Dual giant gravitons in Sasaki–Einstein backgrounds Original Research Article

We study the dynamics of a BPS D3-brane wrapped on a three-sphere in image, 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 image-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, [D. Martelli, J. Sparks, S.-T. Yau, Sasaki–Einstein manifolds and volume minimisation, ]. 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.