Computational explorations of a deformed fuzzy sphere

Abstract

This work examines the deformed fuzzy sphere, as an example of a fuzzy space that can be described through a spectral triple, using computer visualizations. We first explore this geometry using an analytic expression for the eigenvalues to examine the spectral dimension and volume of the geometry. In the second part of the paper we extend the code from Glaser and Stern [J. Geom. Phys. 159, 103921 (2021)], in which the truncated sphere was visualized through localized states. This generalization allows us to examine finite spectral triples. In particular, we apply this code to the deformed fuzzy sphere as a first step in the more ambitious program of using it to examine arbitrary finite spectral triples, like those generated from random fuzzy spaces, as show in Barrett and Glaser [J. Phys. A: Math. Theor. 49, 245001 (2016)].