Vortex String Dynamics in an External Antisymmetric Tensor Field

TL;DR

This paper explores the dynamics of vortex strings in a constant antisymmetric tensor field, revealing exact solitonic configurations and a novel breather solution through duality with the complex sine-Gordon equation.

Contribution

It introduces a new class of string configurations and establishes a duality-based approach to analyze vortex string dynamics in background fields.

Findings

Derived exact solitonic string solutions analogous to fluid vortex phenomena

Discovered a new breather-type string configuration via duality

Extended the understanding of string behavior in antisymmetric tensor fields

Abstract

We study the Lund-Regge equation that governs the motion of strings in a constant background antisymmetric tensor field by using the duality between the Lund-Regge equation and the complex sine-Gordon equation. Similar to the cases of vortex filament configurations in fluid dynamics, we find various exact solitonic string configurations which are the analogue of the Kelvin wave, the Hasimoto soliton and the smoke ring. In particular, using the duality relation, we obtain a completely new type of configuration which corresponds to the breather of the complex sine-Gordon equation.