Elsevier

Nuclear Physics B

Volume 385, Issues 1–2, 19 October 1992, Pages 127-144
Nuclear Physics B

Semi-local strings and monopoles

https://doi.org/10.1016/0550-3213(92)90097-UGet rights and content

Abstract

A variation on the abelian Higgs model, with SU(2)global × U(1)local symmetry broken to U(1)global, was recently shown by Vachaspati and Achúcarro to admit stable, finite-energy cosmic string solutions, even though the manifold of minima of the potential energy does not have non-contractible loops. This new and unexpected feature motivates a full investigation of the properties of the model. Here we exploit the existence of first-order Bogomol'nyi equations to classify all static finite-energy vortex solutions in the Bogomol'nyi limit. We find a 4n-dimensional moduli space for the nth topological (n-vortex) sector. Single-vortex configurations depend on a position coordinate and on an additional complex parameter and may be regarded as hybrids of Nielsen-Olesen vortices and CP1 lumps. The model is also shown to obey Bogomol'nyi equations in curved space, and these allow a simple calculation of the gravitational field of the above configurations. Finally, monopole-like solutions interpolating between a Dirac monopole and a global monopole are found. These must be sorrounded by an event horizon as isolated solutions, but may also arise as unstable end points of semi-local strings.

References (14)

  • R. Leese

    Nucl. Phys.

    (1990)
    P.J. Ruback

    Commun. Math. Phys.

    (1986)
  • A. Achúcarro et al.

    CFA-3384

    (March 1992)
  • A. Comtet et al.

    Nucl. Phys.

    (1988)
  • M. Barriola et al.

    Phys. Rev. Lett.

    (1989)
  • R. Rajaraman

    Solitons and instantons

    (1982)
  • T. Vachaspati et al.

    Phys. Rev.

    (1991)
  • M. Hindmarsh

    Phys. Rev. Lett.

    (1992)
There are more references available in the full text version of this article.

Cited by (87)

  • A classification of semilocal vortices in a Chern-Simons theory

    2016, Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
  • A nonabelian particle-vortex duality

    2016, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
    Citation Excerpt :

    In section 2 we revisit non-abelian T-duality and its relation to the abelian T-duality, extending it in section 3 to three spacetime dimensions, consequently defining a non-abelian particle–vortex duality on a general theory which we illustrate with a simple example of a semilocal vortex in section 4. This article should be viewed as a proof-of-principle of a phenomenon with potential application from condensed matter to cosmology, with a longer companion paper to follow in which we will elaborate further on the duality and provide more substantial examples [17]. Abelian particle–vortex duality has proven a powerful tool in the understanding of bosonic systems that range from anyonic superconductivity through to cosmic strings.

View all citing articles on Scopus

This work is supported in part by funds provided by the US Department of Energy (DOE) under contract DE-AC02-76ER03069 and by CICYT, Spain under contract AE-90-0034.

View full text