Zero Modes and Conformal Anomaly in Liouville Vortices

TL;DR

This paper investigates the conformal anomaly and zero modes in a two-dimensional Abelian gauge model with vortices, analyzing how statistical fluctuations break conformal invariance and evaluating the associated anomaly.

Contribution

It provides a detailed analysis of the conformal anomaly and zero modes in the vortex solutions of the model, highlighting the effects of fluctuations on classical symmetries.

Findings

Conformal invariance is broken by fluctuations except in an exceptional case.

The conformal anomaly has been explicitly calculated.

Zero modes of fluctuations are carefully characterized.

Abstract

The partition function of a two dimensional Abelian gauge model reproducing magnetic vortices is discussed in the harmonic approximation. Classical solutions exhibit conformal invariance, that is broken by statistical fluctuations, apart from an exceptional case. The corresponding ``anomaly'' has been evaluated. Zero modes of the thermal fluctuation operator have been carefully discussed.