# 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

#### 66 Citations

BPS geometry, AdS/CFT, and string theory

- Physics
- 2006

We first study BPS geometries dual to half-BPS states of field theories with 32 supercharges. These field theories are N = 4 SYM on R×S3, M2 brane theory and M5 brane theory. The dynamics of the… Expand

The large-N limit of matrix models and AdS/CFT

- Physics
- 2014

Random matrix models have found numerous applications in both Theoretical Physics and Mathematics. In the gauge-gravity duality, for example, the dynamics of the halfBPS sector can be fully described… Expand

On-Shell Action for Bubbling Geometries

- Physics
- 2007

We study the half-BPS sector of the AdS/CFT correspondence. In the full sector of the correspondence, on-shell actions in type IIB supergravity have been played crucial roles, for example in the… Expand

Geometries and Thermodynamics of Free Fermions

- 2005

Solutions of type IIB supergravity which preserve half of the supersymmetries have a dual description in terms of free fermions, as elucidated by the “bubbling AdS” construction of Lin, Lunin and… Expand

Emergent bubbling geometries in the plane wave matrix model

- Physics
- 2014

A bstractThe gravity dual geometry of the plane wave matrix model is given by the bubbling geometry in the type IIA supergravity, which is described by an axially symmetric electrostatic system. We… Expand

Half-BPS geometries and thermodynamics of free fermions

- Physics
- 2007

Solutions of type IIB supergravity which preserve half of the supersymmetries have a dual description in terms of free fermions, as elucidated by the ``bubbling AdS" construction of Lin, Lunin and… Expand

Emergent bubbling geometries in gauge theories with SU(2|4) symmetry

- Physics
- 2014

A bstractWe study the gauge/gravity duality between bubbling geometries in type IIA supergravity and gauge theories with SU(2|4) symmetry, which consist of N=4$$ \mathcal{N}=4 $$ super Yang-Mills on… Expand

Branes, anti-branes and Brauer algebras in gauge-gravity duality

- Physics, Mathematics
- 2007

We propose gauge theory operators built using a complex Matrix scalar which are dual to brane-anti-brane systems in AdS5 ? S5, in the zero coupling limit of the dual Yang-Mills. The branes involved… Expand

Dynamics of giant-gravitons in the LLM geometry and the fractional quantum Hall effect

- Physics
- 2005

Abstract 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… Expand

Emergent Geometries from the BMN Matrix Model

- Physics
- 2020

We review recent results of emergent geometries in the BMN matrix model, a one-dimensional gauge theory considered as a non-perturbative formulation of M-theory on the plane-wave geometry. A key to… Expand

#### References

SHOWING 1-10 OF 50 REFERENCES

Bubbling AdS space and 1/2 BPS geometries

- Physics
- 2004

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. Configurations… Expand

A toy model for the AdS/CFT correspondence

- Physics
- 2004

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 geometry… Expand

Half-BPS giants, free fermions and microstates of superstars

- Physics
- 2006

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 are… Expand

Giant gravitons in AdS/CFT (I): matrix model and back reaction

- Physics
- 2004

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, giant… Expand

Anti-de Sitter space and holography

- Physics
- 1998

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 of… Expand

Topology Changing Transitions in Bubbling Geometries

- Physics
- 2005

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 the… Expand

BPS geometries and AdS bubbles

- Physics
- 2005

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 as… Expand

Tiny graviton matrix theory: DLCQ of IIB plane-wave string theory, a conjecture

- Physics
- 2004

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 a… Expand

Gauge Theory Correlators from Non-Critical String Theory

- Physics
- 1998

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. The… Expand

Fermions from half-BPS supergravity

- Physics
- 2005

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 this… Expand