On electroweak magnetism

Some exact Bradlow vortex solutions

“…We will thus call the equation the Ambjørn-Olesen-Manton equation. The fact that it resembles the normal vortex equation but with opposite sign of the last term can be interpreted as the effect of anti-screening of the W -boson as opposed to the normal screening effect in Abelian theories [9,10]. In the flat plane, R 2 , the Ambjørn-Olesen-Manton equation does not have a single vortex solution, but instead a lattice of vortices.…”

“…The unnamed equation is, however, not really new as it was found by Ambjørn and Olesen in refs. [9,10] 2 and it describes Wcondensation giving rise to a periodic vortex lattice in the electroweak theory. We will thus call the equation the Ambjørn-Olesen-Manton equation.…”

Symmetry restoration at finite temperature with weak magnetic fields

“…With this, one obtains the simple bound B T 2 [36]. Furthermore, to guarantee stability conditions against the formation of a W -condensate [37], one obtains that the field is also weak compared to m 2 W . We want to study the EWPT transition via the analysis of the EP when its minima change in the presence of magnetic fields, we will work explicitly with the assumption that the hierarchy of scales…”

Magnetic Phases in Dense Quark Matter

“…Similarly to other spin-1 theories with magnetic instabilities [16]- [18], the solution of the zero-mode problem leads to the restructuring of the ground state through the formation of an inhomogeneous gauge-field condensate G, as well as an induced magnetic field due to the back reaction of the G condensate on the rotated electromagnetic field. The magnitude of the G-condensate plays the role of the order parameter for the phase transition occurring at B = B PCFL .…”

“…Once B ≥ B PCFL = m 2 M , one of the modes of the charged gauge field becomes tachyonic (this is the well known "zero-mode problem" for spin-1 charged fields in the presence of a magnetic field found for Yang-Mills fields [16], for the W ± µ bosons in the electroweak theory [17,18], and even for higher-spin fields in the context of string theory [19]). Similarly to other spin-1 theories with magnetic instabilities [16]- [18], the solution of the zero-mode problem leads to the restructuring of the ground state through the formation of an inhomogeneous gauge-field condensate G, as well as an induced magnetic field due to the back reaction of the G condensate on the rotated electromagnetic field.…”