Minisuperspace Quantization of "Bubbling AdS" and Free Fermion Droplets

Abstract

We quantize the space of 1/2 BPS configurations of Type IIB SUGRA found by Lin, Lunin and Maldacena (hep-th/0409174), directly in supergravity. We use the Crnkovic-Witten-Zuckerman covariant quantization method to write down the expression for the symplectic structure on this entire space of solutions. We find the symplectic form explicitly around AdS_5 x S^5 and obtain a U(1) Kac-Moody algebra, in precise agreement with the quantization of a system of N free fermions in a harmonic oscillator potential, as expected from AdS/CFT. As a cross check, we also perform the quantization around AdS_5 x S^5 by another method, using the known spectrum of physical perturbations around this background and find precise agreement with our previous calculation.

22 Pages + 2 Appendices, JHEP3; v3: explanation of factor 2 mismatch added, references reordered, published version

References in corpus (13)

• Gauge Theory Correlators from Non-Critical String Theory
• The fuzzball proposal for black holes: an elementary review
• Bubbling AdS space and 1/2 BPS geometries
• Exactly solvable model of superstring in Ramond-Ramond plane wave background
• Three-Point Functions of Chiral Operators in D=4, $\mathcal{N}=4$ SYM at Large N
• A toy model for the AdS/CFT correspondence
• Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.
• Covariant Actions for the Bosonic Sector of D=10 IIB Supergravity
• Chiral actions from phase space (quantum Hall) droplets
• A matrix model for a quantum hall droplet with manifest particle-hole symmetry
• The Large N Harmonic Oscillator as a String Theory
• Quantization of pure gravitational plane waves
• Canonical quantization of a massive particle on $Ad{S}_3$

Cited by in corpus (69)

• The Library of Babel: On the origin of gravitational thermodynamics
• Black Holes as Effective Geometries
• Large N BPS states and emergent quantum gravity
• Supersymmetric states of N=4 Yang-Mills from giant gravitons
• Instability of non-supersymmetric smooth geometries
• Quantizing N=2 Multicenter Solutions
• Nonplanar Integrability
• Anatomy of bubbling solutions
• D1-D5 black hole microstate counting from supergravity
• Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity
• Comments on 1/16 BPS Quantum States and Classical Configurations
• The Foaming Three-Charge Black Hole
• Quantum Attractor Flows
• General 2 charge geometries
• Geometry Quantization from Supergravity: the case of "Bubbling AdS"
• Spectral Flow, and the Spectrum of Multi-Center Solutions
• Brane Effective Actions, Kappa-Symmetry and Applications
• Matrix Model Maps in AdS/CFT
• 1/16-BPS Black Holes and Giant Gravitons in the AdS_5 X S^5 Space
• Bubbles on Manifolds with a U(1) Isometry
• A description of 1/4 BPS configurations in minimal type IIB SUGRA
• Complex Matrix Model and Fermion Phase Space for Bubbling AdS Geometries
• Free Fermions and Thermal AdS/CFT
• An Infinite-Dimensional Family of Black-Hole Microstate Geometries
• Counting Giant Gravitons in AdS_3
• 1/8 BPS States in Ads/CFT
• Rational foundation of GR in terms of statistical mechanic in the AdS/CFT framework
• Extended Fermion Representation of Multi-Charge 1/2-BPS Operators in AdS/CFT -- Towards Field Theory of D-Branes --
• 1/4-BPS M-theory bubbles with SO(3) x SO(4) symmetry
• The Cheshire Cap
• BPS states in type IIB SUGRA with $SO(4)\times SO(2)_{gauged} symmetry
• Exact probes of orientifolds
• Superposition induced topology changes in quantum gravity
• From Gravitons to Giants
• BPS Chaos
• Supergravitons from one loop perturbative N=4 SYM
• 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
• Topology and geometry cannot be measured by an operator measurement in quantum gravity
• Revisiting the D1/D5 System or Bubbling in AdS_3
• Supersymmetric Giant Graviton Solutions in AdS_3
• Emergent classical spacetime from microstates of an incipient black hole
• Counting D1-D5-P Microstates in Supergravity
• State-space Manifold and Rotating Black Holes
• Dynamics of Giant-Gravitons in the LLM geometry and the Fractional Quantum Hall Effect
• New Supersymmetric Bubbles on AdS_3xS^3
• Covariant canonical formulations of classical field theories
• Dynamics of chiral primaries in $Ad{S}_3\times S^3\times T^4$
• Detecting topology change via correlations and entanglement from gauge/gravity correspondence
• Coherent state operators, giant gravitons, and gauge-gravity correspondence
• Deconstructing the D0-D6 system
• Semi-classical Probe Strings on Giant Gravitons Backgrounds
• Strings on Bubbling Geometries
• Small Black holes vs horizonless solutions in AdS
• Extremal chiral ring states in AdS/CFT are described by free fermions for a generalized oscillator algebra
• Young diagrams, Brauer algebras, and bubbling geometries
• Correlations vs connectivity in R-charge
• Holographic Dissipation from the Symplectic Current
• D-branes and Orbit Average
• Half-BPS Geometries and Thermodynamics of Free Fermions
• Four-point correlators in N=4 SYM from AdS${}_5$ bubbling geometries
• Interior analysis, stretched technique and bubbling geometries
• From Gauss Graphs to Giants
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• BPS R-balls in N=4 SYM on R X S^3, Quantum Hall Analogy and AdS/CFT Holography
• Coherent state superpositions, entanglement and gauge/gravity correspondence
• Precision holography of AdS${}_5$ bubbling geometries
• Minisuperspace quantization of bubbling AdS${}_2\times$S${}^2$ geometries
• Black Hole Production from High Energy Scattering in AdS/CFT