Complex matrix model and fermion phase space for bubbling AdS geometries
Abstract
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 Script 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 twodimensional free fermions, and establish an exact correspondence between the singlet holomorphic sector of the complex matrix model and onedimensional 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 onedimensional fermions. We also show that the above correspondence actually maps the operators of Script N = 4 SYM corresponding to the (dual) giant gravitons to the droplet configurations proposed in the literature.
 Publication:

Journal of High Energy Physics
 Pub Date:
 October 2005
 DOI:
 10.1088/11266708/2005/10/004
 arXiv:
 arXiv:hepth/0507070
 Bibcode:
 2005JHEP...10..004T
 Keywords:

 High Energy Physics  Theory
 EPrint:
 27 pages, 6 figures, some clarification, typos corrected, published version