Brane Vacuum as Chain of Rotators

TL;DR

This paper explores a noncommutative U(1) sigma model linked to vacuum dynamics, revealing a chain of rotators, classical solutions, and the emergence of Polyakov vortices, with extensions to q-deformed spaces.

Contribution

It introduces a novel noncommutative sigma model with spherically symmetric solutions and connects it to chains of rotators and vortex phenomena, including a q-deformed generalization.

Findings

Classical static solutions for the model are derived.

Polyakov vortices appear in the small noncommutativity limit.

The model is extended to q-deformed space for regularization.

Abstract

We analyse the noncommutative U(1) sigma model, which arises from the vacuum dynamics of the noncommutative charged tachyonic field. The sector of ``spherically symmetric'' excitations of the model is equivalent to a chain of rotators. Classical solutions for this model are found, which are static and ``spherically symmetric'' in noncommutative spatial dimensions. The limit of small noncommutativity reveals the presence of Polyakov vortices in the model. A generalisation of the model to q-deformed space, which may serve as a regularisation of the non-deformed model is also considered.