Exactly solvable string models of curved space-time backgrounds Original Research Article

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 = √3) Melvin solutions and the uniform magnetic field solution, as well as some singular space-times. Solvability of the string σ-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 ratio, 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.