We parametrize all classical probe brane configurations that preserve four supersymmetries in (a) the extremal D1-D5 geometry, (b) the extremal D1-D5-P geometry, (c) the smooth D1-D5 solutions proposed by Lunin and Mathur, and (d) global ${\mathrm{AdS}}_3\times S_3\times T^4/K3$. These configurations consist of D1 branes, D5 branes, and bound states of D5 and D1 branes with the property that a particular Killing vector is tangent to the brane world volume at each point. We show that the supersymmetric sector of the D5-brane world volume theory may be analyzed in an effective $1+1$ dimensional framework that places it on the same footing as D1 branes. In global AdS and the corresponding Lunin-Mathur solution, the solutions we describe are “bound” to the center of AdS for generic parameters and cannot escape to infinity. We show that these probes only exist on the submanifold of moduli space where the background $B_{NS}$ field and theta angle vanish. We quantize these probes in the near-horizon region of the extremal D1-D5 geometry and obtain the theory of long strings discussed by Seiberg and Witten.

• Received 5 October 2007

DOI:https://doi.org/10.1103/PhysRevD.77.046011