The Kaluza-Klein Melvin Solution in M-theory

TL;DR

This paper explores the properties and instabilities of the Kaluza-Klein Melvin solution in M-theory, revealing equivalences between different string theories with magnetic flux and analyzing their decay mechanisms.

Contribution

It demonstrates the equivalence of type IIA and 0A Melvin backgrounds via a magnetic field shift and analyzes their decay processes through instantons and brane nucleation.

Findings

Type IIA and 0A Melvin solutions are related by a magnetic field shift.

Partition functions of related string theories are connected through flux shifts.

Instabilities involve brane pair production and bubble nucleation.

Abstract

We study some aspects of the Kaluza-Klein Melvin solution in M-theory. The associated magnetic field has a maximal critical value $B=\pm 1/R$ where $R$ is the radius of the compactification circle. It is argued that the Melvin background of type IIA with magnetic field $B$ and of type 0A with magnetic field $B'=B-1/R$ are equivalent. Evidence for this conjecture is provided using a further circle compactification and a `9-11' flip. We show that partition functions of nine-dimensional type IIA strings and of a $(-1)^F\sigma_{1/2}$ type IIA orbifold both with NS-NS Melvin fluxtubes are related by such shift of the magnetic field. Then the instabilities of both IIA and 0A Melvin solutions are analyzed. For each theory there is an instanton associated to the decay of spacetime. In the IIA case the decay mode is associated to the nucleation of $D6/D\bar{6}$-brane pairs, while in the 0A case spacetime decays through Witten's bubble production.