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 ν=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 X S^5 background, that corresponds to a
circular droplet. The giant gravitons we study are D3-branes wrapping on a
3-sphere in S^5. 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
novel physics of these new states are discussed.Comment: 32 pages, 1 figure; v.2: references added, the relation between the
level shift and filling fraction elaborate