Monopoles and Solitons in Fuzzy Physics
S. Baez, A. P. Balachandran, S. Vaidya, B. Ydri
TL;DR
This paper explores the use of fuzzy physics and noncommutative geometry to develop mathematically consistent discretizations of monopoles and solitons, preserving their topological features.
Contribution
It introduces a fuzzy sigma-model action for the two-sphere that satisfies a fuzzy Belavin-Polyakov bound, advancing discretization methods for topological solitons.
Findings
Fuzzy discretizations preserve topological properties of monopoles and solitons.
A fuzzy sigma-model action for the two-sphere is formulated.
The approach addresses limitations of naive lattice discretizations.
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.
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