Monopoles and Solitons in Fuzzy Physics

Abstract

Monopoles and solitons have important topological aspects like quantized fluxes, winding numbers and curved target spaces. Naive discretizations which substitute a lattice of points for the underlying manifolds are incapable of retaining these features in a precise way. We study these problems of discrete physics and matrix models and discuss mathematically coherent discretizations of monopoles and solitons using fuzzy physics and noncommutative geometry. A fuzzy sigma-model action for the two-sphere fulfilling a fuzzy Belavin-Polyakov bound is also put forth.

Comments: 17 pages, Latex. Uses amstex, amssymb.Spelling of the name of one Author corrected. To appear in Commun.Math.Phys