Topological stability of broken symmetry on fuzzy spheres

TL;DR

This paper investigates the stability of topological configurations in an O(3) scalar field on a fuzzy sphere, revealing finite fluctuations and enhanced stability due to non-commutative geometry effects.

Contribution

It demonstrates that topological configurations on fuzzy spheres have finite fluctuations, contrasting with diverging fluctuations in uniform states, highlighting the role of non-commutative geometry in stability.

Findings

Fluctuations around topological configurations are finite.

Fluctuations around uniform configurations diverge, consistent with Mermin-Wagner-Hohenberg-Coleman theorem.

Topological stability is enhanced on fuzzy spheres.

Abstract

We study the spontaneous symmetry breaking of O(3) scalar field on a fuzzy sphere $S_F^2$. We find that the fluctuations in the background of topological configurations are finite. This is in contrast to the fluctuations around a uniform configuration which diverge, due to Mermin-Wagner-Hohenberg-Coleman theorem, leading to the decay of the condensate. Interesting implications of enhanced topological stability of the configurations are pointed out.