Dual giant gravitons in AdS$_m$ $\times$ Y$^n$ (Sasaki-Einstein)

TL;DR

The paper studies BPS dual giant gravitons in $AdS_5\times Y^5$ and $AdS_4\times Y^7$, showing the BPS phase space is symplectically isomorphic to the Calabi–Yau cone over $Y^5$ with the cone’s Kahler form as the phase-space form, enabling geometric (Kähler) quantization. It provides an explicit construction for $T^{1,1}$ and outlines generalization to $Y^{p,q}$, establishing a one-to-one map between holomorphic wavefunctions of dual giants and gauge-invariant boundary operators, including finite-$N$ effects. A parallel analysis in M-theory on $AdS_4\times Y^7$ identifies a special 8D cone sector with the same quantization structure, suggesting a unified bulk-boundary dictionary across dimensions. The results illuminate how supersymmetric giant/graviton dynamics encode boundary operator spectra and offer a framework for exploring microstate counting and holography in less supersymmetric settings.

Abstract

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.