Complex Matrix Model and Fermion Phase Space for Bubbling AdS Geometries

@article{Takayama2005ComplexMM,
  title={Complex Matrix Model and Fermion Phase Space for Bubbling AdS Geometries},
  author={Yastoshi Takayama and Asato Tsuchiya},
  journal={arXiv: High Energy Physics - Theory},
  year={2005}
}
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… Expand

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References

SHOWING 1-10 OF 50 REFERENCES
Bubbling AdS space and 1/2 BPS geometries
We consider all 1/2 BPS excitations of AdS × S configurations in both type-IIB string theory and M-theory. In the dual field theories these excitations are described by free fermions. ConfigurationsExpand
A toy model for the AdS/CFT correspondence
We study the large-N gauged quantum mecchanics for a single hermitean matrix in the Harmonic oscillator potential well as a toy model for the AdS/CFT correspondence. We argue that the dual geometryExpand
Half-BPS giants, free fermions and microstates of superstars
We consider 1/2-BPS states in AdS/CFT. Using the matrix model description of chiral primaries explicit mappings among configurations of fermions, giant gravitons and the dual-giant gravitons areExpand
Giant gravitons in AdS/CFT (I): matrix model and back reaction
In this article we study giant gravitons in the framework of AdS/CFT correspondence. First, we show how to describe these configurations in the CFT side using a matrix model. In this picture, giantExpand
Anti-de Sitter space and holography
Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product ofExpand
Topology Changing Transitions in Bubbling Geometries
Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) × SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes theExpand
BPS geometries and AdS bubbles
Abstract Recently, 1 2 -BPS AdS bubble solutions have been obtained by Lin, Lunin and Maldacena, which correspond to Fermi droplets in phase space in the dual CFT picture. They can be thought of asExpand
Tiny graviton matrix theory: DLCQ of IIB plane-wave string theory, a conjecture
We conjecture that the discrete light-cone quantization (DLCQ) of strings on the maximally supersymmetric type IIB plane-wave background in the sector with J units of light-cone momentum is aExpand
Gauge Theory Correlators from Non-Critical String Theory
Abstract We suggest a means of obtaining certain Green's functions in 3+1-dimensional N =4 supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory. TheExpand
Fermions from half-BPS supergravity
We discuss collective coordinate quantization of the half-BPS geometries of Lin, Lunin and Maldacena [1]. The LLM geometries are parameterized by a single function u on a plane. We treat thisExpand
...
1
2
3
4
5
...