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

CHAPTER 6. SETTING 77it does. This should be understood as follows. Recall that D- and NS5-branes are BPSobjects. However, this does not mean that we can put them together in an arbitrary wayand expect the result to also be BPS. Such BPS preserving configurations do neverthelessexist for these two objects. This implies that they will configure themselves in sucha way that the sum <strong>of</strong> the gravitational attraction between both objects (attractive)and the force due to the exchange <strong>of</strong> closed strings (repulsive) cancels. If we were toplace a D4-brane in the vicinity <strong>of</strong> the NS5-ring that deviates from such an equilibriumconfiguration, the D4-brane will move due to the non-cancelling <strong>of</strong> the sum <strong>of</strong> mentionedforces till the configuration becomes stable. Once such a stable configuration is reached,it will remain stable forever. As such, we can basically place our D4-brane in any suchequilibrium position, and rest assured that it will stay there. The NS5-branes curve thespatial dimensions normal to its world volume. Hence, the presence <strong>of</strong> the NS5-branesis felt by the D4-brane through the curvature in the x 6 direction. What makes theD4-brane particularly interesting in this setup, is that four <strong>of</strong> its space-time directionscorrespond to a four-dimensional Minkowski space-time. For, and only for bound states,the x 6 direction is “invisible.” A word <strong>of</strong> explanation is in order.Dim: 0 1 2 3 4 5 6 7 8 9NS5 × × × × × ×D4 × × × × ×Table 6.1: Dimensional overlap between D4- and NS5-branes.6.2 What’s in a title?The title <strong>of</strong> this dissertation reads“<strong>DBI</strong> <strong>Analysis</strong> <strong>of</strong> <strong>Open</strong> <strong>String</strong> <strong>Bound</strong> <strong>States</strong> on Non-compact D-branes.”In Part I <strong>of</strong> this document, the concepts <strong>of</strong> open strings, D-branes and the <strong>DBI</strong> actionhave all been reviewed. There remain two concepts that have not been mentioned yet:what do we understand under bound states, and what are non-compact D-branes? It isalso worth sheding a bit <strong>of</strong> extra light on the <strong>DBI</strong> approach.6.2.1 Compact vs. non-compact D-branesWe have seen that D-branes, when present in some direction, are forced to stretch out toinfinity in that direction due to arguments related to charge conservation. There is oneexception to the rule, and that is when D-branes touch NS5-branes. We can considertwo cases: one where a D-brane “hits” only one NS5-brane, and one where it “hits” twoNS5-branes. We provide “hits” with quotation marks, because as mentioned earlier,these configurations are in fact static. Nevertheless, we will assume it to be dynamicjust for the sake <strong>of</strong> argument.