Anomalous U(1) Vortices and The Dilaton

TL;DR

This paper investigates how the dilaton field affects anomalous U(1) vortices in heterotic string theory, revealing that quantum effects cause the dilaton to diverge near vortex cores, making these vortices inherently quantum objects.

Contribution

It introduces a perturbative approach to include the dilaton in vortex solutions, showing the divergence of the dilaton near the core due to anomaly effects.

Findings

Dilaton exhibits logarithmic divergence near vortex core.

Anomaly coupling induces corrections to the dilaton field.

Vortices are inherently quantum mechanical due to dilaton behavior.

Abstract

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.