Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-07-07
JHEP 0510 (2005) 004
Physics
High Energy Physics
High Energy Physics - Theory
27 pages, 6 figures, some clarification, typos corrected, published version
Scientific paper
10.1088/1126-6708/2005/10/004
We study a relation between droplet configurations in the bubbling AdS geometries and a complex matrix model that describes the dynamics of a class of chiral primary operators in dual N=4 super Yang Mills (SYM). We show rigorously that a singlet holomorphic sector of the complex matrix model is equivalent to a holomorphic part of two-dimensional free fermions, and establish an exact correspondence between the singlet holomorphic sector of the complex matrix model and one-dimensional free fermions. Based on this correspondence, we find a relation of the singlet holomorphic operators of the complex matrix model to the Wigner phase space distribution. By using this relation and the AdS/CFT duality, we give a further evidence that the droplets in the bubbling AdS geometries are identified with those in the phase space of the one-dimensional fermions. We also show that the above correspondence actually maps the operators of N=4 SYM corresponding to the (dual) giant gravitons to the droplet configurations proposed in the literature.
Takayama Yastoshi
Tsuchiya Asato
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