Winding Hopfions on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="bold">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>

Kobayashi, Michikazu; Nitta, Muneto

doi:10.1016/j.nuclphysb.2013.08.012

Cited by 20 publications

(12 citation statements)

References 77 publications

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“…However, the domain space of the latter model is the compactified three dimensional sphere S 3 and the Hopfion solutions are classified by the linking number associated with the homotopy group π 3 (S 2 ) = Z. Thus, in some sense the baby Skyrme model can be considered as a planar reduction of the Faddeev-Skyrme model [40].…”

Section: The Modelmentioning

confidence: 99%

Gauged multisoliton baby Skyrme model

Samoilenka

Shnir

2016

Phys. Rev. D

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We present a study of U (1) gauged modification of the 2+1 dimensional planar Skyrme model with a particular choice of the symmetry breaking potential term which combines a short-range repulsion and a long-range attraction. In the absence of the gauge interaction the multi-solitons of the model are aloof, they consist of the individual constituents which are well separated. Peculiar feature of the model is that there are usually several different stable static multi-soliton solutions of rather similar energy in a topological sector of given degree. We investigated the pattern of the solutions and find new previously unknown local minima. It is shown that coupling of the aloof planar multi-Skyrmions to the magnetic field strongly affects the pattern of interaction between the constituents. We analyse the dependency of the structure of the solutions, their energies and magnetic fluxes on the strength of the gauge coupling. It is found that, generically, in the strong coupling limit the coupling to the gauge field results in effective recovering of the rotational invariance of the configuration.

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Section: The Modelmentioning

confidence: 99%

Gauged multisoliton baby Skyrme model

Samoilenka

Shnir

2016

Phys. Rev. D

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“…ref. [144,145]), those on R 2 ×S 1 with an untwisted boundary condition can be twisted closed lump strings wrapping around S 1 [122,[146][147][148][149]. If we impose twisted boundary conditions, we will be able to obtain a fractional Hopfion as a half-twisted lump string wrapping around S 1 .…”

Section: Jhep03(2015)108mentioning

confidence: 99%

Fractional instantons and bions in the O(N) model with twisted boundary conditions

Nitta

2015

J. High Energ. Phys.

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Recently, multiple fractional instanton configurations with zero instanton charge, called bions, have been revealed to play important roles in quantum field theories on compactified spacetime. In two dimensions, fractional instantons and bions have been extensively studied in the CP N −1 model and the Grassmann sigma model on R 1 × S 1 with the Z N symmetric twisted boundary condition. Fractional instantons in these models are domain walls with a localized U(1) modulus twisted half along their world volume. In this paper, we classify fractional instantons and bions in the O(N ) nonlinear sigma model on R N −2 × S 1 with more general twisted boundary conditions in which arbitrary number of fields change sign. We find that fractional instantons have more general composite structures, that is, a global vortex with an Ising spin (or a half-lump vortex), a half sineGordon kink on a domain wall, or a half lump on a "space-filling brane" in the O(3) model (CP 1 model) on R 1 × S 1 , and a global monopole with an Ising spin (or a half-Skyrmion monopole), a half sine-Gordon kink on a global vortex, a half lump on a domain wall, or a half Skyrmion on a "space-filling brane" in the O(4) model (principal chiral model or Skyrme model) on R 2 × S 1 . We also construct bion configurations in these models.

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“…More generally, a vortex string with the winding number Q, along which the U(1) modulus is twisted P times, has the instanton number B = P Q [45] (which was obtained in ref. [46] to calculate the Hopf number for Hopfions by lifting up π 3 (S 2 ) to π 3 (S 3 )). The topological charges of fractional (anti-)instantons with the Z 2 symmetric twisted boundary condition are summarized in table 1.…”

Section: Fractional Instantonsmentioning

confidence: 99%

Fractional instantons and bions in the principal chiral model on ℝ 2 × S 1 $$ {\mathrm{\mathbb{R}}}^2\times {S}^1 $$ with twisted boundary conditions

Nitta

2015

J. High Energ. Phys.

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Bions are multiple fractional instanton configurations with zero instanton charge playing important roles in quantum field theories on a compactified space with a twisted boundary condition. We classify fractional instantons and bions in the SU(N ) principal chiral model on R 2 ×S 1 with twisted boundary conditions. We find that fractional instantons are global vortices wrapping around S 1 with their U(1) moduli twisted along S 1 , that carry 1/N instanton (baryon) numbers for the Z N symmetric twisted boundary condition and irrational instanton numbers for generic boundary condition. We work out neutral and charged bions for the SU(3) case with the Z 3 symmetric twisted boundary condition. We also find for generic boundary conditions that only the simplest neutral bions have zero instanton charges but instanton charges are not canceled out for charged bions. A correspondence between fractional instantons and bions in the SU(N ) principal chiral model and those in Yang-Mills theory is given through a non-Abelian Josephson junction.

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Winding Hopfions on R2×S1

Cited by 20 publications

References 77 publications

Gauged multisoliton baby Skyrme model

Gauged multisoliton baby Skyrme model

Fractional instantons and bions in the O(N) model with twisted boundary conditions

Fractional instantons and bions in the principal chiral model on ℝ 2 × S 1 $$ {\mathrm{\mathbb{R}}}^2\times {S}^1 $$ with twisted boundary conditions

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