Puffed Noncommutative Nonabelian Vortices

TL;DR

This paper introduces gauge-invariant solutions in noncommutative gauge theories where vortices expand into shells, revealing new dynamic and static configurations with potential cosmological implications.

Contribution

It provides the first gauge-invariant descriptions of noncommutative vortex shells and explores their static and dynamic properties, including oscillating and expanding solutions.

Findings

Charge 2 vortices have a well-defined shell radius.

Solutions include oscillating shells and expanding BIon-like configurations.

Shell radius is zero in 2D solutions, non-zero in higher dimensions.

Abstract

We present new solutions of noncommutative gauge theories in which coincident unstable vortices expand into unstable circular shells. As the theories are noncommutative, the naive definition of the locations of the vortices and shells is gauge-dependent, and so we define and calculate the profiles of these solutions using the gauge-invariant noncommutative Wilson lines introduced by Gross and Nekrasov. We find that charge 2 vortex solutions are characterized by two positions and a single nonnegative real number, which we demonstrate is the radius of the shell. We find that the radius is identically zero in all 2-dimensional solutions. If one considers solutions that depend on an additional commutative direction, then there are time-dependent solutions in which the radius oscillates, resembling a braneworld description of a cyclic universe. There are also smooth BIon-like space-dependent solutions in which the shell expands to infinity, describing a vortex ending on a domain wall.