I was wondering if there are any string theory experts on here. I'm studying the subject from a textbook (Barton Zweibach) and am likely to have a lot of questions. If there is anyone, I would be eternally grateful for any help they can give from time to time.

 

First up:

 

The action for a relativistic string (Nambu-Goto action) is the (2D) area of the string. This contrasts with the space-time action in general relativity, which is the volume integral of the Ricci scalar. Intuitively, I would have thought that the two actions should be the same. I know they're different objects, but why the curvature integral for one and just the area / volume for the other?

 

Cheers,

Jonathan

Edited May 23, 201510 yr by JonathanApps

General relativity in 1+1 dimensions is misleading as a model for more dimensions. The field equations reduce to equations involving topological invariants and not the local geometry. Thus you need something different for two dimensional theories.

Cheers. That makes some sense

 

Second question:

 

In the NG action we vary the coordinates of the string in the embedding space X^{\mu} to find the extremum of the action.

That's fine for spatial components but I don't get how we can vary X^{0} (the time component).

 

Explicitly this is \delta t(\tau, \sigma)

 

where \tau and \sigma are timelike and spacelike coorinates in the 2D string repectively. In the static gauge, at least,

 

\tau = t, everywhere on the string

 

so how on earth can we VARY the function t(\tau)? It doesn't make sense. Even if t and \tau aren't the same (some other gauge),

I can't see that \delta X^{0} is physical or necessary. At most it would indicate a reparameterisation of \tau and \sigma....?

 

No Latex here - I've temporarily forgotten how to get it. Apologies, and promise to get it working in the future.

Cheers.

The usual thing to do is look at the equations of motion without fixing a gauge and then see what the equations reduce to once a gauge is fixed.

 

 

No Latex here - I've temporarily forgotten how to get it. Apologies, and promise to get it working in the future.

Cheers.

Use latex enclosed in [ ] at beginning [/] at end with latex word enclosed.

 

[latex]example[/latex]

Use the quote function on the example

[latex]x^2[/latex]

gives

 

[latex]x^2[/latex]

There is a tutorial here - [topic=http://www.scienceforums.net/topic/3751-quick-latex-tutorial/]A Quick Latex Tutorial[/topic]

Hmm .. the topic link BBCode no longer works. Nor does noparse tags.

 

http://www.scienceforums.net/topic/3751-quick-latex-tutorial/''>http://www.scienceforums.net/topic/3751-quick-latex-tutorial/'>http://www.scienceforums.net/topic/3751-quick-latex-tutorial/

While I've looked over string theory time to time. I certainly wouldn't count myself an expert in string theory. Usually I refer to this article.

https://www.coursehero.com/file/6445491/Intro-to-String-Theory-G-terHooft/