Instability of electroweak homogeneous vacua in strong magnetic fields

Instability of electroweak homogeneous vacua in strong magnetic fields Adam Gardner Doctor of Philosophy Graduate Department of Mathematics University of Toronto 2020 We consider the classical (local) vacua of the Weinberg-Salam (WS) model of electroweak forces. These are defined as no-particle, static solutions to the WS equations minimizing the WS energy locally. In the absence of particles, the Weinberg-Salam model reduces to the Yang-Mills-Higgs (YMH) equations for the gauge group U(2). We consider the WS system in a constant external magnetic field, b, and prove that (i) there is a magnetic field threshold b∗ such that for b < b∗, the vacua are translationally invariant, 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 the external magnetic field, and (iii) the lattice minimizing the energy per unit volume approaches the hexagonal one as the magnetic field strength approaches the threshold b∗.