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Instability of Electroweak Homogeneous Vacua in Strong Magnetic Fields

We consider the classical vacua of the Weinberg–Salam (WS) model of electroweak forces. These are no-particle, static solutions to the WS equations minimizing the WS energy locally. We study the WS vacuum solutions exhibiting a non-vanishing average magnetic field of strength b and prove that (i) th...

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Bibliographic Details
Published in:Annales Henri Poincaré 2024, Vol.25 (12), p.5277-5337
Main Authors: Gardner, Adam, Sigal, Israel Michael
Format: Article
Language:English
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Summary:We consider the classical vacua of the Weinberg–Salam (WS) model of electroweak forces. These are no-particle, static solutions to the WS equations minimizing the WS energy locally. We study the WS vacuum solutions exhibiting a non-vanishing average magnetic field of strength b and prove that (i) there is a magnetic field threshold b ∗ such that for b < b ∗ , the vacua are translationally invariant (and the magnetic field is constant), while, for b > b ∗ , they are not, (ii) for b > b ∗ , there are non-translationally invariant solutions with lower energy per unit volume and with the discrete translational symmetry of a 2D lattice in the plane transversal to b , and (iii) the lattice minimizing the energy per unit volume approaches the hexagonal one as the magnetic field strength approaches the threshold b ∗ . In the absence of particles, the Weinberg–Salam model reduces to the Yang–Mills–Higgs (YMH) equations for the gauge group U (2). Thus, our results can be rephrased as the corresponding statements about the U (2)-YMH equations.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-024-01430-5