Random matrix approach to scalar fields on fuzzy spaces

Abstract

We formulate theory of interacting scalar field on the fuzzy sphere as a random matrix model. We then analyze the expectation values of observables of the theory in the large N limit and we demonstrate that the eigenvalue distribution of the matrix M remains the polynomially deformed Wigner semicircle. We also compute distributions involving the matrix Laplacian of M and we show that the correlation between the eigenvalues of these two is different from the free field case.

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Cited by in corpus (11)

• 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
• 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
• The multitrace matrix model: An alternative to Connes NCG and IKKT model
• Correlation functions and renormalization in a scalar field theory on the fuzzy sphere
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• Wilson RG of Noncommutative ${\Phi }_4^4$