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nrqed
Sep27-04, 05:02 PM
Hi,

I'm hoping someone will be able to help me understand this kind of statement. For example when they say that a brane carries a R-R charge. I gues sit all comes out to the fact that one can write an integral which basically sums up the electric flux (or magnetic flux in some cases).

But I am still baffled by these terms. I guess they are meant to be the (higher dimensional) analogue of calculation of flux through gaussian surfaces but I am not sure I get it. Two questions:

Here the integration is over the "higher dimensional surfaces" of the brane, right(which is therefore quite different then the usual calculations of flux which are done over the surfaces of imaginary gaussian surfaces)?

But then, what is the source of these fields? I thought that the branes themselves were the sources, but then one would integrate over "surafces" which would enclose the branes! But it looks to me as if the integrals are over the "surfaces" of the branes themselves!

So I am obviously missing the point. I would appreciate some help.

Regards

Pat

Mk
Oct2-04, 05:18 AM
What the heck are R-R tadpoles?
What is R-R?

selfAdjoint
Oct2-04, 09:48 AM
Here's what Zwiebach says.
Point particles have one-dimensional world-lines and carry electric charges if they couple to a one-index massless gauge field. ... A Dp-brane has a (p+1)-dimensional world-volume and is said to be electrically charged if it couples to a massless antisymmetric tensor field with (p+1) indexes. ... type IIA and type IIB closed superstring theories have additional antisymmetric tensors in the Ramond-Raymond sector ...
IIA: A_\mu, A_{\mu\nu\rho}
IIB: A, A_{\mu\nu}, A_{\mu\nu\rho\sigma}

It turns out that the R-R gauge fields couple electrically to the appropriate D-branes. In type IIA superstring theory A_\mu couples to D0-branes and A_{\mu\nu\rho} couples to D2-branes. In type IIB superstring theory, A_{\mu\nu} couples to D1-branes and A_{\mu\nu\rho\sigma} couples to D3-branes. The field A carries no index, so it does not couple electrically to any conventional D-brane (it couples electrically to an object called a D-instanton).
Charge and energy conservation together imply that a charged object cannot decay if there are no lighter mass candidate decay products that can carry the charge. The D-branes {described here} arein fact stable D-branes, and they cannot decay into open or closed string states. (pp 331-332)

The various sectors of Type IIA and Type IIB supersting theory are described on pages 267 and 268.