DBI Analysis of Open String Bound States on Non-compact D-branes

CHAPTER 6. SETTING 78If we imagine a D1-brane stretching out in x 6 approaching and ultimately hitting anNS5-brane, it will be cut into two pieces, namely two semi-compact D1-branes. Theyare semi-compact, because on one side they stretch out to infinity, while on the otherthey end on the NS5-brane.If we imagine a D1-brane stretching out in x 6 hitting two NS5-branes, it will be cutinto three pieces, namely two semi-compact D1-branes and one compact D1-brane, i.e.a D-brane that ends on both sides on an NS5-brane.Both these possibilities are illustrated in Fig. 6.2. A non-compact D-brane is thussimply a brane that extends to infinity on both sides.D1-braneD1-braneCompactD1NS5-ringSemi-CompactD1Semi-compactD1NS5-ringSemi-compactD1Figure 6.2: Graphical illustration <strong>of</strong> (semi)-compact D1-branes in the presence <strong>of</strong> anNS5-ring.6.2.2 <strong>Bound</strong> statesIt has been mentioned before that open strings can be regarded as excitations <strong>of</strong> D-branes. Such an open string satisfies Dirichlet boundary conditions in the directionsnormal to the brane, meaning in concreto that the endpoints <strong>of</strong> such a string are attachedto the world volume <strong>of</strong> the D-brane. But as long as they remain attached, they are freeto move on it as they please.In the presence <strong>of</strong> an NS5-ring, things change. Focusing again on a D1-branestretched in the x 6 direction, an open string attached to the brane can in principlemove freely along the brane. When the D1-brane is located close enough to the NS5-ring however, something radical happens: some excitations close to the NS5-ring remainbound, i.e. they cannot move anymore! Such a state is exactly what is called a boundstate. This is illustrated in Fig. 6.3.6.2.3 <strong>DBI</strong> approachThe Dirac-Born-Infeld action is said to be a low-energy action. What does this entail?For one, the <strong>DBI</strong> action is constructed entirely out <strong>of</strong> the massless fields present in the((NS,NS)-sector <strong>of</strong> the open) string spectrum. In other words, the <strong>DBI</strong> action onlyconsiders the lowest energy excitations <strong>of</strong> the open string. As such, when we vary the<strong>DBI</strong> action to obtain the excitations <strong>of</strong> the D-brane it describes, and hence the spectrum