2005/07/31 by Yastoshi Takayama, Asato Tsuchiya · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Fermion #Geometry and complex manifolds #Graviton #Holomorphic function #Matrix (chemical analysis) #Phase (matter) #Phase space #Quantum Chromodynamics and Particle Interactions #Singlet state #Space (punctuation) #hep-th
paper · pdf · doi:10.1088/1126-6708/2005/10/004
published as JHEP 0510 (2005) 004 · 27 pages, 6 figures, some clarification, typos corrected, published version
openalex publication_date 2005/10/03 · arxiv created 2005/11/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.