11 - Multiple D-branes and bound states

Summary

In chapter 5, we saw a number of interesting terms arise in the Dp-brane world-volume action which had interpretations as smaller branes. For example, a U(1) flux was a D(p - 2)-brane fully delocalised in the world-volume, while for the non-Abelian case, we saw a D(p - 4)-brane arise as an instanton in the world-volume gauge theory. Interestingly, while the latter breaks half of the supersymmetry again, as it ought to, the former is still half BPS, since it is T-dual to a tilted D(p+1)-brane.

It is worthwhile trying to understand this better back in the basic description using boundary conditions and open string sectors, and this is the first goal of this chapter. After that, we'll have a closer look at the nature of the BPS bound and the superalgebra, and study various key illustrative examples.

Dpand Dp′from boundary conditions

Let us consider two D-branes, Dp and Dp′, each parallel to the coordinate axes. (We can of course have D-branes at angles, but we will not consider this here.) An open string can have both ends on the same D-brane or one on each. The p-p and p′-p′ spectra are the same as before, but the p-p′ strings are new if p ≠ p′. Since we are taking the D-branes to be parallel to the coordinate axes, there are four possible sets of boundary conditions for each spatial coordinate Xⁱ of the open string, namely NN (Neumann at both ends), DD, ND, and DN.