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| Autor principal: | |
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
| Publicado: |
Zenodo
2026
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| Materias: | |
| Acceso en línea: | https://doi.org/10.5281/zenodo.19571171 |
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- <p>Abstract</p> <p>We extend the minimal layered phase framework of Paper I [1] in two steps.</p> <p>First, we introduce the minimal inter-layer synchronisation potential consistent with</p> <p>the global U(1) symmetry of the scalar model. Spontaneous symmetry breaking</p> <p>produces a massless Goldstone mode and N−1 massive relative modes. Canonical</p> <p>normalisation of the Goldstone mode yields the exact coupling suppression geff =</p> <p>gN−1/2, with no adjustable parameters.</p> <p>In the second step, we replace the scalar target space S1 with the vector target</p> <p>space S2, the minimal extension that admits a non-trivial Hopf invariant QH ∈Z.</p> <p>We show that integrating out the massive relative modes generates a Skyrme–</p> <p>Faddeev quartic term in the effective Lagrangian, which evades Derrick’s theorem</p> <p>and stabilises three-dimensional solitons (Hopfions). The Vakulenko–Faddeev en-</p> <p>ergy bound E ≥C(Nf2)1/2κ1/2|QH|3/4 then implies a discrete, topologically pro-</p> <p>tected excitation spectrum. A variational estimate gives Emin(2)/Emin(1) ≈1.63.</p> <p>All results follow from the microscopic Lagrangian and established mathematical</p> <p>theorems without fine-tuning. Exchange statistics of Hopfions are addressed in Pa-</p> <p>per III</p> <p> </p>