Dual Giant Gravitons in Sasaki-Einstein Backgrounds

TL;DR

This paper explores the dynamics and quantization of dual giant gravitons in Sasaki-Einstein backgrounds, linking geometric structures to BPS operators in superconformal field theories.

Contribution

It introduces a geometric quantization framework for dual giant gravitons in Sasaki-Einstein spaces and connects it to counting BPS operators in dual field theories.

Findings

Hilbert space of holomorphic functions on the symplectic cone X

Relation between entropy minimization and Sasaki-Einstein metrics

A grand canonical partition function for multiple dual giants

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.