We discuss superconducting phases of vacuum induced by strong magnetic field in the Electroweak model and in Quantum Chromodynamics at zero temperature. In these phases the vacuum behaves as an anisotropic inhomogeneous superconductor which supports superconductivity along the axis of the magnetic field while in the transversal directions the superconductivity does not exist. The magnetic-field-induced anisotropic superconductivity appears as a result of condensation of electrically charged spin-one particles, which are elementary W bosons in the case of the Electroweak model and composite quark-antiquark pairs with quantum numbers of ρ mesons in the case of QCD. Due to the anisotropic nature of superconductivity the Meissner effect is absent. Intrinsic inhomogeneities of the superconducting ground state are characterized by ensembles of certain topological vortices in an analogy with a mixed Abrikosov state of a type-II superconductivity.Keywords:Q u a n t u mC h r o m o d y n a m i c s ,E l e c t r o w e a kM o d e l ,S t r o n gM a g n e t i cF i e l d ,S uperconductivity PACS numb ers: 11.15. Kc, 12.15.y, 74.90.+n * On leave from ITEP, Moscow, Russia. Strong magnetic fields may lead to many unusual phenomena both in dense matter and in the quantum vacuum. There are various QED effects associated with a critical magnetic field B QED = m 2 e c 3 /~e ⇡ 4.4 ⇥ 10 9 T at which the splitting between zeroth and first Landau electron's levels exceeds the rest energy of an electron, m e c 2 . Such strong fields make the QED vacuum optically birefringent, 1 leading to distortion and magnification of images (a magnetic lens effect), splitting and merging of photons and affecting strongly atomic spectra.
2At much stronger magnetic fields of the order of the QCD scale, B ⇠ 10 16 T various other interesting effects may happen. The magnetic fields of this strength may be created on Earth in heavy-ion collisions at the Large Hadron Collider at CERN in Europe and at Relativistic Heavy-Ion Collider at Brookhaven National Laboratory in the U.S.A..3-5 The colliding ions create the a plasma made of hot quarks, antiquarks and gluons, which are subjected to a short-lived strong magnetic field if the collisions are not central.6 Similar conditions may have also existed in the very early moments of our Universe.
7The chiral magnetic effect 6, 8-11 provides a particularly interesting example of the influence of the magnetic field on hot quark matter. Topological processes at the QCD scale may lead to a chiral asymmetry of quark matter which is characterized by a unequal densities of left and right quarks. The magnetic field may generate a dissipationless electric current in the parity-odd quark-gluon plasma leading to potentially observable phenomena in heavy-ion collisions.
12-15The hadron-scale magnetic field should also induce so-called magnetic catalysis, 16-20 which implies, in particular, a steady enhancement of chiral symmetry breaking in the cold QCD vacuum as the external magnetic field strengthens. A strong magnetic field ba...