Meaning of carrying a Ramond-Ramond charge ?

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In summary, they are equivalent to the Minkowski space of a classical field theory, except that they have an additional antisymmetric tensor in the Ramond-Raymond sector. This sector is important because it couples the charge of a point particle (the R-R tadpole) to the appropriate D-brane.
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Meaning of "carrying a Ramond-Ramond charge"?

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
 
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What the heck are R-R tadpoles?
What is R-R?
 
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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 ...
[tex] IIA: A_\mu, A_{\mu\nu\rho}[/tex]
[tex] IIB: A, A_{\mu\nu}, A_{\mu\nu\rho\sigma}
[/tex]
It turns out that the R-R gauge fields couple electrically to the appropriate D-branes. In type IIA superstring theory [tex]A_\mu[/tex] couples to D0-branes and [tex]A_{\mu\nu\rho}[/tex] couples to D2-branes. In type IIB superstring theory, [tex]A_{\mu\nu}[/tex] couples to D1-branes and [tex]A_{\mu\nu\rho\sigma}[/tex] 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.
 

1. What is a Ramond-Ramond charge?

A Ramond-Ramond (RR) charge is a type of charge that appears in string theory, a theoretical framework that attempts to reconcile gravity with quantum mechanics. It is associated with the Ramond-Ramond field, which is a higher-dimensional generalization of the electromagnetic field. This field carries information about the geometry of space-time and plays a crucial role in string theory.

2. How is a Ramond-Ramond charge different from an electric charge?

A Ramond-Ramond charge differs from an electric charge in several ways. Firstly, it is a property of strings rather than particles, as it arises in the context of string theory. Additionally, while electric charge is always conserved, Ramond-Ramond charge can be created or destroyed in certain processes. Finally, unlike electric charge, Ramond-Ramond charge can take on values greater than or less than zero.

3. What is the significance of carrying a Ramond-Ramond charge?

Carrying a Ramond-Ramond charge has important implications in string theory. It allows for the existence of extended objects known as D-branes, which are essential for constructing consistent string theories. Additionally, it can affect the behavior of strings in the presence of these D-branes and result in interesting phenomena such as supersymmetry breaking.

4. How is a Ramond-Ramond charge measured?

A Ramond-Ramond charge can be measured indirectly through its effects on the behavior of strings. For example, the presence of a D-brane with a non-zero Ramond-Ramond charge can cause strings to interact differently than they would in its absence. This can be observed through scattering experiments and other string interactions.

5. Can a Ramond-Ramond charge be negative?

Yes, a Ramond-Ramond charge can take on negative values. This is in contrast to electric charge, which is always positive. The ability for Ramond-Ramond charge to be negative is a consequence of the higher-dimensional nature of the Ramond-Ramond field, which allows for more complex and diverse charge configurations.

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