Dual giant gravitons in AdS$_m$ $\times$ Y$^n$ (Sasaki-Einstein)
Abstract
Description
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 the phase space for the BPS dual giant gravitons is symplectically isomorphic to the Calabi-Yau cone over $Y^5$, with the Kähler form identified with the symplectic form. The quantization of the dual giants therefore coincides with the Kähler quantization of the cone which leads to an explicit correspondence between holomorphic wavefunctions of dual giants and gauge-invariant operators of the boundary theory. We extend the discussion to dual giants in $AdS_4 \times Y^7$ where $Y^7$ is a seven-dimensional Sasaki-Einstein manifold; for special motions the phase space of the dual giants is symplectically isomorphic to the eight-dimensional Calabi-Yau cone.
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 subsection
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 subsection