Exact primordial black strings in four dimensions

A solution of effective string theory in four dimensions is presented which admits interpretation of a rotating black cosmic string. It is constructed by taking the tensor product of the three-dimensional black hole, extended with the Kalb-Ramond axion, with a flat direction. The physical interpretation of the solution is discussed, with special attention to the axion, which is found to play a role very similar to a Higgs field. Finally, it is pointed out that the solution represents an exact Wess-Zumino-Witten-Novikov σ model on the string world sheet, to all orders in the inverse string tension α'