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arXiv · 2305.15236

The Coulomb-Higgs phase transition of three-dimensional lattice Abelian-Higgs gauge models with noncompact gauge variables and gauge fixing

Claudio Bonati·Andrea Pelissetto·Ettore Vicari
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Abstract

We study the critical behavior of three-dimensional (3D) lattice Abelian-Higgs (AH) gauge models with noncompact gauge variables and multicomponent complex scalar fields, along the transition line between the Coulomb and Higgs phases. Previous works that focused on gauge-invariant correlations provided evidence that, for a sufficiently large number of scalar components, these transitions are continuous and associated with the stable charged fixed point of the renormalization-group flow of the 3D AH field theory (scalar electrodynamics), in which charged scalar matter is minimally coupled with an electromagnetic field. Here we extend these studies by considering gauge-dependent correlations of the gauge and matter fields, in the presence of two different gauge fixings, the Lorenz and the axial gauge fixing. Our results for N=25 are definitely consistent with the predictions of the AH field theory and therefore provide additional evidence for the characterization of the 3D AH transitions along the Coulomb-Higgs line as charged transitions in the AH field-theory universality class. Moreover, our results give additional insights on the role of the gauge fixing at charged transitions. In particular, we show that scalar correlations are critical only if a hard Lorenz gauge fixing is imposed.

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Claudio Bonati, Andrea Pelissetto, Ettore Vicari. 2023-05-24. The Coulomb-Higgs phase transition of three-dimensional lattice Abelian-Higgs gauge models with noncompact gauge variables and gauge fixing. https://arxiv.org/abs/2305.15236

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