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Physical Review D

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Vortices in the extended Skyrme-Faddeev model

L. A. Ferreira^1,*, J. Jäykkä^2,†, Nobuyuki Sawado^3,‡, and Kouichi Toda^4,§

¹Instituto de Física de São Carlos; IFSC/USP; Universidade de São Paulo—USP, Caixa Postal 369, CEP 13560-970, São Carlos-SP, Brazil
²School of Mathematics, University of Leeds, LS2 9JT Leeds, United Kingdom
³Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
⁴Department of Mathematical Physics, Toyama Prefectural University, Kurokawa 5180, Imizu, Toyama, 939-0398, Japan

^*laf@ifsc.usp.br
^†juhaj@iki.fi
^‡sawado@ph.noda.tus.ac.jp
^§kouichi@yukawa.kyoto-u.ac.jp

Phys. Rev. D 85, 105006 – Published 9 May, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.105006

Abstract

We construct analytical and numerical vortex solutions for an extended Skyrme-Faddeev model in a $(3 + 1)$ dimensional Minkowski space-time. The extension is obtained by adding to the Lagrangian a quartic term, which is the square of the kinetic term, and a potential which breaks the $S O (3)$ symmetry down to $S O (2)$ . The construction makes use of an ansatz, invariant under the joint action of the internal $S O (2)$ and three commuting $U (1)$ subgroups of the Poincaré group, and which reduces the equations of motion to an ordinary differential equation for a profile function depending on the distance to the $x^{3}$ axis. The vortices have finite energy per unit length, and have waves propagating along them with the speed of light. The analytical vortices are obtained for a special choice of potentials, and the numerical ones are constructed using the successive over relaxation method for more general potentials. The spectrum of solutions is analyzed in detail, especially its dependence upon special combinations of coupling constants.

Article Text

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