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 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.

27 pages, 6 figures, some clarification, typos corrected, published version

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• Large N BPS states and emergent quantum gravity
• Anatomy of bubbling solutions
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• Fat Magnon
• Extended Fermion Representation of Multi-Charge 1/2-BPS Operators in AdS/CFT -- Towards Field Theory of D-Branes --
• Correlators, Probabilities and Topologies in N=4 SYM
• Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra
• Quantum quench in matrix models: Dynamical phase transitions, Selective equilibration and the Generalized Gibbs Ensemble
• Exact probes of orientifolds
• From Gravitons to Giants
• BPS Chaos
• Exact operator bosonization of finite number of fermions in one space dimension
• Large N Spectrum of two Matrices in a Harmonic Potential and BMN energies
• Free particles from Brauer algebras in complex matrix models
• Emergent bubbling geometries in the plane wave matrix model
• Instantons, supersymmetric vacua, and emergent geometries
• Emergent bubbling geometries in gauge theories with SU(2|4) symmetry
• Stretched Horizon and Entropy of Superstars
• Detecting topology change via correlations and entanglement from gauge/gravity correspondence
• On Classification Of The Bubbling Geometries
• Quarter-BPS states, multi-symmetric functions and set partitions
• The giant graviton expansion in $Ad{S}_5\times S^5$
• Young diagrams, Brauer algebras, and bubbling geometries
• The quantum detection of projectors in finite-dimensional algebras and holography
• BPS Condensates, Matrix Models and Emergent String Theory
• Bubbling AdS and Vacuum String Field Theory
• Half-BPS Geometries and Thermodynamics of Free Fermions
• Target space entanglement in a matrix model for the bubbling geometry
• BPS R-balls in N=4 SYM on R X S^3, Quantum Hall Analogy and AdS/CFT Holography
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Eigenvalue Dynamics for Multimatrix Models
• Shaping up BPS States with Matrix Model Saddle Points
• Black Hole Production from High Energy Scattering in AdS/CFT
• Thermal Phase in Bubbling Geometries