Decay of magnetic fields in Kaluza-Klein theory

Magnetic fields in five-dimensional Kaluza-Klein theory compactified on a circle correspond to ‘‘twisted’’ identifications of five-dimensional Minkowski space. We show that a five-dimensional generalization of the Kerr solution can be analytically continued to construct an instanton that gives rise to two possible decay modes of a magnetic field. One decay mode is the generalization of the ‘‘bubble decay’’ of the Kaluza-Klein vacuum described by Witten. The other decay mode, rarer for weak fields, corresponds in four dimensions to the creation of monopole-antimonopole pairs. An instanton for the latter process is already known and is given by the analytic continuation of the Kaluza-Klein Ernst metric, which we show is identical to the five-dimensional Kerr solution. We use this fact to illuminate further properties of the decay process. It appears that fundamental fermions can eliminate the bubble decay of the magnetic field, while allowing the pair produciton of Kaluza-Klein monopoles. © 1995 The American Physical Society.