8
$\begingroup$

I am getting quite confused with this terminology when I read the papers. Like while constructing the near horizon $AdS_3$ in the $D1-D5$ system one considers $IIB$ on $R^{1,4}\times M^4 \times S^1$ and one "wraps" $N_1$ D1 branes on the $S^1$ and $N_5$ D5-branes on $M^4 \times S^1$. What does it exactly mean?

Coming from reading how D-branes were introduced in Polchinksi's book I would think that in a $9+1$ spacetime Dp branes are some planar streched out stuff with a $p+1$ worldvolume and whose $p$ spatial dimensions are transverse to the $9-p$ spatial dimensions which have been compactified and T-dualized. So are we now saying that its possible that instead of imagining the Dp branes as some set of periodically arranged planes on the T-dual torus we can also think of their spatial world being compactified on some arbitrary p-manifold?

If "wrapping" is really a choice of topology for the p-spatial dimensions of the Dp-brane then what determines this choice? Is this something put in by hand or does this happen naturally?

$\endgroup$
7
$\begingroup$

D-branes are not restricted to planar geometries. They can take on many different forms, and you often encounter branes wrapped around spherical manifolds, like $S^1$ or $S^4$. To determine whether a given configuration is stable, you have to evaluate the action of the D-brane configuration, which is given by the Dirac-Born-Infeld action. For a $Dp$-brane, it is given by

$$S_{DBI}=-T_p\int d^{p+1}x \sqrt{-\text{det}(g_{ab}+2\pi\alpha'F_{ab})},$$

where $T_p$ is the brane-tension, $g_{ab}$ is the metric of the brane, $\alpha'$ is the string length squared and $F_{ab}$ is the field strength of the gauge fields on the brane.

Branes wrapped on nontrivial geometries sometimes have a direct physical interpretation. In holographic QCD, branes wrapped on an $S^4$ correspond to baryons. This can be understood from the fact that this non-trivial topology generates an instanton number which can be identified with the baryon number.

EDIT: For a great introduction to the subject, consult the book "D-Branes" by Johnson, or his shorter lecture notes: http://arxiv.org/abs/hep-th/0007170

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ Brunner Thanks for the answer. Can you give some reference where this analysis is done? I mean is anywhere it is explained how Dp branes can take arbitrary shapes? I mean - what is the mechanism for them to attain some shape? The T-duality argument doesn't seem to lead to any shape information? $\endgroup$ – user6818 Mar 16 '14 at 2:24
  • $\begingroup$ I would recommend Johnson's book "D-Branes", there you should find any answers you want. For a free document, you can also read his shorter lecture notes on D-branes: arxiv.org/abs/hep-th/0007170 $\endgroup$ – Frederic Brünner Mar 16 '14 at 10:40
  • $\begingroup$ Bruinner I have been reading that book - anything specific you can point out there - where this is explained? - as to how wrapping happens "on its own"? What is the dynamics of it? $\endgroup$ – user6818 Mar 18 '14 at 18:56
  • $\begingroup$ The books mentions wrapping in chapter 13.3 and 15.4., for example. $\endgroup$ – Frederic Brünner Apr 11 '14 at 8:27

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.