Supersymmetric Giant Graviton Solutions in AdS₃

We parameterize all classical probe brane configurations that preserve 4 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 $AdS_3 \times S_3 \times T^4/K3$. 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 worldvolume at each point. We show that the supersymmetric sector of the D5 brane worldvolume 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.