Topologically nontrivial field configurations in noncommutative geometry

TL;DR

This paper explores topologically nontrivial spinor fields on a fuzzy sphere within noncommutative geometry, demonstrating symmetry preservation and finite mode regularization in the associated field theory.

Contribution

It introduces a framework for describing spinor fields with nonzero winding numbers on a fuzzy sphere, maintaining key symmetries and finite mode spectra.

Findings

Fields are regularized with finite modes due to noncommutativity.

Standard symmetries like isometries and chiral symmetry are preserved.

The approach provides a finite, symmetry-preserving model of topologically nontrivial fields.

Abstract

In the framework of noncommutative geometry we describe spinor fields with nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding field theory actions conserve all basic symmetries of the standard commutative version (space isometries and global chiral symmetry), but due to the noncommutativity of the space the fields are regularized and they contain only finite number of modes.