• 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
5,030 questions , 2,184 unanswered
5,344 answers , 22,705 comments
1,470 users with positive rep
816 active unimported users
More ...

  Physical interpretation of superstrings

+ 9 like - 0 dislike

The scalar fields $X^\mu$ in bosonic string theory have a clear physical interpretation - they describe the embedding of the string in spacetime.

Adding fermionic fields on the worldsheet is a generalization for sure, gives fermions in the spectrum, has a smaller critical dimension and no tachyons, that's all good - but I don't see how they can have any physical interpretation as nice as the above for the scalars - isn't everything about how a string moves in spacetime described by the $X^\mu$ part?

This post has been migrated from (A51.SE)
asked Dec 11, 2011 in Theoretical Physics by dbrane (375 points) [ no revision ]
Btw, there's no necessity for a clear geometric interpretation in string theory. As far as I understand, any 2D CFT with vanishing central charge can be regarded as a string theory and some CFTs have no clear interpretation as a sigma model.

This post has been migrated from (A51.SE)

1 Answer

+ 11 like - 0 dislike

The worldsheet fermions have to do with internal degrees of freedom, namely the spin -- therefore better name for the superstring is the more old-fashioned "spinning string" (since worldsheet SUSY should not be confused with spacetime SUSY). The worldsheet fermions generate multiplets of some internal symmetry group. If you want those internal degrees of freedom generated by WS fermions to transform under spacetime Lorentz Transformations, rather than an independent internal symmetry, you need to correlate the Lorentz transformations of the worldsheet bosons and fermions. This is what worldsheet SUSY does for you.

All of this is not specific to string theory. If you want to first-quantize a field theory, a "bosonic" worldline theory will give you a (free) scalar field theory. Adding fermions and the corresponding worldline supersymmetries will generate (free) higher spin fields. It is probably a useful exercise to get e.g. classical (free) Maxwell field from a (N=2 SUSY) worldline theory in order to appreciate precisely what the worldsheet structures mean precisely. Wish I had a good reference, but maybe someone can help me out.

This post has been migrated from (A51.SE)
answered Dec 11, 2011 by Moshe (2,405 points) [ no revision ]
I think there's also an alternative point of view, namely that the string lives in a superspace and the fermions are the odd coordinates

This post has been migrated from (A51.SE)
Yes, that is the Green-Schwarz formulation of spacetime supersymmetric strings. But I think the question was about the slightly more familiar R-NS string, and in particular spacetime SUSY is not implied.

This post has been migrated from (A51.SE)

Regarding references to the world-line formalism (including local SUSY on the world-line to account for spin degrees of freedom), there is a series of papers by Henneaux and Teitelboim treating that subject. For instance, the paper "Relativistic Quantum Mechanics of Supersymmetric Particles". The question should also be addressed in their book, "Quantization of Gauge Systems".

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).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights