Fuzzy spaces and new random matrix ensembles

Abstract

We analyze the expectation value of observables in a scalar theory on the fuzzy two sphere, represented as a generalized hermitian matrix model. We calculate explicitly the form of the expectation values in the large-N limit and demonstrate that, for any single kind of field (matrix), the distribution of its eigenvalues is still a Wigner semicircle but with a renormalized radius. For observables involving more than one type of matrix we obtain a new distribution corresponding to correlated Wigner semicircles.

12 pages, 1 figure; version to appear in Phys. Rev. D

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Cited by in corpus (18)

• Effective action and phase transitions of scalar field on the fuzzy sphere
• Lectures on Matrix Field Theory I
• Phase diagrams of the multitrace quartic matrix models of noncommutative Φ^4
• Random matrix approach to scalar fields on fuzzy spaces
• The Phase Diagram of Scalar Field Theory on the Fuzzy Disc
• Asymmetric hermitian matrix models and fuzzy field theory
• Second moment fuzzy-field-theory-like matrix models
• Emergent geometry from random multitrace matrix models
• A Multitrace Approach to Noncommutative Φ_2^4
• Renormalization on the fuzzy sphere
• Quantum Gravity as a Multitrace Matrix Model
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• Correlation functions and renormalization in a scalar field theory on the fuzzy sphere
• The multitrace matrix model: An alternative to Connes NCG and IKKT model
• Beyond second-moment approximation in fuzzy-field-theory-like matrix models
• Wilson RG of Noncommutative ${\Phi }_4^4$
• Fuzzy field theories and related matrix models
• Matrix Models of Fuzzy Field Theories