Anti-de Sitter D-branes in curved backgrounds

We investigate the properties of the AdS D1-branes which are the bound states of a curved D1-brane with n fundamental strings (F1) in the AdS ₃ spacetime, and the AdS D2-branes which are the axially symmetric bound states of a curved D2-brane with m D0-branes and n fundamental strings in the AdS₃ × S³ spacetime. We see that, while the AdS D1-branes asymptotically approach to the event horizon of the AdS₃ spacetime the AdS D2-branes will end on it. As the near horizon geometry of the F1/NS5 becomes the spacetime of AdS₃ × S³ × T⁴ with NS-NS three form turned on, we furthermore investigate the corresponding AdS D-branes in the NS5-branes and macroscopic F-strings backgrounds, as an attempt to understand the origin of the AdS D-branes. From the found DBI solutions we see that in the F-strings background, both of the AdS D1-branes and AdS D2-branes will asymptotically approach to the position with a finite distance away from the F-strings. However, the AdS D2-branes therein could also end on the F-strings once it carries sufficient D0-branes charges. We also see that there does not exist any stable AdS D-branes in the NS5-branes backgrounds. We present physical arguments to explain these results, which could help us in understanding the intriguing mechanics of the formation of the AdS D-branes.