover D'Hoker states in his lectures in Quantum Fields and Strings, that he is not aware of a proof that in a general background a Hilbertspace can be constructed. Is there still none?

I apologize if these questions are too elementary or confused. They were not adressed in the string theory lectures I attended.

This post has been migrated from (A51.SE)
asked Mar 22, 2012 in Theoretical Physics by orbifold (190 points) [ no revision ]
Cross-posted from http://physics.stackexchange.com/q/22159/2451

This post has been migrated from (A51.SE)

1 Answer

+ 2 like - 0 dislike

The massless spectrum depends on the background. What one usually means by masses in a background describing a compactification are masses in the non-compact flat space (most often 4D). That is, you take the momentum in the non-compact directions, you square it and you find the mass.

About your second question, whenever the background has a light-like Killing vector you can build a light-cone Hamiltonian and a Hilbert space. I'm not sure if there are more general situations where a Hilbert space description is available. For a general time-dependent background, I don't think much is known.

This post has been migrated from (A51.SE)
answered Mar 22, 2012 by Sidious Lord (160 points) [ no revision ]
Good answer, +1. I still think that one may expand and/or re-emphasize some points. When one determines masses, they're not just "defined". The mass spectrum of particles contains much of the information about the theory and it has to be calculated; of course that this calculation depends on the background. The massless spectrum depends on the background in field theory, too. It's not a "disadvantage" in any sense; it's a tautology. We're just saying that the most important feature of the dynamical laws, the spectrum, depends on the dynamical laws governing individual particles/strings.

This post has been migrated from (A51.SE)

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$\hbar$ysicsOve$\varnothing$flow
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
...