Dynamics of Giant-Gravitons in the LLM geometry and the Fractional Quantum Hall Effect

The LLM's 1/2 BPS solutions of IIB supergravity are known to be closely related to the integer quantum Hall droplets with filling factor \nu=1, and the giant gravitons in the LLM geometry behave like the quasi-holes in those droplets. In this paper we consider how the fractional quantum Hall effect may arise in this context, by studying the dynamics of giant graviton probes in a special LLM geometry, the AdS_5\times S^5 background, that corresponds to a circular droplet. The giant gravitons we study are D3-branes wrapping on a 3-sphere in internal five-sphere. Their low energy world-volume theory, truncated to the 1/2 BPS sector, is shown to be described by a Chern-Simons finite-matrix model. We demonstrate that these giant gravitons may condense at right density further into fractional quantum Hall fluid due to the repulsive interaction in the model, giving rise to the new states in IIB string theory. Some features of the n