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

CHAPTER 5. BRANES 735.2 NS5-branesYou might be tempted into thinking that “NS-branes are branes on which strings withNeveu-Schwarz boundary conditions end.” This is however as far as possible from thetruth as could be. Matter <strong>of</strong> the fact is that strings cannot end on NS5-branes!We saw that a p-form gauge field can couple electrically to a (p − 1)-brane, andmagnetically to a (D − p − 4)-brane. We also saw that the string, which is a 1-brane,if a Kalb-Ramond field is present, couples electrically to this field. Hence, we shouldexpect that there is also a (D − 1 − 4) = 5-brane that couples to this field. This branedoes indeed exist (by which we mean that it is stable), and is exactly what is called theNS5-brane. It is called such because it arises from a gauge field which originates fromthe NS-NS sector in superstring theories. It is also sometimes referred to as the solitonicfivebrane. Remark that the B µν field is absent from Type I string theory due to the factthat this is an unoriented theory, and hence this theory contains no NS5-branes.NS5-branes are characterized by a string tension T NS5 that goes asT NS5 ∼ 1 gs2 . (5.50)Comparing this to the tension <strong>of</strong> the string (T s ∼ g 0 s) and D-branes (T Dp ∼ g −1s ) revealsthat the NS5-brane is much heavier than other types <strong>of</strong> branes at weak coupling. Anotherimportant property is that NS5-branes are also BPS states. As a consequence <strong>of</strong> this,they do not feel each other, or other BPS states such as D-branes, if they are combinedin such a way that the resulting configuration remains BPS.What makes them very interesting though is that although strings cannot end onthem, D-branes actually can. Which configurations are actually possible, and which arenot, is determined by principles <strong>of</strong> charge conservation. We will not go into this, butinterested parties are referred to [20] and [21]. The same principles <strong>of</strong> charge conservationalso dictate that D-branes and NS5-branes stretch out to infinity; i.e. they can not havedefinite start- and endpoints like e.g. an open string. Only D-branes can have these ifthey end on NS5-branes.5.3 SummaryWe introduced T-duality, and showed that it highly motivates the introduction <strong>of</strong> Dpbranes.Some properties <strong>of</strong> these D-branes were presented, and we analysed whichconfigurations are possible in Type IIA and IIB superstring theory. Finally, we shed adim light on the NS5-brane, and hinted at some <strong>of</strong> its most important features.