  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.
