LargeNBPS states and emergent quantum gravity

This paper provides a heuristic derivation of how classical gravitationalphysics in the AdS/CFT correspondence appears from the strong dynamics of theN=4 SYM theory in a systematic way. We do this in a minisuperspaceapproximation by studying 1/8 BPS configurations. We show that this is relatedto a gauged matrix quantum mechanics of commuting matrices. We can show thatour description matches the semiclassical physics of 1/8 BPS states insupergravity. We also provide a heuristic description of how massive stringsappear in the geometry, and how at strong 't Hooft coupling they become localon the five sphere suggesting that they can be realized as a sigma model on aweakly curved background. In the process we also clarify some aspects of 1/2BPS states. We also have a conjectured realization of some 1/8 BPS giantgraviton wave functions in the dynamics, which captures all 1/8 BPS giantgravitons constructed by Mikhailov. This leads to a lot of different topologychanges which can be treated heuristically.Comment: 54 pages, 8 figures, Latex. v2: typos corrected, improved figures, comments on string tension added. v3: typos correcte