Counting 1/8-BPS Dual-Giants

TL;DR

The paper constructs and quantizes a broad class of 1/8-BPS states in AdS_5 × S^5 by analyzing configurations of dual-giant gravitons and spinning giants that preserve at least four supersymmetries. It shows the counting problem reduces to N bosons in a 3D harmonic oscillator for states with (J_1, J_2, J_3) and to a disc-bounded, yet similarly structured, sector for states with (S_1, S_2, J_1), yielding compact partition functions that reproduce known gauge theory indices. The results reveal a shared underlying structure between giant- and dual-giant pictures and align with recent quantizations of Mikhailov’s 1/8-BPS giants, suggesting dual descriptions of the same state space. Together, these counts illuminate the microstate structure of 1/8-BPS configurations and provide a concrete, protected framework for comparing AdS/CFT across coupling regimes.

Abstract

We count 1/8-BPS states in type IIB string theory on AdS_5 x S^5 background which carry three independent angular momenta on S^5. These states can be counted by considering configurations of multiple dual-giant gravitons up to N in number which share at least four supersymmetries. We map this counting problem to that of counting the energy eigen states of a system of N bosons in a 3-dimensional harmonic oscillator. We also count 1/8-BPS states with two independent non-zero spins in AdS_5 and one non-zero angular momentum on S^5 by considering configurations of arbitrary number of giant gravitons that share at least four supersymmetries.