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I have heard/read a little bit about it and as far as i know it works like this depending on how the strings are attached to the d-branes they have different properties. So the least vibrating string attached to one d-branes which has eletromagnetic charge (Thing I still don't get) would be a photon. And these d-branes can be stacked, and here is where my question comes; for example, the strong force, three stacked d-branes R, B, and G with the strong force on them the different combinations of the string ends (RG, BG, RB, ect...) would form/create the 8 gluons, but the total combinations are 9! The same happens with the weak force instead of three bosons (-W, +W, Z) there are four. So i don't get it.

Oriana L.
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You may know from many-body problems in gravitation, that you can separate the degrees of freedom into: the motion of the center of mass; and the motion of everything else with respect to the center of mass.

I believe this is basically the same thing. The strings attached to the branes come from the quantum vibrations of the branes. For N branes, there are indeed N^2 combinations and N^2 degrees of freedom. But they can be separated into the center-of-mass vibration - the degree of freedom corresponding to all N branes vibrating together - and everything else.

In terms of group theory, the overall degrees of freedom are described by U(N) (NxN complex matrices), but U(N) can be factorized into U(1) x SU(N), where U(1) is a complex number and SU(N) is NxN complex matrices with determinant 1.

At this point, we connect with a question people often ask, just in terms of particles: why are there eight gluons, rather than nine? It is because the symmetry group of the strong force is SU(N) rather than U(N). Or another way to put it is that if the symmetry group was U(N), there would be a "colorless gluon" that acted just like a photon, and didn't interact with the "other" gluons.

It is discussed here. In terms of color-anticolor combinations, the "colorless gluon" is a quantum superposition of red-antired plus green-antigreen plus blue-antiblue. If I am correct (and I have to add that disclaimer because I can't give you the derivation), this corresponds to the center-of-mass oscillation of the whole brane stack that I was talking about.

The references to section 3.8 of "D-Brane Primer" may contain the details, somewhere.

Mitchell Porter
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