Supersymmetric giant graviton solutions inAdS3

Abstract

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 ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{S}_{3}\ifmmode\times\else\texttimes\fi{}{T}^{4}/K3$. 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.