Nuclear Physics B330 (1990) 193-204 North-Holland A CONDENSATE SOLUTION OF THE ELECTROWEAK THEORY WHICH INTERPOLATES BETWEEN THE BROKEN AND THE SYMMETRIC PHASE J. AMBJIORNand P. OLESEN The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark Received 29 May 1989 We discuss a magnetic type solution of the classical electroweak equations with the property that for fields larger than m~/e a W- and Z-condensate is formed. When the average magnetic field reaches the value m~/e cos2 O, the SU(2) X Uy(1) symmetry is restored. We compare to the finite temperature case. It is mentioned that large magnetic fields of order m~/e (realized e.g. near the superconducting cosmic string) can actually be achieved in earth-bound laboratories as the field surrounding quarks in e.g. proton-proton collisions with more than 1 TeV energy. However, we do not know if the field lasts long enough to produce a W-Z plasma. 1. Introduction The electroweak theory has a broken as well as a symmetric phase. When the theory is confronted with experiments in laboratories it is always the former phase which is checked with success, whereas the latter phase is supposed to be available only in the early universe. It is therefore of much interest to ask the question as to whether the symmetric phase could, at least in principle, be observed by some arrangement in earth bound laboratories. There exists an old suggestion that if one could produce large magnetic fields, then the broken phase might make a transition to the symmetric phase in the environment provided by the strong static magnetic field [1]. This suggestion was based in part on the analogy with superconductors. Here it is well known that sufficiently large magnetic fields force the complex order parameter + to vanish, due to the minimal coupling between the electromagnetic field A, and ~b. However, this analogy is somewhat incorrect, since in the electroweak theory the field A~ does not couple to the Higgs field q0 (which can be taken to be real in the unitary gauge). It was therefore suggested that perhaps the radiative corrections might nevertheless produce a transition from the broken to the symmetric phase [1]. It was, however, soon realized [2] that the usual (trivial) electroweak vacuum becomes unstable for large magnetic fields. For example, if one computes the vacuum energy density d ° in the one loop approximation one finds an expression 0550-3213/90/$03.50© Elsevier Science Publishers B.V. (North-Holland)