Melvin solution in string theory

Abstract

We identify 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 σ-model. The latter is a singular limit of the [SL(2,R) × R] R gauged WZW theory. This implies, in particular, that the dilatonic Melvin background is an exact string solution to all orders in α 1. Moreover, the D = 3 model is formally related by an abelian duality to a flat space of 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 Zn orbifold of 2-plane times a circle) and should exhibit tachyonic instabilities.