Multiply Phased Traveling BPS Vortex

TL;DR

This paper introduces multiply phased vortex solutions in a U(1) gauge theory with an SU(N+1) scalar multiplet, featuring traveling waves with different frequencies and additional energy contributions from phase variations.

Contribution

It presents a novel class of vortex solutions with multiple phases and traveling waves, expanding the understanding of vortex dynamics in gauge theories.

Findings

Vortex solutions include traveling waves with distinct frequencies.

Energy depends on topological charge and Noether charge.

Solutions are in the Bogomolny limit with static and dynamic components.

Abstract

We present the multiply phased current carrying vortex solutions in the U(1) gauge theory coupled to an $(N+1)$-component SU(N+1) scalar multiplet in the Bogomolny limit. Our vortex solutions correspond to the static vortex dressed with traveling waves along the axis of symmetry. What is notable in our vortex solutions is that the frequencies of traveling waves in each component of the scalar field can have different values. The energy of the static vortex is proportional to the topological charge of $CP^N$ model in the BPS limit, and the multiple phase of the vortex supplies additional energy contribution which is proportional to the Noether charge associated to the remaining symmetry.