Dual giant gravitons in AdSm× Yn(Sasaki-Einstein)

We consider BPS motion of dual giant gravitons on Ad$S_5\times Y^5$ where$Y^5$ represents a five-dimensional Sasaki-Einstein manifold. We find that thephase space for the BPS dual giant gravitons is symplectically isomorphic tothe Calabi-Yau cone over $Y^5$, with the K\"{a}hler form identified with thesymplectic form. The quantization of the dual giants therefore coincides withthe K\"{a}hler quantization of the cone which leads to an explicitcorrespondence between holomorphic wavefunctions of dual giants andgauge-invariant operators of the boundary theory. We extend the discussion todual giants in $AdS_4 \times Y^7$ where $Y^7$ is a seven-dimensionalSasaki-Einstein manifold; for special motions the phase space of the dualgiants is symplectically isomorphic to the eight-dimensional Calabi-Yau cone.Comment: 14 pages. (v2) typo's corrected; factors of AdS radius reinstated for clarity; remarks about dual giant wavefunctions in T^{1,1} expanded and put in a new subsectio