MELVIN SOLUTION IN STRING THEORY

We identify string theory counterpart of the dilatonic Melvin D = 4 ba ckground describing a ''magnetic flux tube'' in low-energy field theor y limit. The corresponding D = 5 bosonic string model containing extra compact Kaluza-Klein dimension is a direct product of the D = 2 Minko wski 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 par ticular, that the dilatonic Melvin background is an exact string solut ion to all orders in alpha'. Moreover, the D = 3 model is formally rel ated by an abelian duality to a flat space of non-trivial topology. Th e conformal held theory for the Melvin solution is exactly solvable (a nd 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 tac hyonic instabilities.