Supertubes connecting D4 branes

We find and explore a class of dyonic instanton solutions which can be identified as the supertubes connecting two D4 branes. They correspond to a single monopole string and a pair of monopole-antimonopole strings from the worldvolume view point of D4 branes. 1 Introduction Recently there has been a considerable study of the so called supertube solutions. Originally Mateos and Townsend constructed supersymmetric configurations of D2-D0-F1 branes where D2 brane forms a single cylinder with D-particles and F-strings melted in[1]. The corresponding configurations in the matrix model have been found also[2, 3]. As a limit of the elliptic deformation of circular tubes, flat supersymmetric brane antibrane configurations are realized[4] and the wouldbe tachyons present in the ordinary brane-antibrane system become massless exhibiting the stability of the system[5]. In fact the cross sectional shape of the tubes is shown to be arbitrary in the transverse eight dimensions[6]. More recently, the DBI action has been explored to find the supersymmetric configuration for D2 supertubes ending on a D4 brane[7]. The higher dimensional analogue has In this note we are interested in tubular D2 connecting two D4 branes separated, say, in x 9 direction. As argued in Ref. [7], all the constituents of supertubes, i.e. D0, F1 and D2, may end on D4 branes and, hence, such configuration should be consistent with supersymmetries. Viewed from the worldvolume of D4, D0 appears as an instanton generating selfdual field strength and F-string extended along x 9 works as a localized electric source. One direction of D2 is extended in x 9 and the other spatial direction will in general form a curve in D4 worldvolume. Since this curve is magnetically charged, one may call it as a magnetic string from the view point of the D4 worldvolume. The instantons preserve only half of sixteen supersymmetries and F1/D2 breaks further half, so only 1/8 of 32 supersymmetries remain in general. In this U(2) context of two D4 branes, one is ultimately interested in magnetic strings where the shape of curve on D4 is arbitrary, which correspond to tubes of arbitrary cross sections. However such general configurations seem involved for reasons described below. Therefore we shall focus on the monopole and antimonopole strings corresponding to supersymmetric flat D2-D2 connecting two D4 branes. This supersymmetric configuration is composed of a monopole string and an antimonopole string. Simpler situation arises if one considers just one flat D2 (or a …