1206.6205 (Jos Van Doorsselaere)

Properties of symmetry restoration in the electroweak vacuum in very
high magnetic fields    [PDF]

Jos Van Doorsselaere

We discuss properties of the electroweak vacuum as a function of an external magnetic field. The interest in these properties arises due to possible existence of the electromagnetically superconducting phase of QCD in the background of a sufficiently strong magnetic field. The presence of a superconducting vacuum state is known for the electroweak theory with a strong magnetic background and we show how at even higher magnetic fields, the vacuum state is drastically altered. The Higgs condensate vanishes and is replaced with a condensate of vector bosons, taking the form of chromomagnetic vortices in pure Yang-Mills theory. This vector condensate is an exact solution of a Liouville equation and an Abrikosov lattice of vortices can be found, in the form of an exact solution in terms of double periodic Weierstrass functions. We also find that a hypothetical classical interpolating vacuum between the previously known superconducting state and the chromomagnetic vortex lattice would require an exotic vacuum solution, presumably consisting of Alice strings, which are vortices with a fractional winding number.

View original: http://arxiv.org/abs/1206.6205