Incarnations of Skyrmions

Gudnason, Sven Bjarke; Nitta, Muneto

doi:10.1103/physrevd.90.085007

Cited by 46 publications

(80 citation statements)

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“…This means that we can connect all vacua with the spherically symmetric skyrmions. Of course, one could introduce such vacua in Skyrme theory introducing a potential term in the Lagrangian [24]. This is not what we are doing here.…”

Section: Multiple Vacua Of Skyrme Theorymentioning

confidence: 91%

New topological structures of Skyrme theory: baryon number and monopole number

et al. 2017

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Based on the observation that the skyrmion in Skyrme theory can be viewed as a dressed monopole, we show that the skyrmions have two independent topology, the baryon topology π 3 (S 3 ) and the monopole topology π 2 (S 2 ). With this we propose to classify the skyrmions by two topological numbers (m, n), the monopole number m and the shell (radial) number n. In this scheme the popular (non spherically symmetric) skyrmions are classified as the (m, 1) skyrmions but the spherically symmetric skyrmions are classified as the (1, n) skyrmions, and the baryon number B is given by B = mn. Moreover, we show that the vacuum of the Skyrme theory has the structure of the vacuum of the SineGordon theory and QCD combined together, which can also be classified by two topological numbers ( p, q). This puts the Skyrme theory in a totally new perspective.

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Section: Multiple Vacua Of Skyrme Theorymentioning

confidence: 91%

New topological structures of Skyrme theory: baryon number and monopole number

et al. 2017

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“…One simple way to ameliorate this problem is to add further terms to the potential like, e.g., higher powers of the pion mass potential [14], [15], L 0 = a λ 0,a U a π . These higher powers introduce a short-range repulsion between individual nucleons (i.e., B = 1 skyrmions), thereby reducing the overall binding energies.…”

Section: Arxiv:160704286v2 [Hep-th] 19 Sep 2016mentioning

confidence: 99%

Radial vibrations of BPS skyrmions

et al. 2016

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We study radial vibrations of spherically symmetric skyrmions in the BPS Skyrme model. Concretely, we numerically solve the linearised field equations for small fluctuations in a skyrmion background, both for linearly stable oscillations and for (unstable) resonances. This is complemented by numerical solutions of the full nonlinear system, which confirm all the results of the linear analysis. In all cases, the resulting fundamental excitation provides a rather accurate value for the Roper resonance, supporting the hypothesis that the BPS Skyrme model already gives a reasonable approximate description of this resonance. Further, for many potentials additional higher resonances appear, again in agreement with known experimental results.

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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 )).…”

Section: Fractional Instantonsmentioning

confidence: 91%

“…[45], in which stable configurations of (half) Skyrmions inside a vortex string were constructed without the Skyrme term (on R 3 without twisted boundary condition).…”

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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Incarnations of Skyrmions

Cited by 46 publications

References 100 publications

New topological structures of Skyrme theory: baryon number and monopole number

New topological structures of Skyrme theory: baryon number and monopole number

Radial vibrations of BPS skyrmions

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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