Vacuum structure of the electroweak theory in high magnetic fields

Abstract

In the electroweak theory one can reach the unbroken phase SU(2) × U Y (1) by pumping enough magnetic energy into the system. The whole energy is then carried by the fields associated with U Y (1), whereas the fields corresponding to SU(2) are in a vacuum state. We show that the vacuum is non-trivial in the sense that it consists of a condesate of zero-field twists which arise in a smooth way from a condensate of vortex lines existing in the broken phase. An explicit vacuum solution is constructed in terms of Weierstrass' elliptic function. The results mentioned above are strictly valid only in the case when the Z mass equals the Higgs mass.