Melvin solution in string theory

TL;DR

This paper identifies an exact string theory solution corresponding to the dilatonic Melvin background, showing its relation to conformal sigma models, dualities, and potential instabilities, advancing understanding of magnetic flux tubes in string theory.

Contribution

It establishes the Melvin background as an exact string solution via a specific conformal sigma model and explores its dualities and stability properties.

Findings

The Melvin background is an exact string solution to all orders in '

The associated conformal field theory is exactly solvable

Special magnetic field values relate to orbifold CFTs

Abstract

We identify a string theory counterpart of the dilatonic Melvin D=4 background describing a "magnetic flux tube" in low-energy field theory limit. The corresponding D=5 bosonic string model containing extra compact Kaluza-Klein dimension is a direct product of the D=2 Minkowski space and a D=3 conformal sigma model. The latter is a singular limit of the [SL(2,R) x R]/R gauged WZW theory. This implies, in particular, that the dilatonic Melvin background is an exact string solution to all orders in \a'. Moreover, the D=3 model is formally related by an abelian duality to a flat space with a non-trivial topology. The conformal field theory for the Melvin solution is exactly solvable (and for special values of magnetic field parameter is equivalent to CFT for a $Z_N$ orbifold of 2-plane times a circle) and should exhibit tachyonic instabilities.