More on String Breaking in the 3D Abelian Higgs Model: the Photon Propagator

TL;DR

This paper investigates the photon propagator in the 3D Abelian Higgs model, revealing how monopole dynamics and matter fields influence the propagator's anomalous dimension and mass across different phases.

Contribution

It provides a detailed analysis of the photon propagator's behavior, highlighting the effects of monopole pairing and matter fields on anomalous dimensions and mass in the model.

Findings

Anomalous dimension appears in the confinement phase.

Anomalous dimension disappears at the Higgs transition.

Regular gauge field becomes massless at the crossover.

Abstract

We study the Landau gauge photon propagator in the three--dimensional Abelian Higgs model with compact gauge field and fundamentally charged matter in the London limit. The total gauge field is split into singular and regular parts. On the confinement side of the string breaking crossover the momentum dependence of the total propagator is characterized by an anomalous dimension similarly to 3D compact QED. At the crossover and throughout the Higgs region the anomalous dimension disappears. This result perfectly agrees with recent observations that the monopole--antimonopole plasma leads to nonzero anomalous dimension and the presence of the matter fields causes monopole pairing into dipole bound states. The Yukawa mass characterizing the propagator part from regular gauge fields is non-vanishing at the Higgs side and coincides with the mass found for the total propagator. The regular gauge field without anomalous dimension becomes massless at the crossover and in the confinement region.