The Decay of Magnetic Fields in Kaluza-Klein Theory

TL;DR

This paper investigates how magnetic fields in five-dimensional Kaluza-Klein theory decay via instanton solutions, revealing two decay modes: bubble decay and monopole-anti-monopole pair creation, with implications for fermion effects.

Contribution

It introduces a five-dimensional generalization of the Kerr solution to analyze magnetic field decay modes in Kaluza-Klein theory, connecting known instantons and revealing new decay processes.

Findings

Identifies two decay modes: bubble decay and monopole pair creation.

Shows the five-dimensional Kerr solution relates to known instantons for pair production.

Suggests fermions can suppress bubble decay while permitting monopole pair creation.

Abstract

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 generalisation 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 generalisation 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-anti-monopole pairs. An instanton for the latter process is already known and is given by the analytic continuation of the \KK\ 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 production of Kaluza-Klein monopoles.