Non-Abelian Vortex-String Dynamics from Nonlinear Realization

TL;DR

This paper derives the low-energy effective action for non-Abelian vortex-strings using nonlinear realization, revealing a combined Nambu-Goto and ${f C}P^{N-1}$ model structure with higher order corrections.

Contribution

It introduces a novel approach to derive vortex-string dynamics from nonlinear realization, unifying spacetime oscillations and internal orientations in a combined action.

Findings

The effective action has a Nambu-Goto-${\bf C}P^{N-1}$ form.

Higher order derivative corrections are explicitly computed.

The framework extends to general p-brane dynamics with internal symmetry breaking.

Abstract

The dynamics of the non-Abelian vortex-string, which describes its low energy oscillations into the target $D=3+1$ spacetime as well as its orientations in the internal space, is derived by the approach of nonlinear realization. The resulting action correlating these two sectors is found to have an invariant synthesis form of the Nambu-Goto-${\bf C}P^{N-1}$ model actions. Higher order corrections to the vortex actions are presented up to the order of quartic derivatives. General $p$-brane dynamics in terms of the internal symmetry breaking is also discussed.