Noncommutativity vs gauge symmetry

TL;DR

This paper explores the relationship between noncommutative geometries, specifically foliated manifolds with nonvanishing Godbillon-Vey class, and gauge symmetry, suggesting gauge invariance limits the emergence of highly noncommutative spaces.

Contribution

It proposes that gauge invariance constrains the formation of highly noncommutative foliated manifolds with nonvanishing Godbillon-Vey class.

Findings

Gauge invariance likely prevents resilient leaves in foliated manifolds.

Highly noncommutative spaces with nonvanishing GV-class are unlikely in gauge theories.

The paper offers a theoretical argument linking noncommutativity and gauge symmetry.

Abstract

In many aspects the most complicated noncommutative spaces correspond to foliated manifolds with nonvanishing Godbillon-Vey class. We argue that gauge invariance probably prevents a foliated manifold from creating resilient leaves and thus resulting in having nonvanishing GV-class. So these spaces which are of the highest noncommutativity are not likely to appear in gauge theories.