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

TL;DR

This paper explores the phase space and quantization of BPS dual giant gravitons in AdS$_m$ $ imes$ Y$^n$ spaces, revealing a symplectic isomorphism to Calabi-Yau cones and establishing a correspondence with boundary gauge theories.

Contribution

It demonstrates the symplectic structure of dual giant graviton phase space and connects their quantization to Kähler quantization of Calabi-Yau cones, extending to higher dimensions.

Findings

Phase space of dual giants is symplectically isomorphic to Calabi-Yau cones.

Quantization matches Kähler quantization, linking wavefunctions to gauge-invariant operators.

Extension to AdS$_4$ $ imes$ Y$^7$ shows similar symplectic structure in higher dimensions.

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 K\"{a}hler form identified with the symplectic form. The quantization of the dual giants therefore coincides with the K\"{a}hler 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.