Fuzzy spaces and new random matrix ensembles

TL;DR

This paper studies scalar field theories on fuzzy spheres using matrix models, revealing eigenvalue distributions as Wigner semicircles with renormalized radii and correlated distributions for multiple fields.

Contribution

It provides explicit calculations of eigenvalue distributions in fuzzy sphere models, introducing new correlated distributions for multiple matrices.

Findings

Eigenvalues follow a Wigner semicircle with renormalized radius.

Multiple matrices exhibit correlated Wigner semicircle distributions.

Explicit large-N expectation values are derived.

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.