2D fuzzy Anti-de Sitter space from matrix models

Abstract

We study the fuzzy hyperboloids AdS^2 and dS^2 as brane solutions in matrix models. The unitary representations of SO(2,1) required for quantum field theory are identified, and explicit formulae for their realization in terms of fuzzy wavefunctions are given. In a second part, we study the (A)dS^2 brane geometry and its dynamics, as governed by a suitable matrix model. In particular, we show that trace of the energy-momentum tensor of matter induces transversal perturbations of the brane and of the Ricci scalar. This leads to a linearized form of Henneaux-Teitelboim-type gravity, illustrating the mechanism of emergent gravity in matrix models.

25 pages

References in corpus (4)

• Non-Compact Hopf Maps and Fuzzy Ultra-Hyperboloids
• Gravity and compactified branes in matrix models
• The curvature of branes, currents and gravity in matrix models
• Cohomology and Decomposition of Tensor Product Representations of SL(2,R)

Cited by in corpus (26)

• Matrix Model Approach to Cosmology
• Cosmological space-times with resolved Big Bang in Yang-Mills matrix models
• Fuzzy de Sitter Space
• Signature change in matrix model solutions
• Four-dimensional Gravity on a Covariant Noncommutative Space
• Matrix Model Cosmology in Two Space-time Dimensions
• Noncommutative gauge theories on ${\mathbb{R}}_{\lambda }^3$: Perturbatively finite models
• Lorentzian Fuzzy Spheres
• Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massless scalar fields
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Noncommutative Gauge Theory and Gravity in Three Dimensions
• One-loop stabilization of the fuzzy four-sphere via softly broken SUSY
• Cosmic time evolution and propagator from a Yang-Mills matrix model
• Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massive and interacting scalar fields
• Fuzzy $C{P}^2$ Space-Times
• Noncommutative Static Strings from 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
• Laplacian on fuzzy de Sitter space
• Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• The fuzzy BTZ
• 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
• QFT on Fuzzy AdS Spaces: Classical Limit and Boundary Correlation Functions
• Replicas, averaging and factorization in the IIB matrix model