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

PO is now at the Physics Department of Bielefeld University!

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

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  String theory: why not use $n$-dimensional blocks/objects/branes?

+ 3 like - 0 dislike
4491 views

I have a basic question: if we use 1d string to replace 0d particle to gain insight of nature in string theory, and advanced to use 2d membranes, can we imagine that using $3$- or $n$-dimensional blocks/objects/branes as basic units in physics theory? Where is the end of this expansion?

This post imported from StackExchange Physics at 2014-03-07 16:32 (UCT), posted by SE-user ahala
asked Jun 3, 2013 in Theoretical Physics by ahala (15 points) [ no revision ]
retagged Apr 19, 2014 by dimension10
Look at en.wikipedia.org/wiki/D-brane

This post imported from StackExchange Physics at 2014-03-07 16:32 (UCT), posted by SE-user ungerade
Possible duplicate: physics.stackexchange.com/q/55431/2451.

This post imported from StackExchange Physics at 2014-03-07 16:32 (UCT), posted by SE-user Qmechanic
it is important to point out that blanket "blocks/objects " will not work. Strings work because the are a multidimensional expansion of the basic harmonic oscillator. So are membranes ( think of drums) . imo any symmetric potential can have the first term a harmonic oscillator. To go to more complicated shapes of potentials, which maybe is a future possibility, still would preclude blocks.

This post imported from StackExchange Physics at 2014-03-07 16:32 (UCT), posted by SE-user anna v
Furthermore, the 2-D case is singled out by the Weyl invariance, a symmetry of the action that only appears if the fundamental object you deal with is 2-Dimensional.

This post imported from StackExchange Physics at 2014-03-07 16:32 (UCT), posted by SE-user Neuneck

2 Answers

+ 3 like - 0 dislike

There can not only, there have to be heavy higher dimensional objects (as for example D-branes) in string theory, as Joseph Polchinski discovered. So it is strictly speaking no longer appropriate to talk about "string theory", since M-theory is now known to relate all the different string theories known before by dualities and which contains these higher dimensional (from points D0, up to space filling D9 branes if spacetime is 10D) objects.

One way to see why these higher dimensional objects have to be there, is because T-duality transforms (among other things) the von Neuman boundary condition of a free floating open string, that are not stuck on anything, to the Dirichlet boundery condition which means that the endpoints are fixed. So there has to be something the strings can stick on, these objects are called D-branes which can be higher dimensional. That's the way Lenny Susskind introduced D-branes in this last lecture of his string course.

D-branes can for among other things be used to model the interactions of the standard model. For example QCD can be described by 3 D-branes, one for each color.

enter image description here

The mesons are strings which do not need to have both ends on the same "color" brane, quarks and anti-quarks are distinguished by the orientation of the string. Interactions take place when strings break and leave new end points on the brane and when two end points come together.

This post imported from StackExchange Physics at 2014-03-07 16:32 (UCT), posted by SE-user Dilaton
answered Jun 3, 2013 by Dilaton (6,240 points) [ no revision ]

Thanks for the nice link Urs, and it is great to see you again here :-)!

+ 3 like - 0 dislike

There are, actually. Dilaton (I don't mean the massless field in the NS-NS sector that determines the coupling constant, nor the $g_{55}$ component of the Kaluza-Klein Spacetime metric tensor) already covered the reason through T-duality, so I will discuss the requirement of $p$-branes imposed by Ramond-Ramond potentials.

The worldsheet of a string can couple to a Neveu-Schwarz B-field: $$q\int_{}^{} {{{h^{ab}}}\frac{{\partial {X^\mu }}}{{\partial {\xi ^a}}}\frac{{\partial {X^\nu }}}{{\partial {\xi ^b}}}B_{\mu \nu }\sqrt { - \det {h_{ab}}} {{\text{d}}^2}\xi } $$

Now, the $q$ is the EM-charge.

The worldsheet of a string can couple to graviton field (spacetime metric): $$m\int_{}^{} {{{h^{ab}}}\frac{{\partial {X^\mu }}}{{\partial {\xi ^a}}}\frac{{\partial {X^\nu }}}{{\partial {\xi ^b}}}g_{\mu \nu }\sqrt { - \det {h_{ab}}} {{\text{d}}^2}\xi } $$

You can change the "$m$" to any way you like, in terms of the tension/Regge Slope parameter/string length etc.

For a dilaton (now, I DO mean the massless field in the NS-NS sector which determines the coupling) field, $${q }\ell _P^2\int_{}^{} {\Phi R\sqrt { - \det {h_{\alpha \beta }}} {\text{ }}{{\text{d}}^2}\xi } $$ Forget the conformal invariance for the time being.

But what about Ramond-Ramond POTENTIALS? All is fine with the Ramond-Ramond Fields, but the Ramond-Ramond Potentials $C_k$are associated with the Ramond-Ramond field $A_{k+1}$ and it is intuitive (and quite clear) that they can't couple similarly to the worldsheet. But it can for a worldhhypervolume, as long as the world-hypervolume is not 2-dimensional. It would then be given by: $${q_{{\text{RR}}}}\int_{}^{} {C_{{\mu _1}...{\mu _p}}^{p + 1}\frac{{\partial {x^{{\mu _1}}}}}{{\partial {\xi ^{{a_1}}}}}...\frac{{\partial {x^{{\mu _p}}}}}{{\partial {\xi ^{{a_p}}}}}{h^{{a_0}...{a_p}}}\sqrt { - \det {h^{{a_0}...{a_p}}}} {{\text{d}}^{p + 1}}\xi } $$

Just note its similarity to the other couplings! Now, maybe this isn't so much of a necessity .as T-duality's switching of Newmann and Dirchilets, but it is still very important!

Edit: It works with 2-branes (membranes) too, but there's no point stopping there, and t-duality exchanging boundary condition becomes an issue. While in 10-dimensional string theories, all these branes are consistent, in 11-dimensional M-theory, only 2-branes and 5-branes are.

answered Jun 21, 2013 by dimension10 (1,985 points) [ revision history ]
edited Aug 30, 2014 by dimension10

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$\hbar$ysicsOver$\varnothing$low
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
...