Giant Graviton Expansion from Bubbling Geometry: Discreteness from Quantized Geometry.

The superconformal index of half-BPS states in N=4 supersymmetric Yang-Mills with gauge group U(N) admits an expansion in terms of giant gravitons, I_{N}(q)=I_{∞}(q)∑_{m=0}^{∞}q^{mN}I[over ^]_{m}(q), where m is the number of giant gravitons and I_{∞}(q) is the graviton index. The expansion can be viewed as the implementation of trace relations for finite N. We derive this expansion directly in supergravity from the class of half-BPS solutions due to Lin, Lunin, and Maldacena in type IIB supergravity.