String Theory

[JonathanApps]

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, 2015 by JonathanApps

[ajb]

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.

[JonathanApps]

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.

[ajb]

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.

[Mordred]

 

 

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

[imatfaal]

[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/

[Mordred]

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/