Phase Structure of Electroweak Vacuum in a Strong Magnetic Field: The Lattice Results.

Using first-principle lattice simulations, we demonstrate that in the background of a strong magnetic field (around 10^{20}  T), the electroweak sector of the vacuum experiences two consecutive crossover transitions associated with dramatic changes in the zero-temperature dynamics of the vector W bosons and the scalar Higgs particles, respectively. Above the first crossover, we observe the appearance of large, inhomogeneous structures consistent with a classical picture of the formation of W and Z condensates pierced by vortices. The presence of the W and Z condensates supports the emergence of the exotic superconducting and superfluid properties induced by a strong magnetic field in the vacuum.

Casimir Effect in Yang-Mills Theory in D=2+1.

We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principles numerical simulations. Working in two spatial dimensions at zero temperature, we find that closely spaced perfect chromoelectric conductors attract each other with a small anomalous scaling dimension. At large separation between the conductors, the attraction is exponentially suppressed by a new massive quantity, the Casimir mass, which is surprisingly different from the lowest glueball mass.