Fuzzy Spheres in AdS/CFT Correspondence and Holography from Noncommutativity

Abstract

We show that the existent fuzzy S^2 and S^4 models are natural candidates for the quantum geometry on the corresponding spheres in AdS/CFT correspondence. These models fit nicely the data from the dipole mechanism for the stringy exclusion principle. In the AdS_2 X S^2 case, we show that a wrapped fractional membrane can be used to count for the large ground state degeneracy. We also propose a fuzzy AdS_2 model whose fundamental commutation relation may underlie the UV/IR connection.

17 pages, one comment and reference added

References in corpus (2)

• Dielectric-Branes
• Fuzzy Gravitons From Uncertain Spacetime

Cited by in corpus (45)

• Quantum Field Theory on Noncommutative Spaces
• Giant Gravitons in Conformal Field Theory
• Exact Correlators of Giant Gravitons from dual N=4 SYM
• Coherent State Induced Star-Product on $R_{\lambda }^3$ and the Fuzzy Sphere
• Giant Graviton Correlators from Dual SU(N) super Yang-Mills Theory
• Matrix algebras converge to the sphere for quantum Gromov--Hausdorff distance
• Infinitely many star products to play with
• Higher Dimensional Geometries from Matrix Brane constructions
• Perturbative Approach to Higher Derivative and Nonlocal Theories
• Higher dimensional geometries related to fuzzy odd-dimensional spheres
• Noncommutative Gravity in two Dimensions
• Fuzzy Cosets and their Gravity Duals
• Noncommutative D-Brane in Non-Constant NS-NS B Field Background
• Matrix Model for De Sitter
• Covariant 4-dimensional fuzzy spheres, matrix models and higher spin
• Noncommutativity and Non-anticommutativity in Perturbative Quantum Gravity
• Noncommutative $D_3$-brane, Black Holes and Attractor Mechanism
• Matrix Model Approach to Cosmology
• Large N Expansion From Fuzzy AdS_2
• On Higher Dimensional Fuzzy Spherical Branes
• Fuzzy Sphere from Matrix Model
• A unifying perspective on the Moyal and Voros products and their physical meanings
• Non-Compact Hopf Maps and Fuzzy Ultra-Hyperboloids
• Signature change in matrix model solutions
• Hyperbolic Supersymmetric Quantum Hall Effect
• Construction of fuzzy S^4
• Matrix Model Cosmology in Two Space-time Dimensions
• Locality, Causality and Noncommutative Geometry
• Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massless scalar fields
• Gromov-Hausdorff Distance for Quantum Metric Spaces
• Fluctuating Fuzzy Funnels
• CP^n Model on Fuzzy Sphere
• Noncommutative brane-world, (Anti) de Sitter vacua and extra dimensions
• Cosmic time evolution and propagator from a Yang-Mills matrix model
• One-loop stabilization of the fuzzy four-sphere via softly broken SUSY
• Harmonic analysis approach to Gromov--Hausdorff convergence for noncommutative tori
• Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massive and interacting scalar fields
• Noncommutative Static Strings from Matrix Models
• The Fuzzy S^4 by Quantum Deformation
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• Asymptotic commutativity of quantized spaces: the case of ${\mathbb{CP}}^{p,q}$
• Exact solutions for scalars and spinors on quantized (Euclidean) $Ad{S}_2$ and the correspondence principle
• Stringy Spacetime Uncertainty as an Alternative to Inflation
• The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry I: A QM/NCG Correspondence
• The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry II: Noncommutative Quantum Black Holes