Random matrix approach to scalar fields on fuzzy spaces

TL;DR

This paper models interacting scalar fields on fuzzy spheres using random matrix theory, revealing eigenvalue distributions and correlations that differ from free field cases, especially in the large N limit.

Contribution

It introduces a random matrix formulation for scalar fields on fuzzy spheres and analyzes eigenvalue distributions and correlations in the large N limit.

Findings

Eigenvalue distribution remains a polynomially deformed Wigner semicircle.

Eigenvalue correlations involving the matrix Laplacian differ from free field cases.

Large N limit analysis provides insights into the spectral properties of the model.

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.