Matrix Geometry and Coherent States

Abstract

We propose a novel method of finding the classical limit of the matrix geometry. We define coherent states for a general matrix geometry described by a large-N sequence of D Hermitian matrices X_μ(μ=1,2, ..., D) and construct a corresponding classical space as a set of all coherent states. We also express various geometric objects on the classical space such as the metric, Levi-Civita connection, curvature and Poisson tensor, in terms of the matrix elements. This method provides a new class of observables in matrix models, which characterize geometric properties of matrix configurations.

29pages, v5: minor modifications and references added

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• Information metric, Berry connection and Berezin-Toeplitz quantization for matrix geometry
• Quantum (Matrix) Geometry and Quasi-Coherent States
• Noncommutative spaces and matrix embeddings on flat R^{2n+1}
• A Twistorial Description of the IKKT-Matrix Model
• Kähler structure in the commutative limit of matrix geometry
• What lattice theorists can do for superstring/M-theory
• Entanglement entropy in scalar field theory on the fuzzy sphere
• Geometry from Matrices via D-branes
• Contravariant Gravity on Poisson Manifolds and Einstein Gravity
• A toy model for time evolving QFT on a lattice with controllable chaos
• Commutative Geometry for Non-commutative D-branes by Tachyon Condensation
• Correlation functions and renormalization in a scalar field theory on the fuzzy sphere
• A generalized volume law for entanglement entropy on the fuzzy sphere
• Contravariant geometry and emergent gravity from noncommutative gauge theories
• Emergent geometry of membranes
• Diffeomorphisms on Fuzzy Sphere
• Exploring the gravity sector of emergent higher-spin gravity: effective action and a solution
• Oxidation, Reduction and Semi-Classical Limit for Quantum Matrix Geometries