Magnetic flux tube models in superstring theory

Superstring models describing curved 4-dimensional magnetic flux tube backgrounds are exactly solvable in terms of free fields. We first consider the simplest model of this type (corresponding to a 'Kaluza-Klein' a = root 3 Melvin background). Its 2d action has a hat but topologically non-trivial 10-dimensional target space (there is a mixing of the angular coordinate of the 2-plane with an internal compact coordinate). We demonstrate that this theory has broken supersymmetry but is perturbatively stable if the radius R of the internal coordinate is larger than R(0) = root alpha'. In the Green-Schwarz formulation the supersymmetry breaking is a consequence of the presence of a flat but non-trivial connection in the fermionic terms in the action. For R < R(0) and the magnetic field strength parameter q > R/2 alpha', instabilities appear corresponding to tachyonic winding states. The torus partition function Z(q, R) is finite for R > R(0) and vanishes for qR = 2n (n integer). At the special points qR = 2n (2n+1) the model is equivalent to the free superstring theory compactified on a circle with periodic (antiperiodic) boundary conditions for space-time fermions. Analogous results are obtained for a more general class of static magnetic flux tube geometries including the a = 1 Melvin model.