Global vs local cosmic strings from pseudo-anomalous U(1)
  We study the structure of cosmic strings produced at the breaking of an anomalous U(1) gauge symmetry present in many superstring compactification models. We show that their coupling with the axion necessary in order to cancel the anomalies does not prevent them from being local, even though their energy per unit length is found to diverge logarithmically. We discuss the formation of such strings and the phenomenological constraints that apply to their parameters. 
P. Binetruy, C. Deffayet, and P. Peter