Fuzzy spaces and new random matrix ensembles
High Energy Physics - Theory
2020-03-06 v3 Statistical Mechanics
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1109.3349,
title = {Fuzzy spaces and new random matrix ensembles},
author = {V. P. Nair and A. P. Polychronakos and J. Tekel},
journal= {arXiv preprint arXiv:1109.3349},
year = {2020}
}
Comments
12 pages, 1 figure; version to appear in Phys. Rev. D