Tubular Solutions in NS5-brane, Dp-brane and Macroscopic Strings Backgrounds

We present our searches for the tubular bound states of a D2-brane with $m$ D0-branes and $n$ fundamental strings in the NS5-brane, Dp-brane or macroscopic strings background by solving the Dirac-Born-Infeld equation. The geometry of tubular configurations we considered are taken to be parallel to the background branes or macroscopic strings. The $n$ fundamental strings therein may be the circular strings $F_c$ or the straight strings $F_s$, which are along the cross section or the axis of the tube respectively. We show that the stable tubular bound states of ($nF_s$, $m$D0, D2) which are prevented form collapse by the angular momentum, as original found in flat space, could be formed in the NS5-brane, D6-brane and macroscopic strings background. However, they becomes unstable in the D2-brane and D4-brane background. We also show that there are stable tubular bound states of ($nF_c$, $m$D0, D2) and ($m$D0, D2), which are prevented form collapse by the gravitational forces in the backgrounds of D6-brane. We discuss the properties of these tubular solutions and see that only that in the macroscopic strings background is a supersymmetric BPS configuration.