  We consider a new 3-parameter class of exact 4-dimensional solutions in
closed string theory and solve the corresponding string model, determining the
physical spectrum and the partition function. The background fields (4-metric,
antisymmetric tensor, two Kaluza-Klein vector fields, dilaton and modulus)
generically describe axially symmetric stationary rotating (electro)magnetic
flux-tube type universes. Backgrounds of this class include both the dilatonic
(a=1) and Kaluza-Klein (a=\sqrt 3) Melvin solutions and the uniform magnetic
field solution, as well as some singular space-times. Solvability of the string
sigma model is related to its connection via duality to a simpler model which
is a ``twisted" product of a flat 2-space and a space dual to 2-plane. We
discuss some physical properties of this model (tachyonic instabilities in the
spectrum, gyromagnetic ratios, issue of singularities, etc.). It provides one
of the first examples of a consistent solvable conformal string model with
explicit D=4 curved space-time interpretation.
