The open strings we have studied so far were described by coordinates all of which satisfy Neumann boundary conditions. These open strings move on the world-volume of a space-filling D25-brane. Here we quantize open strings attached to more general D-branes. We begin with the case of a single Dp-brane, with 1 ≤ p < 25. We then turn to the case of multiple parallel Dp-branes, where we see the appearance of interacting gauge fields and the possibility of massive gauge fields. We continue with the case of parallel D-branes of different dimensionalities.
Dp-branes and boundary conditions
A Dp-brane is an extended object with p spatial dimensions. In bosonic string theory, where the number of spatial dimensions is 25, a D25-brane is a space-filling brane. The letter D in Dp-brane stands for Dirichlet. In the presence of a D-brane, the endpoints of open strings must lie on the brane. As we will see in more detail below, this requirement imposes a number of Dirichlet boundary conditions on the motion of the open string endpoints.
Not all extended objects in string theory are D-branes. Strings, for example, are 1-branes because they are extended objects with one spatial dimension, but they are not D1-branes. Branes with p spatial dimensions are generically called p-branes. A 0-brane is some kind of particle. Just as the world-line of a particle is one-dimensional, the world-volume of a p-brane is (p + 1)-dimensional. Of these p + 1 dimensions, one is the time dimension and the other p are spatial dimensions.
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