Compact QED in Landau Gauge: a lattice gauge fixing case study

TL;DR

This study explores the lattice gauge fixing of compact QED in Landau gauge, revealing how vortices are quenched and Dirac strings influence photon mass, with numerical evidence showing string density drops at the deconfinement transition.

Contribution

It provides a detailed analysis of gauge fixing in compact QED, highlighting the role of Dirac strings and vortices, and connects these to the photon mass behavior at the deconfinement point.

Findings

Nielsen-Olesen vortices are quenched and do not affect correlation functions.

Dirac strings cause the nonzero photon mass pole.

String density drops sharply at the deconfinement transition.

Abstract

We derive different representations of compact QED fixed to Landau gauge by the lattice Faddeev-Popov procedure. Our analysis finds that (A)Nielsen-Olesen vortices arising from the compactness of the gauge-fixing action are {\it quenched\/}, that is, the Faddeev-Popov determinant cancels them out and they do not influence correlation functions such as the photon propagator; (B)Dirac strings are responsible for the nonzero mass pole of the photon propagator. Since in $D=3+1$ the photon mass undergoes a rapid drop to zero at $\beta_c$, the deconfinement point, this result predicts that Dirac strings must be sufficiently dilute at $\beta > \beta_c$. Indeed, numerical simulations reveal that the string density undergoes a rapid drop to near zero at $\beta\sim \beta_c$.