Anomalous U(1) Vortices and The Dilaton
  The role of the (dynamical) dilaton in the vortices associated with the spontaneous breaking of an anomalous U(1) from heterotic string theory is examined. We demonstrate how the anomaly (and the coupling to the dilaton/axion) can appear in the Lagrangian and associated field equations as a controlled perturbation about the standard Nielsen-Olesen equations. In such a picture, the additional field equation for the dilaton becomes a series of corrections to a constant dilaton vev as the anomaly is turned on. In particular we find that even the first nontrivial correction to a constant dilaton generically leads to a (positive) logarithmic divergence of the heterotic dilaton near the vortex core. Since the dilaton field governs the strength of quantum fluctuations in string theory, this runaway behaviour implies that anomalous U(1) vortices in string theory are intrinsically quantum mechanical objects. 
Bruce A. Campbell, Kirk Kaminsky