Counting Wobbling Dual-Giants

TL;DR

This work derives the BPS constraints for D3-branes in $AdS_5 \times S^5$ preserving two supersymmetries, and shows giant and dual-giant configurations solve these equations. By analyzing the wobbling dual-giants with charges $(S_1,S_2,J_1)$, the authors map their classical configuration space to a hyperbolic version of complex projective space, enabling covariant, holomorphic geometric quantization. They compute the symplectic structure and charges, implement a stringy exclusion principle, and obtain a partition function whose single-particle form matches that of the corresponding giant-giant system and the boundary gauge theory results, thereby supporting a duality in the 1/8-BPS sector. The work also outlines generalizations to other backgrounds and discusses calibrations and potential extensions to 1/16-BPS configurations.

Abstract

We derive the BPS equations for D3-branes embedded in AdS_5 X S^5 that preserve at least two supercharges. These are given in terms of conditions on the pullbacks of some space-time differential four-forms. Solutions to our equations are shown to describe all the known giant and dual-giant gravitons in AdS_5 X S^5. We then argue that the configuration spaces of dual-giants can be mapped to non-compact hyperbolic versions of complex projective spaces, in contrast with the giants, whose configuration spaces have been mapped to complex projective spaces. We quantize the configuration space of the 1/8-BPS dual-giants with two angular momenta in AdS_5 and one angular momentum in S^5 and find agreement with the partition function in the literature obtained both from counting appropriate 1/8-BPS configurations of giants and the boundary gauge theory considerations.