Dual Giant Gravitons in Sasaki-Einstein Backgrounds

TL;DR

The paper develops a geometric framework for dual giant gravitons in AdS_5×L with L Sasaki–Einstein, showing their classical phase space is the Kähler cone X over L and quantising it yields a Hilbert space of L^2-normalisable holomorphic functions on X. The BPS Hamiltonian corresponds to the Reeb flow, and energy eigenstates are holomorphic functions with fixed Reeb charge; partition functions (classical and quantum) are defined and connected via Duistermaat–Heckman localisation, with Sasaki–Einstein metrics minimising an entropy functional. A grand canonical construction counts multi-giant states, relating to the index-character and providing a counting mechanism for mesonic BPS operators in the dual SCFT, consistent with symmetric-product descriptions and previous group-theoretic results. Overall, the work links geometric quantisation, localization techniques, and AdS/CFT operator counting to count BPS states and multi-trace chiral primaries in Sasaki–Einstein backgrounds.

Abstract

We study the dynamics of a BPS D3-brane wrapped on a three-sphere in AdS_5 x L, a so-called dual giant graviton, where L is a Sasakian five-manifold. The phase space of these configurations is the symplectic cone X over L, and geometric quantisation naturally produces a Hilbert space of L^2-normalisable holomorphic functions on X, whose states are dual to scalar chiral BPS operators in the dual superconformal field theory. We define classical and quantum partition functions and relate them to earlier mathematical constructions by the authors and S.-T. Yau, hep-th/0603021. In particular, a Sasaki-Einstein metric then minimises an entropy function associated with the D3-brane. Finally, we introduce a grand canonical partition function that counts multiple dual giant gravitons. This is related simply to the index-character of the above reference, and provides a method for counting multi-trace scalar BPS operators in the dual superconformal field theory.