Anti-de Sitter D-branes in Curved Backgrounds

TL;DR

This paper studies the properties and configurations of AdS D-branes in curved backgrounds like AdS3 and AdS3 x S3, revealing their asymptotic behaviors, stability conditions, and interactions with fundamental strings and D0-branes.

Contribution

It provides new solutions and insights into the behavior of AdS D-branes in curved backgrounds, including their asymptotic approach to horizons and conditions for ending on strings or D0-branes.

Findings

AdS D1-branes asymptotically approach the AdS3 horizon.

AdS D2-branes can end on the horizon or F-strings depending on charges.

No stable AdS D-branes exist in NS5-brane backgrounds.

Abstract

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 $AdS_3 \times S^3$ spacetime. We see that, while the AdS D1-branes asymptotically approach to the event horizon of the $AdS_3$ spacetime the AdS D2-branes will end on it. As the near horizon geometry of the F1/NS5 becomes the spacetime of $AdS_3 \times S^3 \times T^4$ 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.