Lost equivalence of nonlinear sigma and $CP^{1}$ models on noncommutative space

TL;DR

This paper demonstrates that the established equivalence between nonlinear sigma models and $CP^{1}$ models in commutative space fails in noncommutative space, due to the emergence of new BPS solitons absent in the commutative case.

Contribution

It reveals the breakdown of the sigma and $CP^{1}$ model equivalence on noncommutative spaces and introduces new BPS solitons unique to this setting.

Findings

Equivalence breaks down on noncommutative space.

New BPS solitons appear in noncommutative models.

The result challenges previous assumptions about model equivalence.

Abstract

We show that the equivalence of nonlinear sigma and $CP^{1}$ models which is valid on the commutative space is broken on the noncommutative space. This conclusion is arrived at through investigation of new BPS solitons that do not exist in the commutative limit.