# P-branes v.s. Dp-branes

Hi there,

(i) Could anyone tell me the difference between p-branes and D-branes please?

(ii) I have recently read that p-branes are some higher dimensional cousins of the extremal Reissner Nordström black hole, what does that actually mean in type IIB string theory?

(iii) If we have a U(2) gauge boson, does that mean it's a 2x2 matrix that is unitary? What other properties does this gauge boson have?

Thank you to all!

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i) I think that p-brane is just the general name for the p-dimensional objects that are found in string/brane- theory. However, the strings themselves are usually not called 1-branes. A D1-brane is different from a "fundamental string", which can be denoted F-string. Dp-branes are a specific type of p-brane. D means Dirichlet, coming from the Dirichlet boundary conditions imposed on the open strings that connect to it. There are some other types of branes besides the most usual Dp-brane. Check the wikipedia pages for p-brane, D-brane. You can find references there to S-brane, NS5-brane and F-strings, and the relation of all this to M-theory.

ii) Have no idea.

iii) Usually it only means that the gauge boson is a two-component object, ie. spacetime-field that takes values in a 2-complex-dimensional vector space, on which U(2) transformations act when a symmetry transformation is performed. But in some contexts it could also mean what you say. Although I would think they would then call it a U(2) matrix field.

Torquil

(i) p-branes are p-spatial-dimensional extremal black hole solutions of classical supergravity in higher dimensions. A major part of the 2nd superstring revolution is the conjecture of Polchinski that these p-branes correspond to the D-branes of IIB-superstrings in their classical limit ($$\alpha' \rightarrow 0$$). In string theory, D-branes exist for an entirely different reason. This identification has been confirmed by agreements of Bekenstein-Hawking formula for p-branes with that calculated from D-branes.

(ii) In the $$\alpha' \rightarrow 0$$ limit of IIB string theory, one can write the classical action (as a function of various massless fields), along with the identification of the (p+1)-form gauge field coupled to a Dp-brane as a (p+1)-form field coupled to a p-brane.

(ii) Gauge bosons usually reside in the adjoint representation of the gauge group.